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Cognitive mapping of the home environment Rothwell, David Colin 1974

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COGNITIVE MAPPING OF THE HOME ENVIRONMENT by David Colin Rothwell B.A. University of Winnipeg, 1969 M.A. University of British Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of GEOGRAPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1974 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C olumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Geography  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8 , Canada Date jLr- S /?/ i i . ABSTRACT The dissertation describes an experiment in cognitive mapping. Cognitive mapping is the process by which spatial information is acquired, coded, stored, decoded and applied to the comprehension of the everyday physical environment. A cognitive map can also be a physical drawing, produced by hand to communicate the original map in the head. The dissertation uses the term, manual map, to distinguish the graphic hand drawn representation from the actual cognitive map. The experiment required adult household members to sketch a floor plan of their home, complete a spatial aptitude and graphic ability test and supply biographical, socio-economic, and attitudinal information. Children over the age of three also sketched a floor plan and completed an I.Q. test. All seventy sample households (222 respondents) lived in houses with identical floor plans. A major finding of the experiment was that manual maps can be reliable and valid research instrument in the study of cognitive maps. Psychometric techniques were used in the data analysis to test for rel iabi l i ty and validity. Both spatial aptitude and graphic ability were found to be significantly related to the ability of individuals to communicate their cognitive maps. Persons with superior mental faculties have cognitive maps which more closely reflect reality. When psychophysical functions were examined, there appeared to be a linear relationship between i i i . subjective distance and area and real distance and area. Socio-economic variables, biographical data, and the subject's cognitive structure of the home as revealed through the semantic differential, did not produce significant correlations with the ability to communicate cognitive maps. Children's ability to produce a manual map which resembles reality is significantly related to age, spatial aptitude, and graphic abil ity. A child's manual map is a reflection of his general stage of mental development. \ IV . TABLE OF CONTENTS Page 1.0 INTRODUCTION 1 1.1 Cognitive Mapping - Definition and Terms 2 1.2 Goals 5 1.3 Research Setting "9 1.4 Research Context 11 2.0 METHODOLOGY AND PROCEDURES 16 2.1 Design Overview 16 2.2 Pre-Test 18 2.3 Sample Selection 21 2.4 Interviewers and Setting 28 2.5 A Statistical Note 31. 2.51 Data Constraints 31 2.52 Reliability 34 2.53 Validity 35 2.54 Sources of Error 35 2.6 Adult Data 36 2.61 Housing Attitude Survey 36 2.62. Manual Maps 41 2.63 Graphic Ability 54 2.64 Spatial Aptitude 57 2.7 Children Data 60 2.71 Manual Maps 61 2.72 Draw-a-Man Test 64 3.0 ADULT RESULTS 66 3.1 Data Description ; 66 3.11 TRE and MRE Scores 66 3.12 Other Map Data 71 3.13 Spatial Aptitude 72 3.14 Graphic Ability 73 3.15 Questionnaire 74 3.2 Reliability and Validity 81 3.21 Reliability 81 3.22 Validity 83 3.3 Correlation Analysis 85 3.31 TRE vs Spatial Aptitude and Graphic Ability 85 TABLE OF CONTENTS - 2 -3.32 TRE vs Quality Rating 3.33 TRE and Socio-Economic Variables 3.34 TRE and Information Variables 3.35 TRE and Factor Scores 3.36 TRE and Map Errors 3.37 TRE and Added Detail 3.4 Other Correlational Relationships 3.41 Information and Socio-Economic Variables 3.42 Factor Scores 3.43 Map Details 3.44 Non-Codable Maps 3.5 Psychological Relationships CHILDREN RESULTS 4.1 Description 4.2 Reliability 4.3 Correlation Analysis 4.31 Rank, Age, I.Q., and Graphic Abi l i ty , (RAIG) 4.32 Elements of Style and Size of Rooms 4.33 Additional Detail 4.34 Errors 4.35 Non-Significant Correlations 4.4 Discussion = CONCLUSIONS 5.1 Assessment of Goals 5.2 Discussion 5.3 Further Research BIBLIOGRAPHY APPENDIX V I L I S T OF T A B L E S Page 1. Household Sample 25 2. Respondent Sample Size 27 3. Number of Interviews by Interviewer 28 4. Correlation Coefficients and Significance Tests for Different Levels of Measurement 33 5. Frequency of Wall Omissions 51 6. Alternate Form Reliability Coefficients and Standard Errors of Measurement for the Revised Minnesota Paper Form Board Test 58 7. Tesf-Retest Reliability Coefficients 59 8. Means and Standard Deviations of TRE and MRE for Walls by Adult Groups 6 7 9. Means and Significance Levels of Paired T-Test for Absolute Total House Error 69 10. Significance Level of T-Test to Test the Difference Between Error in the Size of Hall and Zero 71 11. Quality Rating of Adults' Manual Maps in Percent 71 12. Orientation of Adults' Manual Maps (percent) 72 13. Manual Map Additional Details 7 2 14. Spatial Aptitude Scores 73 15. Graphic Ability Scores 73 16. Age Breakdowns of Adult Sample 76 V I I LIST OF TABLES Page 17. Adults' Education Level 77 18. Total Family Income 78 19. Matrix of Correlation of Factors with Semantic Differential Variables 79 20. Correlation Matrix Among Factors Calculated from the Factor Scores 80 21. Correlations Between Total House TRE and MRE and Room TRE and MRE 81 22. Alpha Coefficients for Internal Consistency of Manual Maps by Group for Adults 82 23. Intercorrelations-Between Real Ratios and Mean Ratios (Wall by Wall) 84 24. Significance of Correlation Between TRE (Total House) and Graphic Ability and Spatial Aptitude for Adult Groups 87 25. Significance Levels of Correlations Between Spatial Aptitude and Graphic Abi l i ty , and Socio-Economic Variables 88 26. Significance Level of Correlations Between TRE and Quality Rating for Adult Groups 89 27. Significance Level of Correlations Between Quality Rating and Other Variables 90 28. Significance Levels of Correlations Between TRE and Added Detail 93 29. Inter-Correlation of Information and Socio-Economic Variables 95 30. Significance of Correlation of Factor Scores Against Other Variables for Adults 97 v i i i . LIST OF TABLES - 3 Page 31. Significance of Correlations Among Map Details 99 32. Significance Level of Correlation Between Non-Codable Maps and Other Variables for Adults 100 33. Regression Analysis of Real Distance and Area Ratios and Subjective Distances and Area Ratios 103 34. Age Distribution 106 35. Cross Tabulation of I.Q. and Age for Children 107 36. Age Distribution and Elements of Style for Children , 108 37. Orientation of Drawings 109 38. Occurrence of Additional Detail HO 39. Inter-Correlation of Judges (n = 47) HI 40. Correlation of Rank, Age, I.Q. and Graphic Ability HI 41. Significance Levels of Correlations Between RAIG and Elements of Style and Size of Rooms 113 42. Significance Levels of Correlations Between RAIG Variables and Amount of Detail. H5 ix.. L I S T OF F I G U R E S Page 1. Stea-Downs Typology of Cognitive Research -Previous Studies 14 2. Stea-Downs Typology of Cognitive Research -Present Dissertation 14 3. Flow Chart of Research Design 19 4. Builder's House Plan 23 5. Schematic Diagram of House Floor Plan 45 6. Flow Chart of Mean Ratio Error (MRE) and True Ratio Error (TRE) Calculations 47 7. Lurcat Graphic Ability Test 56 x. ACKNOWLEDGEMENTS My f i rst word of thanks must go to those who financially supported this dissertation: C.M.H.C. who provided a research fellowship in the early stages of research and Terry Johnston who not only employed me during the latter stages but who allowed the use of many additional services from his company. Terry also supplied a great deal of encouragement to help me get this dissertation finally finished. My sincere appreciation goes to Dr. Walter Hardwick, my Committee Chairman, for helping me through many diff iculties during my studies at the University of British Columbia. I must also thank Dr. Jim Forbes who is fun to work with and who always had faith that I would complete this dissertation. Dr. John Delac deserves special thanks for his advice on research design and techniques as does Mike Patterson for his help in computer programming. Special mention must be made for John Bottomley who has always been a source of information and a ready listener on which to test half-baked ideas. I would also like to thank Warren Gil l for the time and effort which he extended on my behalf. My two excellent interviewers, Janet Clarkson and Lori Caviglia, deserve many thanks for their efforts. I must also express appreciation to Cathy Wood who performed a great deal of the / coding and Mi mi Gibb who worked endlessly typing the original manuscript from my terrible handwriting and poor spelling. Joanne McDonnell deserves special thanks, not only for typing of the final draft, but for her continued help throughout the research. Dr. Karen Claus was the person who originally directed my interest to the use of psychological techniques to solve geographic problems. I thank her for her insight and teaching. Had i t not been for my wife, Judy, I would have quit this research many times. Beyond her long, long hours of coding, key punching, proof reading, and typing, she has maintained a patience and purpose which has seen this dissertation to its completion. As the wife of a professional student she has experienced many years of personal sacrifice and frustration. I find i t impossible to express my gratitude. xi i . PREFACE Early in 1972 the International Geographic Union issued a l i s t of "priority research areas in human geograpy". Heading the l is t was perception studies: Geographers have for a long time been aware of the difference . between the'objective' (or 'real') environment and the environment as perceived. But i t is only in the last decade or two that a systematic attempt has been made to measure space perception and space preferences, and to evaluate them and to examine the search procedures that people employ to explore the environment in which they find themselves. The field is a very dif f icult one in which to operate. Furthermore, -it clearly overlaps with psychology in terms of basic techniques and with both sociology and planning in terms of the implications and findings . . . Despite the di f f icul t ies, perception studies are of central importance for the study of geography, (p. 13) At the time the above statement was being issued by the IGU, many geographers and psychologists were in the midst of research projects dealing with that very topic. That year (1972) and subsequent years have seen a dramatic growth in the amount of published research on cognitive mapping and related aspects of environmental perception. Recent advancements in cognitive mapping have originated primarily from a coalition of geographers and psychologists • with important contributions from a number of architects and planners. Kenneth Boulding who himself established a milestone in environmental perception with the publication in 1956 of a \ xi i i . book called The Image, has referred to those researchers in cognitive mapping as " . . . an "invisible college" which represents almost a new discipline, cutting across the old discipline of geography and psychology" (Downs & Stea, 1973 p. 11). One of the implicit goals of this dissertation is to provide an example to future students who may wish to pursue research in the "invisible college". As such, this dissertation has adopted a psychological approach to a geographic topic. It has been written in the style of psychological thesis; i t has used tests and measurements developed and employed in psychology, and i t has been designed on a style of scientific research typical in psychology. Although the research design and research instruments may derive from psychology, the research topic, cognitive mapping, is of fundamental concern to geographers. I N T R O D U C T I O N Cognitive mapping has gained widespread acceptance as a viable area of research in geography and in some senses has come into "vogue". The relative infancy of this f ie ld , however, is s t i l l reflected in its lack of a strong theoretical foundation. A great deal of work must be done before congitive mapping can be said to contain any sort of unified and comprehensive theory. As i t presently stands, there is a growing body of individual research projects and experiments, many with conflicting results, waiting to be tied together in some sort of theoretical framework. The usual pattern of events in other disciplines is that theory evolves slowly from a long'"trial of many individual research efforts. As Downs and Stea (1973) point out, "It is important to recognize the degree of compatibility between answers - for once, geographers are beginning to cumulate knowledge by consciously replicative and overlapping studies (p. 320)". Subscribing to the above statement, this dissertation is an attempt to further our degree of certainty about "facts" in cognitive mapping. The dissertation is replicative in that i t employs many of the techniques and methodologies used in other cognitive studies. In this way some degree of rel iabi l i ty can be attached to presently used research techniques. It is also replicative in that researchers will find i t relatively easy to duplicate the experimental situation. The dissertation is overlapping in that its content deals with the classic cognitive maps (hand drawn graphic representation) and psychophyisical analytic techniques currently employed by other geographers in cognitive distance experiments. 2 . Although Downs and Stea claim that . . . "the current ad hoc posture towards methodological questions is acceptable and even necessary in the exploratory stage of any research effort" (1973 p. 7), i t is hoped that the experimental design of the research and the rigor of analysis employed in this dissertation will lend credibility to the results. It is additionally hoped that by example, other research will also employ similar rigor so that the results of the present experiment may be compatible with and comparable to future research. This dissertation describes an experiment (Campbell & Stanley, 1966) in cognitive mapping. 1.1 Cognitive Mapping - Definition and Terms Tolman (1948) f i rst coined the phrase "cognitive map" referring to the spatial mapping processes used by rats to navigate and learn routes through a maze. These, of course, are maps in the non-literal sense. Tolman's mental maps were not a graphic representation, but a spatial structuring of reality as composed of visual, tactile and olfactory input. Since that time, the phrase has been reworked and redefined so as to become a useable construct in environmental cognition research. Hart and Moore (1971) in their outstanding paper on the development of spatial cognition claim that the "terms cognitive maps and cognitive mapping imply map-like representations of geographic or other large-scale environments . . . i t begs the question, however, to suggest that spatial relations are necessarily represented in cartographic form. Therefore, we prefer to use the more inclusive terms of developmental psychology - spatial  cognition and cognitive representation, (p. 7-3)." Kaplan (1973) has probably taken the concept of cognitive mapping the furthest by suggesting an individuals' whole structuring of reality may be considered as a cognitive map " . . . cognitive processes and spatial cognitive maps do not involve essentially different structures . . . a spatial cognitive map might be viewed as a special case of cognitive maps in general (p. 75)." Perhaps the best definition to date and the one adopted in this study has been formulated by Stea (1974): Cognitive mapping is the fundamental process by which spatial information is acquired, coded, stored, decoded, and applied to the comprehension of the everyday physical environment (p. 159). Downs and Stea (1973) in the most complete and comprehensive work on cognitive mapping to date, Image and  Environment, present a detailed discussion of the construct of cognitive mapping. It is their contention (as supported by many other researchers) that "human spatial behaviour is dependent upon the individuals' cognitive map of the spatial environment (p. 9)." They further assert that "the cognitive map [is] the basis for deciding upon and implementing any strategy of spatial behaviour (p. 10)." In other words, we cannot describe, predict, or understand human spatial behaviour accurately and completely unless we f i rs t understand the cognitive mapping process. In v 4. this vein Cadwallader (1973) has shown that cognitive distance is a better predictor of shopping behaviour than real distance. In planning, neighbourhood areas as perceived and defined by area residents ( i .e. their cognitive map) have proven to be a valuable aid in the understanding of local resident goals and actions. Although no one has yet proved that cognitive maps do exist, i t is usually assumed cognitive maps exist i f an individual behaves as i f a cognitive map exists (Stea & Downs, 1970). It must be noted at this point that a cognitive map is not necessarily a "map" per se. "We are using the term map to designate a functional analogue. The focus of attention is on a cartographic representation which has the functions of a familiar cartographic map-but-not_necessarily the physical properties of such a pictorial graphic model . . . cognitive maps are derived from analogies of process, not product Consequently i t is analogy to be used, not believed (Downs & Stea, 1973, p. 11)." Cognitive maps, however, may be actual physical drawings, produced by hand to illustrate or communicate the original manuscript in the head. Stea (1974) describes cognitive mapping as being concerned "with how stabilized fully formed impressions come to be, how mapping takes place in the brain, and the form and content of the maps as represented in graphic or verbal descriptions (i .e. the input, the throughput, the output) (p. 157)." The output in Stea's case can be (among other things) verbal descriptors, model blocks aerial photo interpretation, symbols, and freely-drawn maps. These graphic maps would be termed cognitive representations by Hart and Moore and differentiated from spatial cognition which is the "input" and "throughput" described by Stea. There is therefore a paradox in the term cognitive map. It means both a map in the head and a map by the hand. In terms of making spatial decisions the cognitive map in the head is the only map available to an individual; the world for the individual is how he perceives the world to be. The actual communication of a cognitive map (in the head) may take many forms, one of which may be a graphic representation of the spatial arrangements of objects, commonly termed a "map". To separate the two concepts one may adopte the terms cognitive representations, graphic map, schema, diagram, drawing, picture, etc. to represent the hand map. Distinction between the two concepts for purposes of this dissertation will follow the convention of using cognitive map for the mental, in-head processes involved in assimulating, interpreting and storing spatial information, and manual  map for the graphic, hand drawn representations commonly used to communicate the original copy in the head. Goals This dissertation has four main goals: 1. Develop a valid and reliable quantitative method of analyzing manual maps. To this end the influence of both graphic ability and spatial aptitude are investigaged to determine their effect on the individual's manual map. 2. Determine what form of psychophysical relationship exists between cognitive distance (and area) and real distance (and area). These findings will compliment the growing body of similar research presently being conducted by geographers. 3. Analyze the influence of biographical variables (age, income, length of residence, attitude, etc.) on the individual's manual map of the home. The purpose here is to determine whether hypotheses postulated by other researchers can be: a. tested by the above quantitative methodology b. supported or refuted. 4. Investigate the development of spatial cognition in children. Since all members of the household over three years of age were asked to participate, the experiment offered an excellent . opportunity to examine spatial development in children. This area of research has already received considerable attention by geographers. -This dissertation deals with cognitive mapping but more specifically i t examines the use of manual maps as a research tool in the study of cognitive mapping. For a number of years, manual maps have been used as a research technique to examine spatial "images". Lynch (1960) initiated this technique to study "urban images" and was followed by many others. Although most research of this type has concentrated on problems at the scale of the ci ty, researchers have also used the manual map technique on a global scale (Gould & White, 1974), neighbourhood scale (Ladd, 1970), dwelling scale (Altman et a l , 1972) and room scale (Argyle, 1967). It may also be possible to extend the use of manual maps to the study of "proxemics" (Hall, 1966; Sommer, 1969) but this has not yet been done. It would also appear that this last example, personal space, is beyond the scale of cognitive maps. Several authors make the point that cognitive maps are a structuring of spatial phenomena which cannot be perceived or apprehended at once. In the case of personal space the apprehension may, in fact, be only a memory rather than a true composite map. E v e n though the use of manual maps is widespread, the analysis of such data is almost invariably qualitative. The significance of the results depends upon the researcher's subjective' ^interpretation of the "content" of the graphic representations. Because of this, the research is very di f f icul t to replicate. This does not mean, however, that valid results cannot be obtained using qualitative methods. Validity and rel iabi l i ty can be ensured by having various individuals perform assessments of the data and to test for the correspondence among the judges. Although this latter method of rel iabi l i ty testing is being adopted more frequently, a great deal of research employing manual maps lacks this approach. In al l fairness, i t must be stated that research which lacks estimates of rel iabi l i ty does not necessarily ^ present false results. Lynch for example, did not employ a methodologically sound research design, yet he was able to obtain valuable information which has proved consistently true in many other= studies. Regardless of the pros and cons presented for various types of research, this dissertation attempts to develop a methodology by which manual maps can be analyzed quantitatively in addition to qualitatively. The success of the experiment is relative. If the attempt is positive, then future researchers can look forward to employing a new technique in their analysis with the knowledge that i t appears to have some validity. If the attempt is negative i t will at least illustrate some of the pitfal ls for other researchers who may wish to assail the same problem. There is certainly an appeal for developing a quantitative method. It would mean that data obtained by one researcher could be analyzed consistently anywhere by any number of other researchers. It also means that studies could be. replicated and that the results of various studies could be objectively compared. Such is presently not the case. Research Setting The research setting devised to achieve the goals was to have people sketch a floor plan of their home. A unique feature of the experiment was that all homes had identical floor plans. Although some concern might be expressed about the interpretation of a floor plan being a cognitive map, there does not appear to be any evidence in the current literature to disqualify such an approach. In terms of spatial behaviour, individuals must have some form of cognitive map in order to navigate themselves about their home. Their maps must not only contain information on the relative location of each room but also information on its size, orientation, usage, contents, etc. In other words a cognitive map of the home exists because individuals "behave as i f a cognitive map exists" (Downs & Stea,'1973, p. 10). In a discussion on "mental" maps Stea also says " . . . all persons form conceptions of those significant environments that are too large to be perceived, i .e. apprehended at once. (1969, p. 229)." It is argued here that the home is a significant environment; and that i t cannot be apprehended at once. There are several methodological advantages in using the home as the subject of a cognitive mapping experiment. Most of these have to do with the measurement and interpretation of the manual map used to communicate the individual's cognitive map. The advantages are as follows: 10. 1.. Subjects are familiar with the environment. One criticism leveled at researchers who have subjects draw maps of the city is that the degree of familiarity or lack of knowledge influences the resulting manual map to a degree that cannot be estimated. In the home it is assumed that everyone has at least been in all the rooms. '2. Manual maps of the home are f in i te . Requesting subjects to produce a map of the city or neighbourhood can result in an infinite amount of variation and detail. In the home there are a fixed : " ~ ' number of rooms and walls. It makes the problem of what to measure more manageable. 3. The problem of measurement is simplified. The length of the walls and the area of the floors can be measured on the manual map and compared to the actual floor plan to give the amount of deviation between the cognitive map and the real world. The exact size . and orientation of the real map is already known. A detailed description of the complete research design w i l l , of course, be given in a following chapter. The unique feature of having a large number of families living in essentially the same home affords the opportunity of investigating a number of other interesting relationships in people's spatial perception. For. this reason the dissertation also reports findings which may not bear direct relevance to the main arguments of the experiment, but nevertheless seem important and significant in themselves. 11. Research Context In 1970, Stea and Downs combined their efforts to produce an article which outlined the state of the art (at that time) in cognitive mapping. Their article "From the outside looking in at the inside looking out" is used here as a basis for the context of this dissertation. The Stea and Downs' (1970) article was intended to act as an introduction to a group of original papers in cognitive mapping. As such, Stea and Downs attempted to construct a typology to describe the types of research being conducted in cognitive mapping. They suggested that there were two general research strategies: 1. The holistic approach was concerned with overall system identification, and description. "On this level, a major concern is the establishment of purely functional relationships between, for example, socio-economic status variables and the cognition of different segments of the environment (p. 7)." Research typifying this is that of Ladd (1970), Ley (1974), Appleyard (1970), and Everitt & Orleans (1971). This type of research usually employs manual maps, with most data analysis being of a qualitative nature. 2. "The second strategy involves a search attempt to analyze the system interactions which have been isolated previously. Thus the focus is on the interactions between sets of variables 12. together with the specification of the system parameters" (p. 7). Examples of this type of research are Lee (1964), Lowerey (1970), and Briggs (1969). This second strategy makes extensive use of "quantitative methods of data analysis (p. 8)" and has, until this dissertation, never employed manual maps in the research design. Stea and Downs go further by claiming that there have been three major research foci: 1. Elements Cognitive categories into which information from the spatial environment is coded. Loosely interpreted, elements refer to the objects or landmarks in the spatial landscape. 2. Relations Between Elements Distance and directional system used to define cognitive representations i.e. cognitive distance. 3. Surfaces Resulting from the Relationship Between Elements Overall cognitive representations of a portion of the spatial environment, i .e. manual maps. In previous research the holistic approach has usually dealt with surfaces, hence the popular technique of manual maps/ The system interaction approach has been limited to elements and relations between elements. Figure 1 provides a schematic diagram of the different strategies and research foci . Along each arrow connecting the strategies and foci are examples of researchers whose 13. work falls into the various categories. Some of the research designations are given by Stea and Downs. Other research appearing since the time of their article have been classified by myself. The typology, as constructed by Stea and Downs, provides a useful method of categorizing the various pieces of research in cognitive mapping. Where does this dissertation fall? Figure 2 represents the research covered in this dissertation. The various numbered arrows are described below: 1. First i t must be stated that the essential foci of the research is with "surfaces". Subjects were requested to draw a manual map of their home. The entire spatial environment of the home is the subject of enquiry. The primary research strategy was that of systems interaction. A series of psychometric tests and measurements was employed as well as basic psychophysical techniques. This approach is highly quantified and represents the f i rs t time in geography (to my knowledge) that quantitative methods have been used to analyze surfaces, i .e. manual maps. The present dissertation therefore, differs from all other previous geographic research. 2. A large number of socio-economic variables as well as psychological variables was collected and related to the manual maps. 3. Tests to determine psychophysical functions for cognitive distance and cognitive area (another f i rst in geography) were performed. FIGURE 1: STEA-DOWNS TYPOLOGY OF COGNITIVE RESEARCH - PREVIOUS STUDIES System Interaction Ladd Appleyard Ley Asmussen Surfaces Lee Lowery Briggs Cadwalleder Relations Between Elements Research Strategy Downs Taylor Louviere Margulius Elements Research Foci FIGURE 2: STEA-DOWNS TYPOLOGY OF COGNITIVE RESEARCH - PRESENT DISSERTATION Hoiistic System Interaction Research Strategy (2) • I m T t 0> I I t (4) Surfaces Relations Between! Elements Elements Research Foci 15. 4. A semantic differential was administered and analyzed using factor analysis to determine the underlying cognitive structure of the home. Individuals' factor scores were related to the manual maps. To date, the best representative selection of literature on cognitive mapping occurs in Image and Environment (Downs & Stea, 1973). The book contains a number of "historical milestones" in cognitive mapping literature. Each major section of the book also presents a discussion of other relevant works not included in the book. Although Image and Environment does not contain some- of the more recent works in the f ie ld , i t does represent one of the finest and most complete reviews of cognitive mapping literature. Indeed, i t is diff icult to undertake a review of literature on this topic without subconsciously following the format outlined by Downs and Stea. The only criticism which could be made of this book is that i t does not attempt to present an overall theoretical framework for the literature which i t contains. Downs and Stea counter this cr i t ic i in their preface by stating that they "were more concerned with content areas than with the presence or absence of a theoretical statement, (p. xiv.) ." It would appear, however, that i f such a statement already existed, i t would have been included, at least as one of the many readings. To say that their work lacks a comprehensive framework is perhaps a commentary on the state of the discipline, rather than on Downs and Stea. 1 6 . METHODOLOGY AND PROCEDURES This chapter provides a detailed outline of the research design including sample selection, interview procedures, questionnaire design, psychological tests, and statistical techniques. 2.1 Design Overview A total of 70 families agreed to participate in the experiment. Everyone in the household over the age of three was asked to draw a floor plan or map of his home. All homes had identical floor plans. Members of the family were divided into two groups - adults and children. An adult was defined as a person of age 14 years or older. The reason for this age designation will be explained in more detail later. It can be said now, however, that in terms of spatial aptitude a 14 year old person is considered psychologically equivalent to an adult. The adults were asked to complete: 1. A free hand floor plan of their home. 2. A graphic ability test. 3. A spatial aptitude test. \ 17. 4. A questionnaire containing background information and socio-economic data as well as a semantic differential designed to determine their attitude towards their home. The children (less than 14 years) were asked to complete: 1. A free hand floor plan of their home. 2. The Goodenough-Harris Draw-a-Man Test. For the adults, the manual map of their home was digitized to produce "XY" coordinates for each wall intersection. The lengths of all walls and areas were subsequently reduced to ratio measures using psychometric statistical techniques. Simply expressed, this' procedure converted everyone's drawing to a common and comparable scale. Differences were then calculated between: 1. The subjects' ratio and the real ratios from the building plan. 2. The subjects' ratios and the mean ratios of all the respondents. In effect, these difference scores measured, for each manual map, the deviation from the real world and from the world as generally perceived by the respondents. These difference scores (amount of error) were then used as input data to the statistical analysis performed with 18. the spatial aptitude scores, graphic abil ity scores, other variables taken from the questionnaire and factor scores from the semantic differential. - Other data were taken from the manual maps and included in the statistical analysis of variables. These other data were more qualitative in character and included a quality rating score for each manual map, the number and types of errors in the map, and additions or anomalies in the manual maps. Figure 3 is a schematic diagram illustrating the inter-relationship among the various data used in the adult section of the dissertation. For the children, i t was not possible to digitize the manual maps. Most drawings, especially for the younger children, were so distorted that i t was di f f icul t to recognize them as house plans let alone treat them quantitatively. Instead, all the children's drawings were ranked independently by four separate judges. The average rank was then used as input into an analysis containing data on chronological age, mental maturity, graphic abi l i ty, and quantitative data derived from the drawings. Pre-Test A pre-test of 15 families was done prior to the main experiment to train in the use of the various tests and to minimize any diff icult ies which might arise in the research design. Manual Maps 0 I Ratio Measurements Mean Ratios For All Ss Mean Ratio Error Mean Ratios From Builders Plan Psychophysical Functions Distance Area Analysis (individual rooms and whole house) Graphic Ability Spatial Aptitude Additional Detail Semantic Differential I Factor Analysis I Ss Factor Scores Questionnaire 20. The data from these interviews were not used in the main analysis as the homes in the pre-test had different floor plans from those in the main experiment. The homes were also in a different geographical area and were considerably newer. The main purpose of the pre-test was to test the research instruments, determine the average length of time to do an interview, determine the order of tests to be done, and provide experience in the handling of both adults and children in a test situation. Several minor tests were run to investigate possible sources of error. In the final experiment all manual maps were drawn on standard 8-1/2 by 11 paper. In the pre-test several sizes of paper were tried, with no noticeable difference in results, except that large pieces of paperwere harder to handle. No noticeable difference in the pre-test results could be found between subjects completing their maps while in the kitchen or while in the living room. In the pre-test subjects were asked to draw two floor plans, one at the beginning and one at the end of the interview. Although there appeared to be a learning experience with practice, the difference in scores was not significant. In several instances the scores on the second try were worse as the subjects seemed to tire or did not see the point, and failed to give the second effort as much concentration as the f i rs t . Subjects in the pre-test had moved into their home in a housing development within a year of the study. The developer 21. of the housing subdivision provided an introduction to each of the home owners. This also differed from the main experiment where each owner was contacted by letter and telephone. 2.3 Sample Selection The selection of an adequate sample was di f f icult . The criteria set for the sample was as follows: 1. All homes had to have identical floor plans. 2. The total number of homes had to be large enough to draw a workable sample. 3. Three bedroom homes were desirable so as to ensure a large population of children. 4. Homes had to be of slab construction (no basement) as vertical separation of rooms would be more dif f icult to handle. 5. Homes had to be at least 10 years old so that length of residence could be tested as a variable in cognitive perception.1 Help was given by the Central Mortgage and Housing Corporation, Regional Office, and a number of local builders and developers in the Metropolitan area to locate a sample of the desired homes. Several housing developments were examined with the ^An a priori consideration in the research design was to include the length of residence as a possible variable influencing cognitive mapping. final choice being a group of homes which met all the above criteria. The homes in the sample are J .S . Wood homes built in 1958-59 in the Pigott-Mowbray area of Richmond. Mr. Wood was kind enough to identify the location of the houses as well as to provide a copy of the floor plan. Figure 4 illustrates the builder's floor plan. All the homes are three bedroom bungalows of 1,310 square feet and all have identical floor plans. In total i t was possible to identify 302 houses of the same type. Although there are more homes in the Metro Vancouver area i t is extremely dif f icult to find them. A search of all Richmond building permits since 1958 revealed that 132 of the original 302 had been structurally altered enough to change the floor plan. Although this number may appear high it must be remembered that these homes have no basement ^ so that storage and ut i l i ty space is very small. The most common practice has been to append a ut i l i ty room, covered garage, etc. to the side or back of the house and to knock down an interior wall next to the kitchen to form a dining area out of the small ut i l i ty room already in the house. This appears to have been a very common practice, with one builder doing at least 54 homes in this manner. •' ' Subtracting homes with altered house plans left a total of 170 possible sample households. This number was enlarged by eight to increase the possible sample to 178. These eight consisted of new residents who moved into the houses sampled during the \ \ FIGURE 4 BUILDERS HOUSE PLAN 1972-73 sample year. This meant i t was possible to sample the same house twice but with two different households. Because of rejections this actually occurred only once. When all the possible sample homes were identified, names of the occupants were obtained through the City Directory, voters' l i s t s , and the Municipal Assessment Department. Letters were sent to each occupant asking i f they would participate in a housing study being conducted by the University of British Columbia (see letter Appendix 1). Postcards were included in each letter with instructions to return the card i f the person did not want to participate, otherwise someone would phone him to set a suitable time for the interview. Table 1 illustrates the actual household sample through the two sampling seasons. Interviewing was suspended during the summer because of an extremely high rejection rate. Many valuable samples were lost prior to the suspension of sampling during the summer of 1973. A brief explanation of each category follows decline - respondents who did not wish to participate. accept - respondents who were interviewed. \ 25. reject - interviews which could not be used (house plan altered without permit, incomplete interviews, did not or could not follow interview instructions). unavailable - could not locate resident or resident did not have listed phone number. TABLE 1 HOUSEHOLD SAMPLE Sample Year 1972-73 1973-74 Total Decline 52 47 99 Accept 32 38 70 Acceptance Rate 38.1% 44.7% 41.4% Reject 2 3 •5 Unavailable - 4 4 Total 86 92 178 In total the 70 households have yielded 222 valid respondent samples. Only five interviews proved to be totally unusable or not valid. This means that there was an average of 3.17 respondents per household. In the majority of cases all family members participated, with the most general exception being high school children who were attending activities during the time of the interview. It was frequently very dif f icult to schedule interviews so as to f i t households with several children. The largest single household sample was nine. - - - - The following table (Table 2) outlines the number of respondents by sex and test category. A brief outline of each category follows: 1. Adult Male Head of Household - usually the husband. 2. Adult Female Head of Household - usually the wife (includes al l married women). 3. Male Child - child less than 14 years of age. 4. ; Female Child - child less than 14 years of age. 5. Other Male Adult - any household member 14 years of age or over but not head of household. 6. Other Female Adult - any household member 14 years of age or over but not head of household. \ 27. TABLE 2 RESPONDENT SAMPLE SIZE Number Percent Male Head (Husband) 61 27.5 Female Head (Wife) 70 31.4 Male Child 34 15.3 Female Child 23 10.4 Male Adult 17 7.7 Female Adult 17 7.7 Total 222 100.0 There were nine more female heads (70) than male heads (61). This is due to the fact that there were 2 divorced, 1 separated, 1 widowed, 2 single, 1 husband not home at time of test, and 2 female heads who could not be classified. The 2 single are spinster ladies of 67 and 73 years of age. The original goal had been to secure 100 household samples, but unfortunately this could not be done. The number of homes with altered floor plans out of the original 302 was almost 44 percent. Of the remaining valid sample, the acceptance rate of 41 percent was too low to achieve the goal. Considering the fact that it was often diff icult to get families together at one time, and that no financial remuneration was offered, the acceptance rate was quite high. 28. In the types of statistical analysis that were performed, mainly correlation and t-test, the sample sizes were large enough to produce valid results. In the factor analysis that was performed there was a total of 165 subjects with 25 work pairs each. This sample size was sufficiently large to return reliable results. It must also be remembered that the sample was not collected to be representative of the population as a whole; i t was not an attitude or opinion survey. In terms of normal samples for psychological experiments the total of 222 subjects is much higher than most. 2.4 Interviewers and Setting A total of four interviewers were used. Table 3 indicates the number of interviews conducted by each person as well as the percentage of total interviews. TABLE 3 NUMBER OF INTERVIEWS BY INTERVIEWER Interviewer Number Percentage of Total Rothwel 1 22 31.4 Caviglia 29 41.4 Clarkson 18 25.7 Gil l 1 1.5 Total 70 100.0 29. All the interviewers were trained by myself. L. Caviglia worked in the 1972-73 sample year while J . Clarkson worked in the 1973-74 sample year. 1 The training sessions for the two interviewers consisted of a thorough briefing and their attendance at two interviews before they proceeded on their own. In the f i rst of these two interviews, they merely observed. On the second, they conducted the session with myself in attendance as an observer. A series of telephone call backs for every fourth household was also initiated to ensure that the interviewer was courteous and that instructions were followed. To test whether the investigators had different effects upon the research results, a correlation analysis was performed between the interviewers and all other numerical variables. Except for one instance, there was no significant correlations (a = .05) between the interviewers and other variables. The only "variable which seemed to be related to the interviewer was the respondent's occupation (<*= .03). A cross tabulation of results indicated that Rothwell had a propensity for lower job status respondents. One possible explanation for this was that since I made the telephone calls to set up the interviews and assigned the person to do the interviewing, I somehow allotted myself more low job status people. W. G i l l , a geography graduate student, who was familiar with the research design, was able to f i l l in on one occasion. 30. This may be due to the fact that when I perceived that the interview might be dif f icult ( i .e. the respondent was reluctant to participate or seemed not to understand what was being asked) I took the interview myself. When people were friendly, open, and cheerful over the telephone I usually assigned another interviewer. It may be possible then, that persons of lower job status respond differently over the telephone for requests to participate in research experiments. Except for the single anomoly of occupation, none of the variables was influenced to a significant degree by the interviewers. The interview setting was in the respondent's home, with the living room (90 percent) the usual location. An attempt was made early in the research design to have respondents gather at a neutral location but this proved infeasible. The pre-test indicated that there was no difference between the living room or kitchen in interview setting. Final analysis also indicated that even though most respondents were in the living room, the kitchen was generally drawn with less error. Although i t can be argued that there might be a difference i f the respondents were in a neutral setting, the experimental situation was uniformly consistent for a l l subjects. On a theoretical basis, i t should be pointed out that the interview setting for other cognitive mapping studies is usually located within the area being mapped. It should \ 31. also be noted that the manual map of the house is not simply a visual perception. The home environment is so constructed that i t "cannot be apprehended at once". In the interview situation very few subjects looked up to guage the size of the room and none got up to walk around and refresh their perception although they were not told to refrain from this. The actual interview lasted between 45 minutes and one hour, although conversation following the interview sometimes lasted several hours. Each person in the household was presented with a clip board containing all the material in the test. Children were very responsive and presented no problems to the interview. If the children finished their tasks before their parents (which frequently happened) the interviewer would discuss with them what they had drawn and perhaps ask them to draw something else. Except in one or two instances, all families were very friendly and helpful. Respondents who asked to have their tests returned were granted their requests after the tests were marked and photocopied. 2.5 A Statistical Note 2.51 Data constraints. The data contained in this dissertation are at all four levels of measurement: 1. nominal: sex, handedness, etc. 2. ordinal: income, education, etc. 3. interval: age, spatial aptitude, etc. 4. ratio: ratio measurements of walls and floors. \ 32. It was therefore, frequently necessary to employ non-parametric tests of association and significance. Even when interval and ratio data were used, tests for normality1 in distribution revealed that some variables did not meet the assumptions of parametric tests. Parametric tests were employed only where the data permitted. Because of the nature of the data (several levels and non-normal distributions) i t was not possible to use tests of analysis of variance. Unfortunately, a non-parametric analysis of variance employing several levels of data has not yet been discovered. Multiple correlation (for non-interval data) was another analytic tool which could not be used. For the most part, analysis of data consisted of various forms of correlational analysis and t-tests (or the non-parametric t-test equivalent, the Mann-Whitney U Test). The following table (Table 4) names the various correlation coefficients and their tests of significance: Tests for normality were tests based on skewness and kurtosis. 33. TABLE 4 CORRELATION COEFFICIENTS AND SIGNIFIANCE TESTS FOR DIFFERENT LEVELS OF MEASUREMENT Data Level of Measurement Coefficient Test of Significance Interval-Interval Pearson product moment coefficient (rj F-test Interval-Nominal Correlation ratio (R) F-test Interval-Ordinal Jaspen's coefficient of multi serial correlation (M F-test Nominal-Nominal Guttman's symmetric coefficient of predict-ability (X) Chi-Square Nominal-Ordinal Freeman's coefficient of determination (0) Chi-Square Ordinal-Ordinal Goodman's and Kruskal's coefficient of Kank association (G) Test of G = 0 It should be noted that the above correlation coefficients are not tests of association which are numerically equivalent. For example, a Pearson r_ of .90 will not be equivalent to a Jaspen's M of .90. The only way to compare the actual coefficients is through the various tests of significance. Because the reporting of actual coefficients tends to be misleading, only the results of tests of significance will be given (except where otherwise important). ' See Freeman (1965) and UBC CORN (1973). Similar to Spearman's r g but easier to calculate for ties. 34. Unless otherwise stated the level of significance has been chosen to be a = .05. This will ensure that the relationship between variables is statistically significant. In almost al l instances, the lower the level of analysis (i .e. nominal-nominal being the lowest and ratio-ratio the highest) the greater the loss of information and thus the greater the risk of overlooking significant relationships among variables. The analysis therefore runs the risk of omitting some relationships which might exist but are not revealed because of the manner in which the data were measured.1 It does have the benefit, however, of indicating that those variables which are shown to be inter-related are, in fact, significantly so. 2.52 • • Reliability. Reliability refers to the accuracy of data in terms of stability and repeatability. Reliability has been defined as "the ratio of the true score variance to the variance in the scores as observed (Helmstadter, 1964, p. 61)." Where applicable such methods as test-retest, parallel form, split-half and Kuder-Richardson techniques are used and reported. Reliability of published tests (spatial aptitude, graphic abi l i ty, and Draw-a-Man) will be reported from the test manuals. Variables like sex (male-female), however, cannot be measured other than at a nominal level. 35. 2.53 Validity: Validity refers to the extent to which the instrument actually measures what i t is designed to measure. The validity of an I.Q. test, for example, is that i t measures intelligence. In a sense then this entire dissertation is an attempt to determine the validity of manual maps as a measure of cognitive maps. Other researchers have relied upon face validity (Helmstadter, 1964, p. 89) stating that a cognitive map exists when the individual behaves as i f the map exists, i .e. because we can draw manual maps, cognitive maps must also exist. A more complete discussion of validity in manual maps will follow in a later section where there are statistics to verify the analysis. The validity of published tests will be reported from the test manuals. 2.54 Sources of error. Despite the most rigorous research designs there is always some error introduced when reactive (as opposed to unobtrusive) measures are used. Webb et al (1966) classify four types of error resulting from the respondent: 1. Awareness of being tested. 2. Role selection. 3. Measurement as an agent of change in the subject. 4. Response sets. \ 36. Except for the f i rst error type, i t is dif f icult to imagine how these errors could influence to any great extent the results of the experiment. To help reduce the f i rst error - awareness of being tested - interviewers were instructed to engage in a period of conversation before the actual experiment to help ease any tension. The f i rst few questions of the f i rst questionnaire were very easy, some having the sole purpose of getting the subjects into the right frame of mind. Error can also be introduced by the investigator. There is overwhelming evidence that a large number of biases are introduced by the interviewer (Webb et a l , 1966). In the present study, however, the correlation analysis indicated that investigator error did not vary significantly among the interviewers thus indicating l i t t le influence on the data. 2.6 Adult Data This section discusses each of the four data sets that were used in the experiment. Each data set is discussed in the order in which i t was complted by the respondents. Each data . set is in turn discussed in two sections, the instrument and the analysis. 2.61 Housing attitude survey. The Housing Attitude Survey as shown on the following pages is identical to the one presented to the respondents. There are four basic groups of variables: 37. HOUSING ATTITUDE SURVEY university of British Columbia F O R O F F I C E U S E O N L Y DATE FID TIME : : : SID EEO INTERVIEWER >~-* •• > TRS ED COMMENTS P O M O s O wO 1. How long have you lived at your present address? years. 2. How many times have you changed your place of residence in the last 10 years? 3. How do you feel about the amount of living space in your present residence. It is : a. much too small • b. small but adequate enough • c. just right • d. more space than really needed • > If you answered a. "much too small" - which rooms in particular do you find too small? 4. Are you satisfied with the arrangement of rooms in your present home? a. yes • b. no • 5 . How many bedrooms would be adequate for your family? 6 . Do you feel you are getting your money's worth out of your present residence? a. yes • b. no • 2 7. From what you have learned and experienced about housing, what do you feel 38. are the most important considerations in choosing a home? 8. In comparison to other places in the Lower Mainland, how would you rate your neighborhood as a place to live: a. excellent • b. very good • c. good • d. fair • e. poor • 9. Do you anticipate moving within the next two years? a. yes • b. no • 10. We would like to know how you feel about your present house. For each of the following pairs of words, mark on a scale of 1 to 7 how the words best describ< your feelings toward your home. 1 2 3 4 5 6 7 good — — bad dirty — — clean light dark empty ' . full complicated — simple gloomy — — — — bright cramped _ roomy private — — — — — public . peaceful . • • — disturbing dangerous _ safe depressing happy feminine — — . masculine warm — — — — — — cold dull . — interesting unusual — — conventional formal — — — informal forbidding _ — welcoming light heavy invigorating — — boring small — — _=.•_-.-— — — _— large open . closed discordant — harmonious substantial — -— — — — thin ordinary —_ : — — imposing 3 39. At this point we would like to ask you a few questions about yourself so that we can properly classify our information: 11. 12. 13. 14. Age Occupation Your father's occupation Education (check highest level) Grade School University e 1 • Grade 8 • Years 1 • 2 • 9 • 2 • 1 3 • 10 • 3 • 4 • 11 • 4 • 5 • 12 • BA, BSc • 6 • 13 • MA, MSc • 7 D PhD Other n Technical Training Years 1 • 2 • 3 • • j 4 • Diploma • Other The following two questions need only be answered by the head of the household. 15. Income (total family income) a. less than $4,000 • b. $4,000 - $6,000 • c. $6,000 - $8,000 • d. $8,000 - $10,000 • e. $10,000 - $15,000 $25,000 • f. $15,000 - • g. $25,000 - $50,000 • h. more than $50,000 • 16. First name and ages of children living at home. Name Age Grade 40. 1. Unobtrusive variables such as handedness, eye glasses, nationality, marital status, difficulty with interview, etc. were recorded in the "comments" section of the f i rst page. The SID number on the f i rst page identified the respondent's sex and position in the household (husband, wife, child, and other relatives). 2. Questions 1 to 9 are general background variables designed to collect information and to get the respondent in the right frame of mind. Most of the questions also appear in Sanoff and Sawhney (1971) and Sanoff et al (1971). 3. Question 10 is a semantic differential designed to determine the cognitive structure of the respondents' attitudes toward their home. The actual adjective word pairs used in the questionnaire were taken from a study by Honikman (1971). Although there were a number of studies from which to borrow a semantic scale for architectural structures^, Honikman's paper offered the advantage that the semantic scale had been used in a study on living rooms. There was, therefore, the opportunity to compare the factor structure of Honikman's study with the factor structure in the present experiment. 4. Questions 11 to 16 dealt primarily with socio-economic variables. See Craik (1968), Collins (1969), Canter (1969), and Hershburger (1970). 41. Because of the method of response for education and income categories, these variables were treated as ordinal variables Analysis (except for the semantic differential) consistedof calculating correlations between each variable and all other variables in the study. Descriptive statistics (means, standard deviations, medians, distributions) and cross tabulations were completed as a matter of course. The semantic differential was analyzed using a principal axis factor model with varimax rotation (UBC FAN). As will be seen in the next chapter the program extracted three unrotated factors with eigenvalues greater than one. The respondents' factor scores on each factor were then calculated and correlations were performed between the factor scores and all other variables. 2.62 • Manual maps. The manual maps or floor plans were very simple in concept. Each adult was asked to make a free hand drawing of the floor plan of his home. He was told " that i t was a very important part of the study and therefore to draw it the best he could trying to put the rooms in the right location and of the correct relative size. It was also stated that doors, windows, and furniture were not required. There was no time limit and respondents could try as many times as they desired. 42. Although the instrument was simple the analysis is complicated. The basic concept relies on a psycho-physical technique known as ratio estimation. In ratio estimation "the subject is instructed to adjust a variable stimulus so that i t appears subjectively equal to a certain fraction of the standard (Ekman, 1958, p. 287):" A common practice in subjective distance experiments is to have the subject mark a line so that i t is proportional to a line representing a fixed distance. Ratio estimation is a standard technique used by both psychologists and geographers in studies on cognitive perception Of geographic distances 1. Recent Ph.D. theses in geography employing this technique are Louviere (1973) and Cadwallader (1973). The usual method of ratio estimation involves the matched pair comparison of two distances (i .e. perceived distance and a standard distance). Earlier research (Rothwell, Bottomly and Forbes 1971) indicated that subjects could See Lee (1970), Golledge, Briggs and Demko (1969), Kunnapas (1960) Ekman and Bratfisch (1965), Bratfisch (1969), Lowerey (1971), Briggs (1969), Teghtsoonian (1971), Cadwallader (1973), and Howard, Chase and Rothman (1973). 43. estimate six distances simultaneously with high rel iabi l i ty . In this experiment no standard distance was given as the subjects merely marked on a line the distance between themselves and a group of targets. Research by Howard, Chase, and Rothman (1973) employed the simultaneous ratio scaling of eight geographic points. This research is interesting in the fact that subjects "were asked to draw a partial map of the environment which would indicate the location, shape, orientation, and main door (if relevant) of the eight points which were listed for them (p. 258)." This is very similar to the maps in this dissertation except for the fact that the subjects (in Howard et al) "were given a reference Tine representing the distance between points 1 and 5 (p. 258)." This research would also seem to indicate that the general method of using manual maps in a ratio estimation technique may work in a broader environmental setting. This dissertation also employed ratio estimation. The walls depicted in the manual maps were treated as subjective distance estimates. The respondents supplied their own reference line in the form of the outside walls of the house1. 1 An earlier experiment (Rothwell, 1970) was conducted to determine i f subjects could complete the interior walls of a building more accurately i f they were supplied with a scaled outline of the exterior walls than i f they drew the whole building free hand. Results indicated that there was no significant difference between the groups although the group supplied with the outline had more error than the free hand group. 44. Although the actual measurements were made on individual walls, when the drawing was completed i t represented the entire cognitive map of the house. This, of course, was the advantage of the research design - the number of possible measurements was f inite. Figure 5 is a schematic diagram of the sample house. This diagram was used in the process of digitizing and coding the data. Each of the 24 wall intersections was labelled with a letter (A through X). These letters were used to designate the XY coordinates when the manual map was digitized. All walls could then be described using the letter designations of the intersections, for example the bathroom walls were BC, CG, GF and FB. All rooms in the house were given number designations 2 to 10 with the number 1 reserved for the whole house. Appendix 2 gives a complete l i s t of all wall designations and room designations. There was a total of 41 discreet distances and 10 areas. The ultimate task was to convert the free hand drawings to error measurements. Figure 6 outlines the tasks involved in the conversion process. Each step inthe process will be described below: 1. Intersection Designation The intersection of each wall with all others had to be marked and identified with a letter. The location of the intersection point was sometimes a matter of interpretation, especially FIGURE 5: Schematic diagram of house floor plan 46. when lines were not joined or corners were rounded. The following criteria were established for subjective judgements: a. Where walls did not join, the lines were continued by the marker in the same direction as the subject until an intersection was formed. b. On rounded corners any marked deviation inthe direction of the curve was considered a corner, or for symmetric curves the center of the arc was chosen. Of the approximate 165 maps processed^, about 50 percent were marked by myself and the other 50 percent by Mrs. C. Wood. To determine the amount of subjective error which might occur, 51 maps (31 percent) were processed independently by both markers. When digitized, there was a mean difference between the estimates 2 of .042 inches (s.d. .007) on 1,224 simulatenous observations . The differences were normally distributed about the mean. The average manual map had 46.74 inches of line. A small number of adult maps (17) could not be digitized because of gross errors. Actual digitizing tolerance by eye is small, .001 inch. 47. Manual Maps 1 Intersection Designation I Digitize XY Coordinates I Calculate Distance And Area I Calculate. Ratio Scales For Ss I Calculate Mean Ratio Scales I Calculate Difference Between Ss and Mean Ratios (MRE) Calculate Ratio Scales for Builders Plan Calculate Difference Between Ss and True Ratios (TRE) FIGURE:6: Flow chart of Mean Ratio Error (MRE) and True Ratio Error (TRE) calculations. 48. Error, i f accumulated on all 24 points, would represent only 2.4 percent of this total line length. Because error was Distributed normally about the mean, i t would not have a cumulative effect. Some error would therefore balance out the other producing an average error of less than 2.4 percent. ,Pi gi t i ze XY Coordi nates The UBC Gradicon digitizer was used to produce XY coordinates for all 24 wall intersections. The accuracy of the digitizer is .001 inch or about the limit of the human eye to detect differences in location. Calculate Distance and Area The XY coordinates were stored on a cassette tape. A Wang 600 was programmed to Calculate the 41 distances and 10 areas from the coordinates. The algorithms to calculate distance and area from polar coordinates were those given in Davis et al (1966, p. 483). Calculate Distance and Area Ratio Scales The purpose of this calculation was to standardize the distances and areas so that all maps were equivalent to the same scale. The methodology for calculating the geometric mean ratio scale, Ri , (of any wall or area) is described by Ehman (1958). A matrix is constructed in which any cell contins the ratio of the value of the row, Rai, to the value of the column, Raj. \ The row and column values were the 41 distance measurements (for distance ratios) or 10 area measurements (for area measurements). The sums of any row, r i , and any column, c j , are given by the equations: ri = Rai 2 (1/Raj) cj = (2Rai)/Raj The ratio scale of any single distance or area is then calculated by Ekman's formula 14: The ratio scales for 41 distances and 10 areas were calculated for all manual maps. Calculate Ratio-Scales for Builder Plan In order to compare the true distance to subjective distance (i .e. cognitive map to the real world), the equivalent ratio scales for al l walls and floor areas were calculated for the building plan. Calculate Mean Ratio Scales In order to compare individuals' manual maps to the group of respondents as a whole, the mean ratio scales for all walls and areas for all subjects were calculated. 50. 6a. Calculate Difference Between Individual Ratio Scales and  Mean Ratio Scales To determine the deviation between individuals and the norm, the absolute difference between individual and mean ratio scales was calculated to produce a mean ratio error (MRE) for each . individual. The MRE was the sum of the absolute differences on each wall and on the whole area of the house. MRE figures were also calculated for each room. 6b. Calculate Difference Between Individual Ratio Scales and  the True Ratio Scales The same procedure was followed as above to produce true ratio  error (TRE). (For detailed example see Appendix 8.) The output of this exercise produced, for each subject, MRE and TRE figures for the total house and nine rooms. A brief mention should be made about codable responses. If an individual omitted more than two walls from his drawing, the map was designated as non-codable and not digitized. There were 17 or 10.3 percent non-codable adult manual maps. There were many individuals who omitted a wall. In fact 64.2 percent of subjects neglected to draw the wall VW (see Figure 4) which was a short wall producing a small "L-shape" in the living room. The frequency of wall omissions is shown in 51. Table 5. Although mother walls were also omitted, this only occurred in non-codable maps. TABLE 5 FREQUENCY OF WALL OMISSIONS Wall Percent of Subjects (N = 148) VW 64.2 NR 7.3 UV 3.2 BC 0.7 FG 0.7 This omission of walls, however, necessitated the use of a correction factor in the ratio measurements. A missing wall did not invalidate the ratio scales (the matrix was 2 2 40 instead of 41 ) but did tend to produce relatively lower ratio scores depending upon the length of the wall. Of course, for the true builder's plan, the sum of the ratios equals 41. To account for missing walls, correction factors were calculated for any single wall or combination of two walls. Each ratio scale for" the walls that were drawn was then multiplied by the correction factor to make i t equivalent to the case where no walls were missing. The ratio scale value of the missing wall was zero so that the MRE or TRE for the wall was, in fact, the value of the mean ratio or true ratio. In addition to MRE and TRE values, other data were also extracted from the manual maps - quality rating, errors, and additions and anomalies: 1. Quality Rating After extensive study of all the manual maps, i t seemed possible to categorize them according to the "quality" of the drawing. There is no objective definition of quality here. Rather, quality seemed to mean the ability to graphically portray a floor plan. Quality ratings were assigned on a four point scale: non-codable (1), poor (2), average (3), excellent (4). Appendix 3 illustrates actual floor plans which fall into these categories. Since I was the only person to subjectively determine quality there is no available method of checking the rel iabi l i ty of this measure. When the quality ratings were correlated against all other variables, however, the analysis tended to reveal my own biases in the rating of quality in manual maps. In some ways i t acts as a measure of my objectivity. 2. Errors In addition to the missing wall code 1, a binary code was established for drawings which did not have corners joined. 1 Missing Wall code 1 = none, 2 = VW, 3 = NR, 4 = UV, 5 = VW and NR, 6 = UV and NR, 7 = BC and FG, 9 = non-codable. 5 3 . Additions and Anomalies Since the subjects were given a blank piece of paper, they could draw their manual map in any orientation they wished. Subjects were also asked to write the names of the rooms on their map. From this the orientation (i .e. map drawn as i f the person was looking towards the street, or drawn as i f the person was looking towards the backyard) of the manual map was coded. If the subject indicated which bedroom was theirs, the number of the bedroom was coded. Although respondents were told that doors, windows, and furniture were not necessary, almost all included additional information. It appeared from subjective assessment that subjects who had better quality drawings also had more additional information on their map. This hypothesis was examined by coding the presence of any additional information. This data had a simple nominal code - present/absent. If there was any indication that the subject attempted to draw a certain thing the variable was coded as present. In the adults' manual . maps the following additional items were observed: - doors '"~ - refrigerator - kitchen table - closets - furnace - steps - bath tub - washer - bathroom sink - toilet - dryer - windows - kitchen sink - kitchen counter - fireplace - Stove 54. Appendix 4 presents manual maps which contain some of the above items. In summary, then, the data obtained from the manual maps were: 6. ut i l i ty 7. bedroom J 8. bedroom N 9. living room 10. hall - MRE and TRE values for: 1. the total house 2. bedroom A 3. bathroom 4. kitchen 5. storage - quality ratings - errors - additions and anomalies. 2.63 Graphic abil i ty. The object of this test was to gain some measure of the subjects' eye-hand coordination and faci l i ty with a pencil. Although there are several manual dexterity tests available (for example, Bennett Hand-Tool Dexterity Test, Stromberg Dexterity Test, Crawford Small Parts Dexterity Tests), these did not appear to be really suitable. Various forms of printing tests which measured graphic ability were also available, but these were designed for small children and appeared unsuitable for adults. \ 55. The eventual choice was the Lurcat Test of Graphical Abilities (Lurcat and Kostin 1970). The following page (Figure 7) shows the five figures used in the test. Subjects were instructed to reproduce exactly in size and shape the figures they saw on the test page. No straight edges and no copying were allowed. The test was marked by using a transparent key which was fitted over the figures. Graduated scales on the key allowed the marker to measure the amount of deviation in both size and shape to produce a total score. Since the marking was a visual exercise and somewhat subjective, two markers were used. Mrs. C. Wood and myself marked 50 common tests. A correlation between the two sets of marked scores yielded a significant r value of .97 indicating the high rel iabil i ty of the marking. < One problem with the Lurcat Test of Graphical Ability is that i t is not a widely used test and most work with i t has been done on French school age children (Lurcat, 1966), although i t is now being used to some extent in the United States (Lurcat and Kostin 1970). Reliability measures take the form of test-retest and in France have produced a mean rel iabi l i ty coefficient of .78^. Lurcat (1966) seems to demonstrate that her test does have predictive validity, but again this was for children. No rel iabi l i ty coefficients for the American tests. FIGURE 7 LURCAT GRAPHIC ABILITY TEST 57. To obtain some indication of rel iabi l i ty the Lurcat Test was administered twice to 94 undergraduate geography, students between the ages of 17 and 49 with a week separating the test periods. A test-retest procedure described by Helmstadter (1964) produced a significant rel iabi l i ty coefficient of .89. The only type of validity that can be assumed is content validity. Content validity "refers not to what the test actually measures, but what i t appears on the basis of subjective evaluation to measure (Helmstadter, 1964, p. 89)." "It is of some importance that the items and the test as a whole appear to be plausible and relevant to the stated purpose (p. 90)." It would appear that the Lurcat test - graphic reproduction of geometric forms - does at least have content validity. 2.64 Spatial aptitude. The spatial aptitude test used was the Revised Minnesota Paper Form Board Test (1970 edition) with series AA being used. Appendix 5 contains a copy of the test. As a test of spatial aptitude the MPFB has gained widespread usage in both education and industry. The rel iabi l i ty and validity of the test is well established. An example of alternate form rel iabi l i ty is illustrated in Table 6 while Table 7 illustrates some test-retest rel iabi l i t ies for children as young as 10 years of age. \ 58. TABLE 6 Alternate Form Reliabi l i ty Coefficients a n d Standard Errors of Measurement for the Rev ised Minnesota Paper Form Board Test First Testing Second Testing Group " Series N Mean SD Mean SD ' 12 S E M b 1. Grade 10 and 11 boys (Louisville, Kentucky) AA-BB" MA-MB d 172 175 43.9 44.3 9.5 7.0 47.5 49.0 9.3 7.5-.78 .73 4.5 3.7 2. Grade 11 boys and girls (Salt Lake City, Utah) AA-BB C MA-MB d 180 123 44.9 44.9 8.6 8.4 48.2 47.7 8.6 8.7 .78 .77 4.1 4.0 3. Engineering students (University of Michigan) 8 MA-MB d 98 48.6 6.4 52.7 6.2 .77 3.1 4. High school students (Michigan)' MA-MB d 164 49.2 6.4 53.5 6.8 .71 3.4 •The time interval between tests was from 2 to 11 days for Group 1, and 4 days for Group 2. Groups 3 and 4 were retested immediately. Al l testing was conducted in 1969. b S E M = S D V l — r i 2 . The SD of the first testing was used to compute the S E M . 0 For some students, the test-retest order was AA-BB; for others, it was BB-AA. Since equivalence of forms has been established (see Table 1), all data from the first testing were combined without regard to form. The same procedure was followed for data from the second testing. d For some students, the test-retest order was MA-MB; for others, it was MB-MA. Since equivalence of forms has been established (see Table 1), all data from the first testing were combined without regard to form. The same procedure was followed for data from the second testing. • Students were 96% male. ' Group 4 consisted of 109 males and 55 females in geometry and drafting courses; 87% of the sample was in Grade 10. Source: Rensis and Quasha, 1970, p. 13. TABLE 7 TEST-RETEST RELIABILITY COEFFICIENTS Age at Second Testing 11 years 12 years 13 years 14 years Age at First Testing N r l 2 N r12 N r12 N r12 10 years 109 .87 156 .86 135 .77 73 .81 11 years 208 .90 210 .85 87 .82 12 years 259 .87 91 .80 13 years 87 .79 Other test-retest studies on adults have shown the rel iabil i ty to be equally high. A great deal of work has also been done on MPFB validity. The test would appear to have construct, predictive, and factor validity. Appendix 5 also contains coefficients of correlation between the MPFB and other tests as well as coefficients of correlation between MPFB and various criteria. It is important to note that the MPFB has significant correlations with: The terms "first testing" and "second testing" are relative only to the particular correlation being computed. In actuality, many children took the test three, four, or five times in the course of the-longitudinal study. Source: Rensis and Quasha, 1970, p. 12. - intelligence (Wechsler-Bellevue and Standford-Binet) - numeric ability - spatial ability - manual ability and manual dexterity - clerical ability - drafting and design success - art ist ic success r job success 1. Factor analysis of intelligence reveals that spatial aptitude is consistently among the f i rs t four factors to be extracted in the analysis. Although verbal aptitude is generally the f i rst factor, spatial and numeric aptitude are close behind. The MPFB is a timed test of 20 minutes and was administered according to manual instructions. There was no correlation between the interviewer and spatial aptitude scores. The test was marked according to the key provided. Children Data Children were asked to complete only two tasks, manual map and Draw-a-Man Test. Job success measure in efficiency, performance, rating of job success, rank and salary. 61. 2.71 Manual maps. Instructions to the children were very similar to those of the adults. They were asked to draw a floor plan or map of the house. If they did not seem to understand the interviewer showed them a line drawing of a floor plan, saying "see here is the kitchen, and bedroom, etc.". They were told that i t was not a map of their home but someone elses. If this approach did not work the interviewer asked the children to draw a picture to show where the rooms in the house could be found. "If I didn't know where to find your bedroom or bathroom or kitchen could you draw me a map so that I could find my way." If this did not work they were simply asked to draw a picture of their house. A few refused to draw anything. There were six sets of data derived from the children's manual maps: 1. Rank Four judges independently ranked the floor plans^. The judges were shown a real floor plan of the house and instructed to: rank all of the children's maps into the order which you think they depict reality. N = 47, 10 out of the 57 either refused to do anything or drew an outside view of the house. 62. Elements of Style In the children's drawings there appeared to be certain styles that emerged. The style types are illustrated in Appendix 6 and described below: Some older children used a sketching technique of short pencil strokes to form a continuous line. Artists frequently use this style. Thick walIs or two dimensional walls was a frequent occurrence. Here the children did not simply put in a line for a wall but showed the thickness of the wall. Many drawings were non-square. The outside walls of the house were not straight lined and rectangular but rather the house was put together like a group of non-uniform blocks. The other extreme to this was the box house where a square or rectangle formed the exterior walls and rooms were placed inside this perimeter like loose blocks. There was also the appended room houses in which the rooms were drawn separately with no exterior boundary and connected by lines representing hallways. Some young children also had interior side views, which showed one or two rooms with doors and furniture. And finally two children who did produce floor plans, also put a roof in the drawing (so did one adult, but the response was non-codable). Errors The wall "NR" seemed to be significant to the children because i t was not perpendicular to other walls in the house. The 6 3 . omission of this wall was coded. Missing rooms and rooms out of place were also coded. Orientation This variable1 Was"the same for adults and children except that the orientation for some children was not evident. Size of Rooms Some children greatly exaggerated certain rooms, particularly their bedrooms and the bathrooms. This was coded i f a bedroom was as large or larger than the living room or was as small or smaller thanthe bathroom, i f the bathroom was larger than at least two other rooms, and i f the hal1 occupied about one fifth or more of the house area. Like the adults the children frequently included other details. These were noted and coded as with their parents. The following is a l i s t of details: Details - wall VW present kitchen sink kitchen table - furnace bathroom sink kitchen counter - master bedroom bath tub beds - house codable stove steps - doors refrigerator toys - closets wi ndows - fireplace washer The word "master" written in. 64. 2.72 Draw-a-Man Test. The Goodenough-Harris Draw-a-Man Test (Harris, 1963) was used to determine the children's mental age and graphic abil i ty, the test is very easy to administer. The child is simply asked to draw a picture of a man. The test takes only five to ten minutes. The test focuses on the child's accuracy of observation and on the development of conceptual thinking, rather -than artistic s k i l l . The number of scorable items or points is 73. Appendix 7 contains a test booklet and short scoring guide. The 1 r ^scoringiterns were selected from a pool of about 100 on the basis of age differentiation, relation to total scores on the provisional form, and relation to group intelligence test scores. Raw scores are converted to standard scores with a mean of 100 and standard deviation of 15. This means that the children's score is roughly equivalent to a standard I.Q. score. Score rel iabi l i t ies are usually over .90. In part, such interscorer agreement reflects the fullness of the scoring instructions and the care exercised in selecting items that can be scored with a minimum of uncertainty. Split-half rel iabi l i t ies are in the .70's and' .80's. Retest rel iabi l i t ies obtained over intervals as long as three months fa l l mostly in the .60's and .70's. Short term fluctuations in performance are negligible. Examiner variance has proved insignificant, as has the effect of art training in school upon test scores. \ 65. An alternative way of evaluating performance utilizes the Quality scale. (This scale technique was not used in the present research.) These scales substitute a simplified, global qualitative assessment of the entire drawing for the detailed point scoring. The score simply chooses one of twelve sample drawings that most closely matches the performance level of the subject's product and assigns the scale value of that sample to the drawing (see Appendix 7). Interscore rel iabi l i t ies for the Quality scales are mostly in the .80's. Harris (1963) summarizes correlations obtained between Draw-a-Man tests and the Stanford-Binet, WTSC, WAIS, PMA, and a few other intelligence and special aptitude tests. Nearly all these correlations are significant and most are substantial (see Appendix 7). The principal evidence for the validity of the Draw-a-Man Test derives from the item analysis procedures followed in developing the scales. In the test, items 63 to 69 can be used as a subtest for graphic abil ity. Harris says that these items "concern the quality of the child's control of the pencil. These items evaluate the firmness and sureness of l ine, quality of line junctions, corners, etc." These items require "the child's deliberate direction of the pencil to produce a good form. The child's work must show that he has exercised control, firmly and surely, (pp. 262-623)". A D U L T R E S U L T S Results of the adult data will begin with a brief description of the data broken down according to: 1 . - TRE and MRE scores - other map data 2. spatial aptitude 3 . graphic ability 4 . socio-economic data. Where applicable, the data will be broken down into the categories male head, female head, and others. Following a description of the data, various analyses were used to test the rel iabi l i ty and va l id i tyof the. manual map as a research instrument. The next section contains the correlation analysis between error scores and other sets of data (socio-economic, factor scores, spatial aptitude, graphic abi l i ty, etc.) The final section deals with the psychophysical relationships in distance and area perception. 3.1 Data Description 3.11 TRE and MRE scores. Table 8 shows the means and standard deviations for absolute TRE and MRE scores for TABLE 8 MEANS AND STANDARD DEVIATIONS OF TRE AND MRE FOR WALLS BY ADULT GROUPS Total Male Head Female Head Other TRE : MRE TRE MRE TRE • MRE TRE MRE Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Bedroom A .70 .41 .68 .40 .69 .33 .69 .36 .64 .37 .61 .35 .84 .46 .81 .41 Bathroom . .61 .56 .58 .55 .66 .78 .62 .75 .60 .40 .57 .42 .56 .30 .54 .35 Kitchen .85 .59 ,.78 .57 .83 .69 .77 .67 .86 .49 .78 .47 .87 .50 .75 .49 Storage .74 .32 .58 .38 .76 .30 .59 .40 .73 .23 .57 .34 .74 .26 .60 .35 Utility .58 .43 .55 .42 .57 .55 ~ .54 .55 .61 .29 .58 .30 .51 .32 .50 .29 Bedroom J .75 .38 .69 .38 .79 .39 .73 .36 .68 .29 .60 .33 .82 .32 .80 .37 Bedroom N .84 .51 .79 .48 .84 . .57 .83 .55 .86 .46 .78 .41 .82 .32 .74 .32 Living Room 1.04 .57 1.03 .56 1.02 .54 1.02 .50 1.09 .54 1.07 .53 .98 .50 .84 .50 Hall .94 .59 .71 .47 .85 .51 .68 .50 1.06 .59 .76 .47 .96 .39 .82 .37 Total House 8.52 3 .56 8.05 3.33 8.48 2.94 8.06 2.92 8.76 2.61 8.12 2.61 8.12 2.46 7.93 2.45 Room error is the sum of the absolute error of all walls of a room, total error is the sum of all wall errors for the house. all rooms and the total house. For the most part the TRE and MRE analyses were concerned solely with the subjects' wall distance error. 1 The error in the area of a room was generally omitted. This was done because error in area was found to be a direct linear combination of the error in walls. (This made sense since the area of a room was defined by the walls). To report both linear area and area error would, therefore, have been redundant. On the basis of error scores male household heads produced manual maps which were closer to reality than their female counter parts. The male heads, however, were in turn out done by their children. A series of t-tests was performed among the three7groups and revealed no significant differences in the means. A paired comparison t-test between husbands and wives revealed no significant difference in the means. The conclusion here must be that there was no significant difference between male household heads, female household heads, and others. A paired comparison t-test was also performed to determine i f there existed a significant difference between TRE and MRE values. Table 9 presents the means and 1 Total room error was the sum of the absolute errors for all walls of any room. \ significance levels for the absolute total house error, indicating that there was no significant difference. TABLE 9 MEANS AND SIGNIFICANCE LEVELS OF PAIRED T-TEST FOR ABSOLUTE TOTAL HOUSE ERROR : Male Head Female Head Other TRE MRE t Significance 8.4795 8.0616 .5182 8.7578 8.1246 .2360 8.1206 7.9322 .7947 The above table is significant. It indicates that in terms of people's ability to communicate cognitive maps of the home environment there is l i t t l e difference between the real world and the world as people perceive i t ( i .e. the norm approximates the real thing). In this instance, the respondent's error from reality and error from the norm were about equal; TRE = MRE. So far only absolute error has been examined. Absolute error is the difference between the standard (true ratio or mean ratio) and the individual observation, regardless of sign. Absolute error is used because i t represents the total sum of all committed errors. If relative error were used the positive and negative errors would tend to cancel one another out. In the case of absolute error the total average absolute house error of 8.52 represents 20.8 percent of the summated real ratios (41). Relative error, however, can be used to determine i f some rooms are perceived to be larger or smaller than reality. Relative errors were computed for al l rooms for the three subject groups. A t-test was then performed to determine i f there was a significant difference between relative error and zero. If there was no error or i f a group was dicotomously split the relative error would be zero. This t-test also indicates the direction of the error. The t-test revealed that there was no significant difference between the relative room errors and the mean of zero, except for the hal l , where the significance of the results were different for the various groups (Table 10). It would appear that all groups perceive the main hall as larger than reality. It is important to note, however, that the difference was marginal and occurred only for one room. In general, when relative error is considered, TRE = MRE = 0. This also indicates that the cognitive map is a close approximation of the real world. \ TABLE 10 SIGNIFICANCE LEVEL OF T-TEST TO TEST THE DIFFERENCE BETWEEN ERROR IN THE SIZE OF HALL AND ZERO Significance Level Total .037 Male Head .057 Female Head .024 Other .031 Other map data. Table 11 outlines the quality rating for the adults' manual maps. TABLE 11 QUALITY RATING OF ADULTS1 MANUAL MAPS IN PERCENT . Total (N=165) Male Head (N=61) Female Head (N=70) Others (N=34) Non-codable 10.3 12.8 17.0 4.3 Poor 24.7 23.4 22.6 17.4 Average 52.0 51.1 50.9 56.5 Good 13.0 12.8 9.4 21.7 Orientation of drawings appears in Table 12. 72. TABLE 12 ORIENTATION OF ADULTS' MANUAL MAPS (percent) Total Male Head Female Head Other Wall AS (towards the bedrooms) 5.7 4.3 5.7 8.7 AE (towards the backyard) 40.7 42.6 34.0 52.2 SE (towards the street) 46.3 48.9 50.9 30.4 XE (towards the ut i l i ty room) 7.3 4.3 9.4 8.7 Other variables from the map which may appear interesting are the details included by the adults. Table 13 is a l i s t of these"details and the percent of times they were drawn by the total sample of 165. TABLE 13 MANUAL MAP ADDITIONAL DETAILS Detail Percent Occurrence Detail Percent Occurrence Doors 81.3 Washer 15.4 Closets 52.8 Dryer 14.6 Bath Tub 16.3 Counters 17.1 Toilet 14.6 Kitchen Table 7.3 Kitchen Sink 16.3 Steps 26.0 Stove 10.6 Bathroom Sink 13.8 Refrigerator 10.6 Windows 19.5 Furnace 57.7 Fireplace 30.9 3.13 Spatial aptitude. Table 14 presents the means and standard deviations for the MPFB test. TABLE 14 SPATIAL APTITUDE SCORES Mean SD Total 39.34 12.91 Male Head 37.70 14.00 Female Head 40.66 12.08 Other 39.65 12.64 A series of t-tests revealed no significant differences among the groups in their spatial aptitude. As a whole the group tested did relatively poorly. Their average scores are well below the 50th percentile of all educational and industrial groups. The others (which are primarily high school students) score in the 25th percentile for their particular norm. The frequency distribution of spatial aptitude scores when analyzed proved to be normal. Graphic abil i ty. Table 15 outlines the means and standard deviations for the Lurcat Test. TABLE 15 GRAPHIC ABILITY SCORES2 Mean SD Total 12.95 6.41 Male Head 13.15 6.54 Female Head 12.81 6.50 Other 12.87 6.22 Higher scores represent a greater spatial aptitude. Higher scores represent a lower graphic abil i ty. Again there were no significant differences among the group scores. The graphic ability scores also approximate a normal distribution. Questionnaire. The questionnaire can be broken down into three sets of data - general information, socio-economic information, and the semantic differential. 1. General Information The housing development is approximately 15 years old. The mean length of residence (8.7 years) and median length of residence (8.5 years) are very close. However, the mode of this distribution is 15 years. There appear to be two distinct groups - the established group who are s t i l l the original owners (14 years^ or more residence, 34.2 percent) and the newly purchased group-(3 years or less residence, 23.6 percent). It is also interesting to note that 52.1 percent of the others (mostly high school children) have lived there 14 or more years. The community sampled is not very mobile with the average change of residence being two times in the 10 years and the median being one time (47.2 percent have never moved). Only 8.1 percent of respondents were left handed, 14.6 percent wore eye glasses to do the test, 12.2 percent were non-Canadian, and 15.4 percent in the opinion of the interviewer seemed to experience some diff iculty in understanding or completing the tasks. Because the sample period spanned two years the development was only 14 years old in 1972. \ The remainder of the general information is probably best conveyed by replicating the questionnaire format: - How do you feel about the amount of living space in your present residence. It is : a. much too small 16.3% b. small but adequate enough 43.9% c. just right 37.4% d. more space than really needed 1.6% - Are you satisfied with the arrangement of rooms in your present home? a. yes 82.9% b. no 16.3% - How many bedrooms would be adequate for your family? (mean 3.1, median 3.0). - Do you feel you are getting your money's worth out of your present residence? a. yes 95.1% b. ho 4.9% - In comparison to other places in the Lower Mainland, how would you rate your neighborhood as a place to l ive: a. excellent 20.3% b. very good 44.7% c good 27.6% d. fair 7.3% e. poor 0.0% 76. - Do you anticipate moving within the next two years? a. yes 13% b. no 87% 2. Socio-Economic Table 16 illustrates the age breakdowns for the various groups. TABLE 16 AGE BREAKDOWNS OF ADULT SAMPLE N Mean SD Median Range Male Head 61 38.9 10.65 39 24 - 71 Female Head 70 37.3 12.17 36 22 - 73 Others - Male 17 18.4 2.31 16 14 - 20 Others - Female 17 19.4 3.45 16 14 - 72 Occupations were coded according to the Blishen Scale (1958). Male household heads had an average score of 51.59 and female household heads an average score of 53.30 (only 32.1 percent were employed). Of those not employed, 55.7 percent were housewives, 34.4 percent were students, 8.2 percent were retired and one person was unemployed. For male heads of household their father's occupation had an average score of 46.47, significantly lower than their own and for female heads 77. their father's occupation had an average score of 49.21, significantly lower than their own or their husband's occupation. There was no significant difference between husband and wife's father's occupations. Table 17 provides a breakdown of the subjects' educational level. TABLE 17 ADULTS' EDUCATION LEVEL Male Head Female Head Other Grade 8 or Less 4.3 1.9 17.4 Grade 9 - 1 3 55.3 56.6 74.3 Some University or Technical Training : 19.2 34.0 8.3 BA, B .SC, Diploma 17.0 7.5 -MA or above 4.3 - -Table 18 provides a family income breakdown for the 70 families in the study. TABLE 18 TOTAL FAMILY INCOME Income (total family income) Percent Families less than $4,000 — $4,000 - $6,000 1.4 $6,000 - $8,000 1.4 $8,000 - $10,000 19.1 $10,000 - $15,000 51.1 $15,000 - $25,000 21.3 $25,000 - $50,000 2.8 more than $50,000 -no answer 2.8 One third (33 percent) of households did not have children while 19.5 percent had one, 26.0 percent -had two, and 13.0 percent had three. Semantic Differential The semantic differential was analyzed with a principal axis factor model with varimax rotation. The lower limit on eigenvalues was set at 1. r i Three unrotated factors with eigenvalues greater than one emerged from the analysis. Table 19 contains a l i s t of variables and their correlations with factors. The independence of the factors is shown in Table 20 which contains a correlation matrix calculated from the factor scores. \ TABLE 19 MATRIX OF CORRELATION OF FACTORS WITH SEMANTIC DIFFERENTIAL VARIABLES Variable Factor 1 Factor 2 Factor 3 1. gloomy - bright .68* -.03 -.07 2. dull - interesting .66* -.18 -.06 3. depressing - happy .59* -.06 -.04 4. forbidding - welcoming .54* .26 .01 5. discordant - harmoneous .53* -.09 -.19 6. dangerous - safe .47* .13 .03 7. hard - soft .36 .08 -.03 8. dirty - clean .36 -.13 -.18 9. private - public -.34< -.34< .31< 10. heavy - light -.34< -.26< .05 11. light - dark -.38* -.22< .23< 12. substantial - thin -.50* -.22 .02 13. invigorating - boring -.59* .06 .15 14. good - bad -.60* -.08 .25 15. warm - cold -.62* -.21 -.01 16. unusual - conventional -.19 .51* .02 17. formal - informal .09 .48* .09 18. complicated - simple .03 .43* -.09 19. feminine - masculine -.15 -.21 -.03 20. open - closed -.24< -.32< .26< 21. ordinary - imposing .14 -.69* .06 22. empty - full .37< .23< .39< 23. peaceful - disturbing -.32< -.28< .36< 24. small - large .06 -.09 .72* 25. cramped - roomy .20 .02 .85* indicates a magnitude greater than or equal to .40 <variables correlated with two or more factors almost equally. TABLE 20 CORRELATION MATRIX AMONG FACTORS CALCULATED FROM THE FACTOR SCORES Factor 1 2 3 1 1.000 2 .035 1.000 3 -.050 .005 1.000 Although a number of variables could possibly be used to describe two or more factors (variables 9, 10, 11, 20, 22, 23), the factor structure of semantic differential variables appears to be fair ly straight forward. Putting names to these factors they could be described as: 1. mood (gloomy, dul l , warm, good, depressing, invigorating, forbidding, discordant, substantial, dangerous). 2. aesthetic (unusual, formal, complicated, ordinary). 3. space (small, cramped). Although the factors do not coincide very well with Honikman's (1970) factor structure, they do f i t very well into the factor classifications developed by Hershberger (1972) and Seaton and Collins (1972). \ 81. The factor scores for all individuals on each factor were calculated and used as input to further analysis. This provided a means of comparing the subject's cognitive structure of the home to other variables. 3.2 Reliability and Validity 3.21 Reliability. The main concern for rel iabi l i ty in this experiment is for the rel iabil i ty of the manual maps. Nunnally (1970) states that "reliabil ity of a test can be estimated from the internal consistency of the items within i t . If the average correlation between the items within a test is high, the internal consistency is high (p. 550)". In the case of the manual maps, correlations were calculated between each room TRE and MRE and the total house TRE and MRE. Table 21 reports the correlation coefficients (Pearson r) which were all significant at the a = .001 level. TABLE 21 CORRELATIONS BETWEEN TOTAL HOUSE TRE AND MRE AND ROOM TRE AND MRE House TRE House MRE Bedroom A .40 .39 Bathroom .50 .53 Kitchen .66 .69 Storage .48 .56 Uti l i ty .35 .41 Bedroom J .44 .42 Bedroom M .50 .45 Living Room .65 .67 Hall .59 .66 The internal consistency for items by group was examined using Cronback's (1951) alpha coefficient: a = (A) (1 --S-V1 ) v t where = variance of test item i = variance of total score n = number of parts. Table 22 presents the rel iabi l i ty coefficient alpha for each analysis showing that the manual map has rel iabi l i ty through internal consistency. TABLE 22 ALPHA COEFFICIENTS1 FOR INTERNAL CONSISTENCY OF MANUAL MAPS BY GROUP FOR ADULTS Male Head Female Head Others TRE .63 .69 .70 MRE .64 .70 .70 - The pre-test also allowed for a test-retest situation to determine rel iabi l i ty . On 31 manual maps the correlation between total TRE scores was .72 and MRE scores .77. It can be concluded that the manual maps used in this experiment did represent a reliable test instrument. Maximum a = 1.0. Validity. The most important question, of course, is whether manual maps measure cognitive maps. Is a manual map a valid tool for representing what might be contained in a cognitive map? As mentioned previously, an article by Howard et al (1973) dealt with this question. Examining the various forms of validity they correctly point out that "Predictive validity requires that we know precisely what a cognitive map is good for and content validity requires that we know what a cognitive map is . Since none of us is capable and most of us are unwilling to meet these conditions, predictive and content validity . . . (p. 255)" cannot be considered appropriate tests. Construct validity, however, can be used as a test. In their research, Howard et al conclude that: Since the attribute being measured in this example is subjective distance, the better the relationship between the true distance and the subjective distance, the better we might suppose the method, as i t is very unlikely that these distances should be approximated by the subject unless the true distances were present in the cognitive map. (p. 256). If this statement is correct, then a clearly definable relationship between objective and cognitive distance would indicate that the manual map did have validity. 84. Section 3.11 has already shown (Table 9) that there is l i t t l e difference between the real world and the world as people perceive i t (at least in terms of their ability to draw a house plan). Further analysis was conducted by performing a correlation analysis between the true ratios for all 41 walls and the mean ratio for corresponding walls by subject groups. Table 23 reports the results. (Appendix 8 contains a l i s t of ratios.) TABLE 23 INTERCORRELATIONS1 BETWEEN REAL RATIOS AND MEAN RATIOS (WALL BY WALL) Real Total Male Head Female Head Others Real 1.000 Total .9815 1.000 Male Head .9899 .9951 1.000 . Female Head .9865 .9936 .9978 1.000 Others .9907 .9957 .9946 .9921 1.000 Pearson r_. It is evident from the table that there is a very strong correspondence between real and cognitive distance. This correspondence is also very strong across the group. \ It can be concluded here that this form of manual map represents a valid research tool. This validity is confirmed by the Howard et al (1973) study in which the method of ratio estimation was shown to be a valid research technique in cognitive mapping research. Correlation Analysis It has been determined so far that the manual map can be a reliable and valid research tool, something which has not been demonstrated to date by other research. On an individual subject basis, however, there are variations in the amount of deviation from the real world. It remains to be seen what variables may influence individual differences in manual maps. The analysis will be presented as the correlation between TRE (and MRE) scores1 and other sets of data. Intra-correlation of variables in a data set will be examined in another section. TRE vs spatial aptitude and graphic  abil i ty. The perception of space and the abil ity to communicate that perception in graphic form would seem to depend to some 1 TRE and MRE are very similar; the results of one analysis being almost identical to the other. For this reason the MRE analysis is henceforth omitted. 86. extent upon the individuals' abilit ies in these areas. There has, however, been no research relating spatial aptitude (or even intelligence) to manual mapping. (Beck, 1967 is perhaps the closest.) Most previous research has tried to relate environmental, cultural, socio-economic or role variable to differences in maps. Ladd (1970), Assmusen (1971), de Jonge (1962), Gulick (1963), Ley (1972), Michelson (1970). Very l i t t l e work has been spent in the search for psychological or physiological variables which might influence cognitive maps. It is quite possible that psychological variables have more influence than cultural variables. It should be pointed out that related v/ork including psychological variables does exist, especially for those concerned with finding the psychophysical function for cognitive distance perception and by those whose interest focuses upon attitude formation and its influence. Correlation analysis of the spatial aptitude scores and graphic ability scores shows that they are both highly related to each other (a = .000). Both scores also correlate with TRE. Table 24 presents the significance levels of correlations of spatial aptitude and graphic abil i ty for the sample groups. \ TABLE 24 SIGNIFICANCE OF CORRELATION BETWEEN TRE (TOTAL HOUSE) AND GRAPHIC ABILITY AND SPATIAL APTITUDE FOR ADULT GROUPS Graphic Ability Spatial Aptitude Total .047 .014 Male Head .106 .030 Female Head .089 .029 Others .108 .034 Although spatial aptitude is significantly related to error scores across all groups, graphic ability appears to be significant only for larger sample sizes. It can be concluded here that spatial aptitude is a variable which may strongly influence an individual's cognitive map. To a lesser degree graphic ability may also influence the manual map. It would appear that the quality of the cognitive map may be dependent, to some degree, upon the recording instrument ( i .e. spatial aptitude) and that the quality of the manual map may be dependent, to some degree, upon the quality of the playing instrument ( i .e. graphic abil i ty) . Future research employing the use of manual maps should perhaps take into account these qualities. It is interesting to note that spatial aptitude and graphic ability are also significantly related to a number of socio-economic variables. Table 25 illustrates the 88. significance of various socio-economic variables with spatial aptitude and graphic abi l i ty. TABLE 25 SIGNIFICANCE LEVELS OF CORRELATIONS BETWEEN SPATIAL APTITUDE AND GRAPHIC ABILITY, AND SOCIO-ECONOMIC VARIABLES Variable Spatial Aptitude Graphic Ability Age .000 .000 Occupation .000 .005 Education .004 .001 Income .025 .048 It should be remembered that spatial aptitude has been significantly related in previous studies to job status and income levels. It would also appear in the present study that the higher the spatial aptitude the more education, the higher the income, and the greater the job status for individuals. There is a significant negative correlation between age and spatial aptitude and graphic abil i ty. This is consistent with the fact that mental faculties tend to decrease with increasing age starting at about 18. 3.32 TRE vs quality rating. As explained previously the quality rating (scaled 1 to 4) was a subjective ' judgment based on the experience gained in examining the manual maps. The quality rating scale, however, did produce highly significant correlations with TRE (see Table 26). TABLE 26 SIGNIFICANCE LEVEL OF CORRELATIONS BETWEEN TRE AND QUALITY RATING FOR ADULT GROUPS Significance Level Total .000 Male Head .004 Female Head .013 Others .111 Although the previous section indicated that the quality of manual maps may be influenced by psychological variables, the analysis here indicates that a qualitative approach to the analysis of manual mapping may s t i l l be a valid method of investigation and research. In geographic literature there is l i t t l e research dealing with the validity of subjective evaluation of manual maps. The above analysis would suggest, however, that there was some justification for previous research based on a qualitative approach. The quality rating variable also correlated highly with a number of other variables (see Table 27). TABLE 27 SIGNIFICANCE LEVEL OF CORRELATIONS BETWEEN QUALITY RATING AND OTHER VARIABLES Variable Significance Level Spatial Aptitude .000 Graphic Ability .000 Length of Residence .015 Age .000 Number of Children at Home .001 Closets .000 Furnace .000 Since spatial aptitude and graphic ability were also related to TRE it is easy to see why these variables are also related to quality rating. For length of residence the longer people had lived in the homes the lower the score they generally received. [Although there was no significant correlation between TRE and length of residence a = .247 there existed a negative correlation 1.] The older they were and the more children they had the lower were their scores. Because quality rating is a nominal variable there can be no direction in the correlation coefficient, hence no negative correlations. 91. Examining my own impressions, I find that i f the subjects included either a furnace room or closets they tended to receive higher quality ratings. As will be shown later, however, both these variables were also significantly correlated with the TRE. 3.33 TRE and socio-economic variables. There were no significant correlations between TRE and socio-economic variables except for number of children at home, which had a significant negative correlation (<*= .03) with TRE. It should be noted that the community was very homogeneous in socio-economic status (especially income). If there was greater diversity then perhaps some relationship between the socio-economic variables and manual maps would have emerged. All that can be said is that subjects from the same socio-economic level tended to have similar responses on the manual maps. 3.34 TRE and information variables. Only one general information variable was significantly correlated with TRE - amount of living space (« = .000). Those individuals who responded that their home was "much too small" tended to 92. have more accurate manual maps (TRE lower). Presumably, this awareness of need for space has made them more conscious of their environment and able to perceive i t more accurately. 3.35 TRE and factor scores. There was no significant correlations between TRE and factor scores. It would appear that the cognitive structure of the home (as measured by the semantic differential) was not related to their spatial cognitive map. 3.36 "TRE and map errors. A significant correlation existed between TRE and the missing walls variables. If subjects had omitted a wall they tended to have more general error in their maps. This occurrence showed a marked difference between groups of subjects with both male and female household heads (« = .002 and .046 respectively) showing a significant correlation but others (mostly high school children) showing no correlation at all (« = .597). Missing walls, as would be expected, correlated highly with spatial aptitude (a = .000), graphic ability (« = .000) and age (<* = .000), with older persons making more mistakes. This relatively simple measure could be used to predict accurately the total error in the maps. This would tend to support \ 93. (in some degree) a qualitative approach to manual map analysis as this variable is very noticeable and produces an immediate impression on the viewer who is familiar with the house plan. 3.37 TRE arid added detail. As noted earlier, there were a number of significant correlations between TRE and . additional detail included in the maps. Table 28 indicates the variables and their significance levels. TABLE 28 SIGNIFICANCE LEVELS OF CORRELATIONS BETWEEN TRE AND ADDED DETAIL Variable Significance Level Variable Significance Level doors - washer .020 closets 1 .082 dryer .039 bath .011 kitchen counters .002 toilet .006 kitchen table -kitchen sink .008 steps -stove .055 bathroom sink .006 refrigerator .055 windows -furnace1 .002 fireplace -Total occurrences of added detail had a significance level of a = .000. TRE and added detail were completely independent in terms of what they actually measured. In fact all respondents were told that they did not have to include doors, windows, or furniture and only did so under their own init iative. Identified by quality rating scores. 94. The conclusion to be reached is that those individuals who endeavoured to make their maps more complete through the addition of detail also had a more accurate perception of their environment. This result supports other researchers in cognitive maps who claim that the amount of detail illustrated in manual maps is a measure of the quality of the subjects' cognitive maps of specific areas (Everitt and Orleans, 1973; Asmussen, 1971). The qualitative approach is also supported by this finding. 3.4 Other Correlational Relationships There are a number of interesting correlations among the various sets of data themselves. Although they do not bear directly upon the main focus of research, their interest deserves reporting. 3.41 Information and socio-economic variables. Table 29 contains the cross correlations of information and socio-economic variables. Actual correlations are given because i t is interesting to see the direction of the correlations for interval variables. In examining the information variables, those persons who had lived there a longer time thought they needed more bedrooms. People who had moved a lot also thought they needed more bedrooms but were also planning to move in two years. TABLE 29 INTER-CORRELATION OF INFORMATION AND SOCIO-ECONOMIC VARIABLES 1 2 3 4 5 6 7 8 9 10 11 12 1. length of residence (I) 2. change of residence (I) -.74 3. amount of living space (N) .02 .14 4. arrangement of rooms (N) .12 .10 .02 5. number of bedrooms (I) .43* .35* .07 .02 6. money's worth (N) .05 .10 .07 .04 .04 7. neighborhood (N) .15 .19 .02 .06 . .02 .01 8. move in two years (N) .07 .23* .12 .11 .09 .02 .02 9. age (I) .09 -.14 .29* .00 .38* .13 .21 .21* 10. occupation (I) .03 .03 .25 .01 .43* NC .12 .01 -.04 11. education (0) -.16 .30* .12* .04 .16 .51 .21 .28 .08 .49* 12. income (0) .34* .32* .05 .07 .07 .04 .01 NC .56* .53* .57* 13. number of children (I) .38* -.25* .48* .78* .78* .01 .17 .06 .07 .14 .12 .28 *significant at a = .05 NC no correlation available; this happens with nominal variables where one cell has less than 5 percent of the observations. I interval variable N nominal variable 0 ordinal variable 96. Among the socio-economic variables, i t is not surprising to find that income correlated highly with age, occupation, education, and number of children. Occupation and education were also related. In addition, those persons living in the house the longest had higher incomes and more children. Those who changed their residences more frequently had higher incomes, more education, but fewer children. Respondents who indicated that the home was too small were generally older, had more education and more children. Persons who wanted more bedrooms were older, had higher job status, and had more children. Finally, .the older the people became, the less likely they were to move. 3 . 4 2 Factor scores. As indicated previously, factor scores did not correlate with TRE or quality rating. The factor scores did, however, correlate with a number of other variables when taken group by group. Factor 1 , mood, did not correlate with anything. Table 30 outlines the significance levels of the variables that did correlate with the aesthetic factor and space factor. The space factor appears to be the most important for al l groups. Various aspects of the plumbing fixtures in the house appear to be related to the young adult's cognitive structure of the home. No explanation is offered TABLE 30 SIGNIFICANCE OF CORRELATION OF FACTOR SCORES AGAINST OTHER VARIABLES FOR ADULTS Variable Factor 2 - Aesthetic Factor 3 - Space Male Female Other Male Female Other Spatial Aptitude - .034 - - - -Graphic Ability .005 - - .006 .000 -Living Space - - - .025 - .000 Number of Bedrooms - - .022 .000 .000 .002 Number of Children - - - .002 .000 Quality Rating - - - - .021 -Education - .009 .049 - - -Furnace - - - - .037 -Doors - - - - - .029 Bath Tub - - .000 - - -Toilet - - .000 - • - -Bathroom Sink - - .006 - - -Kitchen Counters - - .005 - . - -Kitchen Sink - - .000 - - -98. here for this occurrence. A correlation analysis was performed between husbands and wives to determine i f their cognitive structures of the home were similar. The analysis indicated no significant relationship between husbands and wives on the mood or aesthetic factors. Their space factor, however, was highly correlated (a =• .004). The data did not allow for an adequate analysis between children and parents. 3.43 Map details. Table 31 indicates the significance level of the intra-relationship of map details. Closets and furnaces appear to be the most important details with steps and fireplaces close behind. No explanation is offered here as to why these variables are intercorrelated. 3.44 Non-codable maps. Non-codable manual maps were significantly correlated with spatial aptitude, graphic abil i ty, and age. Table 32 indicates the significance of these correlations and the means for this group1. It would appear that the ability to communicate cognitive maps is impaired in older people. This imapirment also occurs in other psychological attributes. Since no "others" had non-codable responses only male and female heads are included. TABLE 31 SIGNIFICANCE OF CORRELATIONS AMONG MAP DETAILS 1. Doors 2. Closets 3. Bath 4. Toilet 5. Kitchen Sink 6. Stove 7. Fridge 8. Furnace 9. Washer 10. Dryer 11. Kitchen Counters 12. Kitchen Table 13. Steps 14. Bathroom Sink 15. Windows 16. Fireplace .00 ,00 .00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 .00 .01 .02 ,02 .00 .00 .00 .00 .01 .01 .00 .00 .00 .03 .03 100 TABLE 32 SIGNIFICANCE LEVEL OF CORRELATION BETWEEN NON-CODABLE MAPS AND OTHER VARIABLES FOR ADULTS Variable Significance Level Non-Codable Means Group Means Spatial Aptitude1 .000 16.6 39.9 2 Graphic Ability .000 22.0 13.0 Age .000 61.4 39.1 Psychophysical Relationships 3 Based on Steven's psychophysical power law , a number of researchers have attempted to empirically determine the power function for visually perceived indoor distance (Kunnapas, 1960 and Teghtsoonian & Teghtsoonian, 1969) and outdoor distance (Gibson, et a l , 1954, 1955; Gilinsky, 1951; Harway, 1963; Luria, et a l , 1975; Teghtsoonian & Teghtsoonian, 1970) by estimating the value of the exponent n. The results thus far seem to indicate that indoor experimental situations yield accelerating power functions (n >1), while outdoor environments tend to have nearly linear or decelerating functions with physical distance (n <1). Higher scores indicate greater spatial aptitude. Higher scores indicate less graphic ability Stevens psychophysical power law; 4/ = a4>n where: ^ = is the subjective distance estimate 4> = is the physical distance n = is an exponent that systematically varies a = is a constant depending on the units of measurement. 101. In an attempt to uncover the psychological foundations of mental mapping a few researchers have attempted to relate Steven's law to cognitive distance perception. In a study of distance between world cities Ekman and Bratfisch (1965), using a ratio scaling technique and an algorithm similar to Steven's law, produced a power function for the exponent, n, of .78 for log actual distance against log of the ratio estimations of cognitive distance. Later experiments by Bratfisch (1969) produced exponents of .58, .90, and 1.08. These experiments, however, were not concerned solely with "subjectively perceived geographical distance" but were in i t ia l ly designed to test the relation between the subjects' "emotional involvement" towards various cities and their estimation of distance between those ci t ies. The experiment produced a much stronger relationship between emotional and objective distance'. Lowerey (1970) estimated the value of n for subjective and real distances for each subject's mental map of ten different city locations (e.g. school, park, bus stop, etc.) using three different ratio scaling techniques. "The regression coefficients for logs of subjective ratios fitted to logs of real' distance ratios ranges from 0.112 to 2.065" (p. 67). He suggests that this wide range of exponent values may reflect different personality characteristics and he also suggests the "Differences in psychophysical functions for faci l i ty types could appear in the same way modality function differences have been found in psychophysics". 102. Rothwell et al (1973), in an experiment comparing visual and cognitive distances, approximated Steven's law and produced cognitive exponents between .42 and .68. Cadwallader (1973), on the other hand, compared methodological methods in data collection of cognitive and real distance and concluded that the relationship "appears to be linear, with Pearson correlation coefficients of .94 and .96 (p. 194)." Howard et al (1973) tend to confirm Cadwallader's findings. In an experiment using four different scaling and psychophysical methods they concluded that "All four show a strong linear relationship between subjective and actual distance, (p. 263)". Analysis of the manual maps in this dissertation tends to confirm the linear hypothesis. Several regression models were applied to determine the best f i t between real distance ratios (plus area ratios) and mean group ratios. Table 33 presents the results of this analysis. As the table indicates the best f i t belongs to the linear model. Since area in this case relies directly upon the walls of the house, i t is not surprising that area and distance follow the same model. The total sample points for area (N = 9) is actually too small to produce a valid model. Similar analysis performed on the various groups of subjects (male head, female head, and others) produced identical results (see Table 22, Chapter 3.22). TABLE 33 REGRESSION ANALYSIS OF REAL DISTANCE AND AREA RATIOS AND SUBJECTIVE DISTANCES AND AREA RATIOS Regression Model Distance (N = 41) Area (N = 9)* r b a r b a 1. linear (y = a + bx) .98 1.00 -.02 .99 1.00 -.03 2. power curve (y = ax^ .97 1.06 .96 .98 .96 .96 3. exponential (y = ae b* .88 .44 .69 .88 .43 .69 *0nly the nine rooms were used as the area of the whole house was a sum of the rooms. 104. The one to one slope of the curve in the linear model also indicates that there is a direct relationship between cognitive distance and real distance. It must be noted, however, that the maximum stimulus range of 45 feet is rather small. This factor could tend to produce a linear model. This chapter has demonstrated that manual maps can be a reliable and valid research instrument. The psychological variables of spatial aptitude and graphic ability were shown to influence to some degree the process of cognitive mapping. On the other hand, socio-economic, attitude, and environmental variables did not appear to affect significantly the subjects' ability to communicate their cognitive maps. Evidence was presented which also supported the qualitative approach to analysis of cognitive mapping. \ 105. CHILDREN RESULTS Analysis of the children's data followed a pattern similar to the adults. The f i rst section of this chapter is a description of the various variables followed by an analysis of the rel iabil i ty of the rank assigned to each child's map. The main variables in the children's study were: 1. Rank of manual map. 2. Chronological age. 3. I.Q. 4. Graphic abil ity. A correlation analysis was performed among these variables (rank, age, I.Q.,'and graphic abi l i ty, RAIG) as well as between the RAIG variables and other variables taken from the manual maps. 4.1 Description Table 34 presents the age distribution of the children by sex. The mean age of the total group was 8.4 years (boys 8.3 and girls 8.4). 106. TABLE 34 AGE DISTRIBUTION Age Male Female Total 13 1 2 3 12 6 2 8 11 2 2 4 10 3 3 6 9 4 3 7 8 4 3 7 7 3 -2 5 6 4 1 5 5 5 2 7 4 1 2 3 3 1 1 2 Total 34 23 57 The norms of the Draw-a-Man Test are valid to the age of 15 while the MPFB spatial aptitude test can be validly administered at the age of 10. So as not to overlap, the age of 14 was chosen as a separation point. The age of 14 is usually representative of the age at which children enter grade 9, or high school. In the sample that was selected, al l students of 14 were in high school, while only one person of age 13 was in high school. TABLE 35 CROSS TABULATION OF I.Q. AND AGE FOR CHILDREN Age I.Q. 3 4 5 6 7 8 9 10 11 12 13 Total 135+ 1 1 1 • 3 131-135 1 1 1 2 1 1 7 126-130 0 121-125 2 1 1 4 116-120 1 1 1 3 111-115 (1) : l (1) 1 1 2 7 106-110 (l) 2 2 2 1 2 2 . 1 13 101-105 (l) (2) 1 1 1 1 1 1 9 96 -100 (1) 1 •V 1 4 91 - 95 (1) 1 2 86 - 90 • (2) 2 81 - 85 1 1 76 - 80 0 71 - 75 2 2 Total 2 3 7 5 5 7 7 6 4 8 3 57 r ( ) denotes a subject who did not do a manual map. TABLE 3 6 AGE DISTRIBUTION AND ELEMENTS OF STYLE FOR CHILDREN Age Style 3 4 5 6 7 8 9 10 n 12 13 % Of -j Total' Sketching Technique 1 i 1 6.4 Thick Walls 4 5 2 3 6 2 48.9 Non-Square 1 1 1 2 1 2 2 5 1 34.0 Box 4 2 1 2 1 1 23.4 Appended Rooms 1 1 1 2 2 2 -19.1 Side View 3 6.4 Roof 1 1 4 .3 Room Size Large Bath 1 2 2 2 14.9 Large Hall 1 1 2 1 2 2 19.1 N = 47 . Subjects can have more than one style present in their drawing. \ 109. A cross tabulation of age and I .Q . is given in Table 35. The children's average I.Q. was 113.4, well above the norm. The frequency distribution of I.Q. did not appear to be normal with the category 131 - 135 having seven children in i t 1 . The average graphic ability score was 3.6 . Of the 57 children only 47 or 82.4 percent completed or attempted a map. Some refused and some did an' outside picture and would not try a floor plan. Table 36 presents an age distribution for various elements of style and room size discrepancies. As shown in Table 37 the majority of children oriented their drawings towards the rear of the house. TABLE 37 ORIENTATION OF DRAWINGS Direction Percent of Total AS (towards the bedroom) 17.5 AE (towards the back) 42.5 SX (towards the street) 17.5 EX (towards the ut i l i ty room) 7.0 None 17.5 This might be expected in such a small sample. In one family (the Andersons) with seven children, six had I.Q.'s 131 or greater. "Scores ranged from 0 to a maximum value of 7. The following table (Table 38) presents the frequency of occurrence of additional detail in the manual maps TABLE 38 OCCURRENCE OF ADDITIONAL DETAIL Variable % Occurrence Variable % Occurrence Wall VW 8.5 Bathroom Sink 8.5 Furnace 23.4 Bath Tub 12.7 Master Bedroom 12.8 Stove 17.1 House Codable 23.4 Refrigerator 10.6 Doors 74.5 Windows 6.3 Closets 36.1 Washer 10.6 Fireplace 19.1 Kitchen Table 10.6 Kitchen Sink 8.5 Kitchen Counter 8.5 Toys 4.2 'Beds 17.1 Steps 8.5 Reliability The main concern for rel iabi l i ty is with the rankings of the four judges. Table 39 demonstrates the reliabil of the judges through a correlation matrix. All correlations are significant at the .000 level. \ m . TABLE 39 INTER-CORRELATION OF JUDGES (n = 47) • Judge Rothwel1 Gil l George Clarkson Rothwell -Gill .80 -George .84 .87 Clarkson .83 .81 .79 The average rank was assigned to each subject for further analysis. 4.3 Correlation Analysis 4.31 Rank, Age, I.Q., and Graphic Ability (RAIG). The f i rst set of correlations was done to determine the relationship between rank, age, I.Q. and graphic abil ity. Table 40 presents the correlations and their significance. TABLE 40 CORRELATION OF RANK, AGE, I.Q. AND GRAPHIC ABILITY Rank1 Age I.Q. Graphic Ability Rank -Age -.64* -I.Q. -.32* .00 Graphic Ability -.62* .58* .40* *<*= .01 1 Signs are negative because the best drawing was ranked as 1 and the poorest as 47. 112. It can be concluded that the quality of the children's drawings is significantly related to age, I.Q., and graphic abil ity. The analysis also showed that there was no correlation between age and I.Q. If there had been a strong relationship i t would have thrown doubt upon the validity of the Draw-a-Man Test. Instead it has shown that the norms used to convert raw score to I.Q. appear to be reliable. Since raw scores were used in the graphic ability test (nine items out of the I.Q. test) i t is not surprising that graphic ability is related to age. This should be the case. Since graphic ability is a subtest of the overall I.Q. test, there is also a correlational relationship between the two. 4.32 Elements of style and size of rooms. Table 41 shows the significance of correlations between RAIG1 and elements of style and size of room. It can be seen that: 1. Higher ranks tend to draw thick walls while lower ranks tend to have a box style. RAIG (rank, age, I.Q. and graphic ability) TABLE 41 SIGNIFICANCE LEVELS OF CORRELATIONS BETWEEN RAIG AND ELEMENTS OF STYLE AND SIZE OF ROOMS Style Rank Age I.Q. Graphic Ability Sketching Technique - - -Thick Walls .002 .002 - .04 Non-Square - .024 - .02 Box .000 .001 - .000 Appended Rooms - - - -Side View - .033 - -Roof - - - -Size of Rooms Large Bathroom .000 .001 - .002 Large Hall .000 .015 - .001 114. 2. Older children tend to produce non-square homes with thick walls while younger children have a box style or side view. 3. Children with higher graphic ability tend to draw thick walls and non-square houses while those the less ability have a box style. 4. Young, low ranked children with less graphic ability tend to draw larger bathrooms and bedrooms. There is l i t t l e theoretical background on which to base statements concerning the style of drawing. There did not appear to be any basis for using the concept of egocentricity (see Hart and Moore, 1971; Asmussen, 1970) when analyzing the children's drawings1, 4.33 Additional detail. As with the adults, the more additional detail contained in the child's map the more likely i t was to receive a higher rank. Table 42 shows that the furnace and closets (as with adults) correlated highly with all RAIG variables. There are three main systems of geographic orientation: egocentric (based on the position of the person), real is t ic (the direction of nearby major features) and coordinated (orientation to the cardinal directions). Other researchers have found that young children's manual maps are characterized by an action centered egocentric reference system. TABLE 42 SIGNIFICANCE LEVELS OF CORRELATIONS BETWEEN RAIG VARIABLES AND AMOUNT OF DETAIL Rank Age I.Q. Graphic Ability Wall VW - .021 - -Furnace .000 .016 .021 .000 Master Bedroom .014 - - .014 House Codable .000 .0407 .002 .000 Doors - - - -Closets .000 .003 .000 Fireplace - - - -Kitchen Sink - - - _ Bathroom Sink - - - -Bath Tub - - - -Stove - - - -Fridge - - - -Windows - - - -Washer - - - -Kitchen Table - - - -Kitchen Counter - - - -Beds . 044 .042 . - -Steps - - - -Toys - - - -Total Detail .000 .000 .000 .000 116. If the house was codable (i .e. could be digitized) i t also correlated highly with the RAIG variables. Again, this is a point for qualitative analysis. It is a fairly easy task to judge whether the drawing comes close to reality at all on the criterion of codability. Most children who drew a codable map were older or brighter. The youngest child to draw a codable map was 8 years old and had an I.Q. of 150, while a 13 year old of I.Q. 96 could not complete the task. Younger children tended to include their beds into their maps. 4.34 Errors. Number of errors had a significant negative correlation with all RAIG variables. 4.35 Non-significant correlations. There were no significant correlations between sex and any variables. This does not coincide with studies by Asmussen (1973) or Blaut (1969). Orientation of the drawing did not appear to be related to any other variables. Unfortunately, because of data constraints (nominal-nominal) i t was not possible to perform correlations between style and detail variables. (With such a small sample the matrix frequently has cells with 5 or less observations.) 117. Size of bedrooms was not correlated with any other factors although there was a tendency (not significant) for young children to leave out their parents' bedroom. Discussion The results of this analysis support the findings of other researchers that as a child develops, his awareness of the world around him increases, as does his ability to accurately communicate his perceptions. This study has shown that mental faculties and graphic ability also relfect a child's developmental patterns. The Goodenough-Harris Test focuses on the child's accuracy of observation and on the development of conceptual thinking. This concept could also be applied to the manual map of the home, where the accuracy of scale and fullness df detail reflect the child's stage of intellectual development. The results presented here would tend to support the concept of Kaplan (1973) that the entire cognitive structure of the subject may be considered a cognitive map. It is interesting to note that I.Q. reaches its peak in an individual shortly after puberty and begins to decline after 18 years old. In terms of drawing manual maps i t appeared that by the age of 9 or 10 half the subjects could produce a codable'map equivalent in quality to the adults. By age 14 all subjects could 118 complete this task; in fact, high school children tended to do better than their parents. The youngest subject to understand the task and attempt a map was 3 years old (I.Q. 132) while the oldest child to fai l the task was 8 years old 1 (I.Q. 91). The youngest child to do a codable map was also 8 years old (I.Q.150). There appears to be a very^ide range* in children's ability to produce manual maps. This consideration should be carefully weighed in future studies. He refused to try and drew an outside view instead. 119. CONCLUSIONS Assessment of Goals The conclusions will follow the format of the four goals as outlined in the introduction. 1. It has been shown that manual maps can be a reliable and valid research instrument in the study of cognitive maps. Several statistical techniques and meausres by which manual maps may be analyzed in a quantitative manner are presented and tested. Both spatial aptitude and graphic ability were found to be significantly related to the ability of individuls to communicate their cognitive maps. It would appear from this study that psychological variables exercise considerable influence in the individual's cognitive deviation from the real world. The experiment demonstrated that persons with superior mental faculties have cognitive maps which more closely reflect reality. The research also showed that as mental faculties decline with age the ability to produce a manual map also declines. Most persons over age 65 could only produce maps of similar quality to 6 and 7 year olds in the same study. Evidence is also presented which supports the traditional qualitative approach to the study of cognitive maps. Future researchers may wish to rely on these findings to support the validity of their own investigations. . 120. 2. Psychophysical functions for subjective distance and area perception proved to be linear. 3. Socio-economic variables, general biographical data, and the subject's cognitive structure of the home as revealed through the semantic differential, did not produce significant correlations with the ability to communicate cognitive maps. It is probable that significant relationships did not emerge because the sample was very homogeneous in character. Greater diversity in these variables may result in significant relationships in future studies. 4. Children's ability to produce a manual map which resembles reality is significantly related to age, spatial aptitude and graphic abil ity. In a broader context, i t would appear that the quality of a child's manual map is a reflection of his general stage of mental development. Ability to communicate cognitive maps increases until puberty when the child approaches full adult development. Discussion The research has shown that manual maps can be a reliable and valid research instrument. This lends credibility and support to previous studies employing this research technique1 but Using basically the same research techniques are works by Appleyard (1969, 1970), Saarinen (1969), de Jonge (1962), Gulick (1963), Stea and Wood (1971) and Everitt and Orleans (1971), Lynch (1960, Ladd (1970) and Ley (1972). 121 which have not dealt with the questions of validity and rel iabi l i ty . This dissertation also supports findings of Howard et al (1973) who tested four methods of ratio estimation for cognitive distance perception and found all of them to be valid and reliable. Cadwallader' (1973) work on the rel iabi l i ty of ratio-estimation techniques in cognitive distance experiements is also supported. ••• • ' ; ' • • I r T a d d i t i o n to providing some validity for other studies employing manual maps, evidence is presented for the use of qualitative techniques of analysis. The research has illustrated that a sense of "quality" of the manual map derived from ' long study and appreciation could also be a good predictor of error. This finding should prove to be significant to those researchers who are endeavouring to employ subjective judgements of quality as input data in other perception studies. One of the more important results is that spatial aptitude and graphic ability appear to significantly influence an individual's cognitive and manual map. To date, these factors have been ignored. It would appear, however, that the quality of cognitive maps (and presumably the quality of spatial decisions an individual could make) is dependent upon the quality of the recording instrument, i.e. the human brain. Nevertheless, most studies in cognitive mapping have attempted to account for differences in manual maps through such variables as race (Ladd, 1970; Ley 1972) culture \ 122. (Stea and Wood, 1971), role (Everitt and Orleans, 1971), socio-economic status (Michelson, 1970), travel patterns (Lee, 1964; Briggs, 1969), and sex Amussen (1971). It is perhaps time that more effort was expended at the level of the individual to determine the psychological parameters of cognitive mapping. Because the brain is the depository of all cognitive maps, i t seems reasonable that by understanding the mechanism itself we may hope to understand the processes involved in cognitive mapping. Numerous socio-economic, biographical, and attitude variables were included in the analysis. None appeared to be significantly related to the manual maps. This does not coincide with the research of Michelson (1970), Appleyard (1969), Ladd (1970) and many others. The sample, however, was so homogeneous on almost all variables that no difference could be detected with the statistical tests which were used. The analysis indicated, however, that when socio-economic variables are held relatively constant, i t is the psychological variables which appear to cause differences in individual manual maps. It would be an interesting experiment to maintain consistency in spatial aptitude and vary socio-economic status. Sample selection, however, would be a diff icult task. The psychophysical function for distance and area perception proved to be linear. This supports the findings of both Cadwallader (1973) and Howard et al (1973) who also used ratio estimation as a research technique. The research, however, conflicts 123. with results presented by Lowery (1970), Briggs (1969), and Lundberg (1973) who contend that the psychophysical function for cognitive distance perception approximates Stevens power law. All experiments to date have used slightly different research designs and all use different geographic scales. Although Howard et al (1973) appear to have used the most rigorous research design, only replicative experiments using the same scale of distance will be able to settle the debate between linear and non-linear models. This dissertation supports the linear psychophysical function of cognitive distance perception. This dissertation generally supports the work conducted by Blaut (1969), Blaut and Stea (1971) and Hart and Moore (1971) in the study of spatial development and learning in young children. As the child develops and matures in his mental faculties, his perception of the world and ability to communicate that perception also improve. The development cognitive mapping closely approximates the development of mental maturity. Unlike other studies (Amussen, 1971), however, significant difference could be detected for sex or socio-economic status. 5.3 Further Research Although this dissertation accomplished its goals, the scope of study was rather confined. Not only were the variables limited but the actual geographic scale was small. The \ 124. methodology used in this dissertation and the results obtained should be tested on a larger geographic area. Howard et al (1973) have already shown that this approach may be f ru i t fu l . There is need for further research on this topic to determine i f geographic scale has an influence upon the basic methodology. Although cultural variables are important in the development of cognitive maps, not enough attention has been given to the investigation of psychological and physiological variables. As Kaplan says "The ways we deal with the environment are largely dependent upon the sorts of mechanisms that have evolved for this purpose" (p. 64). There is certainly a need for research into the variables that make an individual's cognitive map unique. Only by understanding the cognitive processes at the individual level can we hope to truly understand its significance on behaviour. 125. BIBLIOGRAPHY Altman, I., Nelson, P.A., Lett, E.E. The ecology of the home environments. Washington: U.S. Department of Health, Education, and Welfare, 1972. Appleyard, D. City designers and the pluralistic city. In Rodwin, L. et a l , (Ed.), Planning, urban growth, and regional development: The experience of the quayana program in Venezuela. Cambridge, Massachusetts: MIT Press, 1969, 422-452. Appleyard, D. Styles and methods of structuring a city. Environment and  behavior. 1970, .2, 100-118. Argyle,M. The psychology of interpersonal behaviour. Baltimore: Penguin, 1967. Asmussen, D.G. Childrens cognitive organization of space. Ph.D. dissertation. Seattle: University of Washington, 1971. Beck, R. Spatial meaning, and the properties of the environment. In D. Lowenthal (Ed.) Environmental perception and behavior. Department of Geography Research Paper No. 109, University of Chicago. Chicago: University of Chicago Press, 1967. Blaut, J.M. Studies in developmental geography. Place perception research  reports. No. 1. Worchester: Clark University, 1969. ....Blaut, J.M;, & Stea, D. Place learning.Place perception research reports. , -No. 4 Worchester: Clark University, 1969. Blaut, J .M. , McCleary, G.F. , & Blaut, A.S. Environmental mapping in young children. Environment and behavior. 1970, 3., 335-349. Blishen, B. The construction and use of an occupational class scale. Canadian  Journal of Economics and Political Science. 1958, XXIV, 453-457. 126. Boulding, K.E. The image. Ann Arbor: University of Michigan Press, 1956. Bratfisch, 0. A further study of the relation between subjective distance and emotional involvement. Acta Psychologica. 1969, 29_, 244-255. Briggs, R. The scaling of preferences for spatial locations: An example using shopping centers. Ph.D. dissertation. Cincinnati: Ohio State University, 1969. Briggs, R. Urban cognitive distance. In Downs, R.M., & Stea, D. (Eds.), Image and environment. Chicago: Alpine Publishing, 1973. Cadwallader, M.T. An analysis of cognitive distance and its role in consumer spatial behavior. Ph.D. dissertation. Los Angeles: University of California, 1973. Campbell, D.J. and Stanley, J .C. Experimental and quasi-experimental design  for research. Chicago: Rand-McNally, 1966. Canter, D. An intergroup comparison of connotative dimensions in architecture. Environment and behavior. 1969, J_, 37-48. Collins, J .B. Perceptual dimensions of architectural space validated against behavioral criteria. Ph.D. dissertation. Salt Lake City: University of Utah, 1969. Craik, K.H. The comprehension of the everyday physical Environment. Journal  of the American Institute of Planners. 1968, 34 (T), 29-37. Cronback, L.J . Coefficient alpha and the internal structure of tests. Psychometrica, 1951, 1_6, 297-334. Davis, R.E., Foote, F.S. , Kelly, J.W. Surveying: Theory and practice. New York: McGraw-Hill, 1966. 127. de Jonge, D. Images of urban areas, their structures, and psychological foundations. Journal of the American Institute of Planners. 1962, 28_, 266-276. Dornic, S. Subjective distance and emotional involvement: A verification of exponent invariance. Reports from the psychological laboratores. Stockholm, 1967, 237, 1-7. Downs, R.M. The cognitive structure of an urban shopping center. Environment and behavior. 1970, 2_, 13-39. Downs, R.M. & Stea, D. Image and environment. Chicago: Aldine Publishing Co., 1973. -Ekman, G. Two generalized ratio sealing .methods. The Journal of Psychology. 1958, 45, 287-295. Ekman, G. , & Bratfisch, 0. Subjective distance and emotional involvement: A psychological mechanism. Acta Psychologica. 1965, 24, 430-437. Everitt, J . , & Orleans, P. Factors associates with environmental cognition and usage. Paper presented at the 79th annual convention of the American psychological association. Washington, D.C., 1971. Freeman, L.C. Elementary applied statistics. New York: John Wiley & Sons. 1965. Gould, P., & White, R. Mental maps. Markham: Penguin Book, 1974. Gulick, J . Images of an Arab city. Journal of the American Institute of  Planners. 1963, 29, 179-198. : Hall , E.T. The hidden dimension. New York: Doubleday, 1966.--• : Harris, D.B. Children's drawings as a measure of intellectual maturity. New York: Harcourt Brace & World, 1963. 128. Hart, R.A. & Moore, G.T. The development of spatial congition: A review. Place perception reports. Report No. 7, 1971. Helmstadter, G.C. Principles of psychological measurement. New York: Appleton-Century-Crofts, 1964. Hershberger, R.G. A study of meaning and architecture. E.D.R.A. 1, 1970. Hershberger, R.G. Toward a set of semantic scales to measure the meaning of architectural environments. E.D.R.A. 3, 1972. Honikman, B. The investigation of a method of relating the personal construing of the built environment to the designer. In B. Honikman (Ed.) Proceedings of the architectural psychology conference at  Kingston Polytechnic, Sept. 1-4, 1970. RIBA Publications, 1971. Howard, R.B., Chase, S.D., Rothman, M. An analysis of four measures of cognitive maps. E.D.R.A. 4, 1973, 254-264. International Geographic Union. Newsletter. No. 2, December, 1972. Kaplan, S. Cognitive maps in perception and thought. In R.M. Downs, and D. Stea (Eds.) Image and environment. Chicago: Aldine Publishing Co., 1973. Kempler, B. Stimulus correlates of area judgements: A psychophysical development study. Developmental psychology. 1971, 4(2), 158-163. Kunnapas, T.M. Scales for subjective distance. Scandinavian Journal of  Psychology. 1960, J_, 187-192. Ladd, F.C. Black youths view their environment: Neighborhood maps. Environment and behavior. 1970, 1_3 64-79. Lee, T.R. Psychology and living space. Transactions of the Barlett Society. 1964, _2, 9-36. 129. Lee, T.R. Perceived distance as a function of direction in the city. Environment and behavior. 1970, j?, 40-51. Ley, D. The black inner city as a frontier outpost: Images and behavior of a North Philadelphia neighborhood. Ph.D. dissertation. Philadelphia: University of Pennsylvania, 1972. Louviere, J . J . A psychophysical-experimental approach to modeling spatial behavior. Ph.D. dissertation. Iowa City: University of Iowa, 1973. Lowery, R.A. Distance concepts of Urban residents. Environment and behavior. 1970, _2, 52-73. Lurcat, L. Genese de lacte graphic. Bulletin de psycho!qie. 1966, 19, 506-515 Lurcat, L. & Kostin, I. Study of graphical abil i t ies in children. Perceptual  and motor sk i l ls . 1970, 30, 615-630. Lundberg, V. Emotional and geographical phenomena in psychophysical research. In Downs, R.M., & Stea, D. (Eds.) Image and environment. Chicago: Aldine Publishing, 1973. Lynch, Kevin. The image of the city. Cambridge, Mass.: M.I.T. Press, 1960. Margulius, H.L. Consumer perception and the intra-urban journey-to-shop: A case study of Newark, New Jersey. Ph.D. dissertation. Iowa City: University of Iowa, 1972. Michelson, W. Man and his urban environment: A sociological approach. Reading, Mass.: Addison-Wesley, 1970. Poulton, E.D. The new psychophysics: Six models for magnitude estimation. Psychological bulletin. 1968, 69, 1-19. Rensis, L. and Quasha, W.H. Revised Minnesota Paper Form Board Test. New York: The Psychological Corporation, 1970. \ 130. Rothwell, D. Mental mapping of interior space. Unpublished paper. Vancouver: University of British Columbia, 1971. Rothwell, D . C , Bottomley, J . , Forbes, J.D. Cognitive perception of distance for mental mapping. In Leigh, R. (Ed.) Malaspina papers: Studies in human and physical geography. Vancouver: Tantalus Research Ltd. , 1973. Saarinen, T.F. Perception of environment. American Association of Geographers Resource Paper No. 5, 1969. Sanoff, H., & Sawhney, M. Residential l i v ib i l i tv : A socio-phvsical perspective. North Carolina University Urban Affairs and Community Service Center, 1971. Sanoff, H., Burgwyn, H., Adams, J . , McNamara, M. Housing: Research and  development. North Carolina University: School of Design, 1971. Seaton, R.W., & Collins, J.B. Validity and rel iabi l i ty of ratings of simulated buildings. E.D.R.A. 3. 1972. Stea, D., & Downs, R.M. From the outside looking in at the inside looking out. Environment and behavior. 1970, 2, 3-12. Stea, D. The measurement of mental maps: An experimental model for studying conceptual space. In R. Cox and R.G. Golledge (Eds.) Behavioral  problems in geography: A symposium Evanston: Northwestern University, 1969. Stea, D. Architecture in the head: Cognitive mapping. In J . Lang, C. Burnette, W. Moleski, & D. Vachon. Designing for human behavior. Stroudsbury: Dowden, Jutchenson & Ross, 1974. Stea, D., & Wood, D. A cognitive atlas: Explorations into the psychological geography for four Mexican ci t ies, Report no. 10. Place perception  research. Chicago: Environmental Research Group, 1971. Sommer, R. Personal space. New York: Prentice-Hall, 1969. 131. Stevens., S.S. On the psychological law. Psychological review. 1952, 64, 153-181. ~ Stevens, S.S. On the new psychophysics. Scandinavian Journal of Psychology. 1960, 1_, 27-35. Taylor, M. Spatial perspectives at the consumer store interface. M.A. thesis. Vancouver: University of British Columbia, 1972. Teghtsoonian, R. On the exponents in Stevens' law and the constant in ' • Ekman's law. Psychological review. 1971 , 78, 1 , 71-80. ' •• 1 1 ' J ' ^ -Teghtsoonian, R., & Teghtsoonian, M. Scaling apparent distance in a natural outdoor setting. Psychonomic science. 1970, 21(4), 215-216. Teghtsoonian, R., & Teghtsoonian, M. Two varieties of perceived length. Perception and psychophysics. 1970, 8_[6j, 389-392. Teghtsoonian, M., & Teghtsoonian, R. Scaling apparent distance in natural indoor settings. Psychonomic science. 1969, j!0, 281-283. Tolman, E.C. Cognitive maps in rats and men. Psychological review. 1948, 55, 189-208. UBC CORN. Parametric and non-parametric correlations and tests of significance. Vancouver: UBC Computing Center, 1973. Webb, J . E . , Campbell, D.T., Schwartz, R.D., Sechrest, L. Unobtrusive  measures: Nonreactive research in the social sciences. Chicago: Rand McNally, 1966. 132. a APPENDIX 1 Dear Mr. Rothwell, I do not wish to participate in your research project and respectfully request that you do not telephone my place of residence. (please print) \ 133. a APPENDIX 2 WALL AND ROOM DESIGNATIONS WITH TRUE RATIO SCALES 1. House 6. Storage AE 4.14 *HI 1.02 AS 2.55 HP- .64 SV 2.43 PQ 1.02 VW .18 QI .64 WX 1.71 XC 2.73 7. Bedroom J 2. Bedroom A JK 1.00 JS 1.46 HB 1.25 ST 1.00 AJ 1.09 TK 1.46 JL 1.25 LB 1.09 8. Bedroom M 3. Bathroom TM 1.16 MN .54 BC .64 NR .48 BF .77 RV .82 FG .64 VT 1.00 GC .77 9. Living Room 4. Kitchen UV .43 CD 1.23 *vw .18 CO 1.18 *wx 1.71 OP 1.14 XQ 1.41 PD 1.32 QO 2.16 OU 1.22 5. Uti l i ty 10. Hall DE 1.02 DH .68 OG .61 HI 1.02 OM .93 IE- . 68- r MF • .56 *FG .64 *Occurs more than once. \ 134.a APPENDIX 3 135. Non-Codable (Note roof) 137. Non-Codable Poor Poor 143. Average Excel!ent Excellent 146. APPENDIX 4 148. yr \7 1 ^ - -—--s /I IT 0 £ C7 Cb O o A' HAIL -7 / < I T - C H S : / J / i n rt- o rrv- • 0 -4 .-1 s 4 BrL.D£<9£)M -9 7 •*"*•'• I —,_~ —• Additional Detail Additional Detail 150. No Detail \ 151.a A P P E N D I X 5 DIRECTIOiNS A 1 N D PRACTICE r K O B L E M S HEAD THE FOLLOWING DIRECTIONS V E R Y C A R E F U L L Y W H I L E T H E E X A M I N E R R E A D S T H E M A L O U D Look at the problems on the right side of this page. You will notice that there are eight of them, numbered from 1 to 8. Notice that the problems go DOWN the page. First look at Problem 1. There are two parts in the upper left-hand corner. Now look at the five figures labelled A, B, C, D, E. You are to decide which figure shows how these parts can fit to-gether. Let us first look at Figure A. You will notice that Figure A does not look like the parts in the upper left-hand corner would look when fitted together. Neither do Figures B, C, or D. Figure E does look like the parts in the upper left-hand corner would look when fitted together, so E is PRINTED in the square above [TJ at the top of the page. Now look at Problem 2. Decide which figure is the correct answer. As you will notice, Figure A is the correct answer, so A is printed in the square above [if] at the top of the page. The answer to Problem 3 is B, so B is printed in the square above (jT] at the top of the page. In Problem 4, D is the correct answer, so D is printed in the square above | 4 | at the top of the page. Now do Problems 5, 6, 7, and 8. PRINT the letter of the correct answer in the square above the number of the example at the top of the page. DO THESE PROBLEMS NOW. If your answers are not the same as those which the examiner reads to you, RAISE YOUR HAND. DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SO. Some of the problems on the inside of this booklet are more difficult than those which you have al-ready done, but the idea is exactly the same. In each problem you are to decide which figure shows the parts correctly fitted together. Sometimes the parts have to be turned around, and sometimes they have to be turned over in order to make them fit. In the square above (Tj- write the correct answer to Problem 1; in the square above f_2] write the correct answer to Problem 2, and so on with the rest of the test. Start with Problem 1, and go DOWN the page. After you have finished one column, go right on with the next. Be careful not to go so fast that you make mistakes. Do not spend too much time on any one problem. PRINT WITH CAPITAL LETTERS ONLY. MAKE THEM SO THAT ANYONE CAN READ THEM. DO NOT OPEN THE BOOKLET BEFORE YOU ARE TOLD TO DO SO. YOU WILL HAVE EXACTLY 20 MINUTES TO DO THE WHOLE TEST. E A B D 151 21 i • D / D 1 E / AA A B A c / D A E \ Coefficients of Correlat ion between the Rev ised M i n n e s o t a Paper Form Board Test a n d Other Tests MPFB Other Tests Test Group Measures of Intelligence, General Ability, and Reasoning Wechsler - Bellevue Intelligence Scale 11 Full Scale Verbal Scale Performance Scale Stanford-Binet Intelligence Scale, Form L , 1937 Revision Army Group Examination Alpha Army Group Examination Alpha; Form 5 Revised Beta Examination Otis Self-Administering Tests of Mental Ability: Higher Examin-tion, Form A Otis Self-Administering Tests of Mental Ability: Higher Examina-tion, Form A (20-minute time limit) The Henmon-Nelson Tests of Mental Ability, Form B (for Col-lege Students) N High school students, aged 16.5-19.5 100 (Magsdick, 1950) 74 boys and 87 girls, age 10, in the 161 Brush Foundation Study of Child Growth and Development (Ebert & Simmons, 1943) Male prison inmates, aged 15+, 994 modal age = 17 (R. T. Norlund, personal communication, from 1948 manual) Male prison inmates, aged 18-57 1000 (Gurvitz, 1950) Male prison inmates, aged 18-57 1000 (Gurvitz, 1950) Male applicants to a large eastern 53 manufacturing company for posi-tions as machine apprentices, aged 17-26, mean age = 20.3, mean grade completed = 12.0 (Personal communication, 1956) Male supervisors (mostly assistant 40 foremen) in an aircraft factory (Sartain, 1946) Male inspectors in an aircraft factory 46 (Sartain, 1945) College freshmen, 150 male and 150 300 female (Alteneder, 1940) .61** .47** .62** .54** .47** .68** .71** .52** .39* .62** .45** Series Mean SD A A A A A A A A 39s 34.5 12.1 A A A A o r B B 33.3 11.7 41.0 11.0 10.5 41.2 10.1 Mean 94.0 28.6 43.3 SD 113b 15.3 53b 9.5 60b 7.6 13.7 30.3 14.1 30.3 14.1 65.0C 10.1 47.8d 11.9 9.5 11.3 (Table continued on next page) TABLE 7 (continued) Coeff icients of Correlat ion between the Revised Minnesota Paper Form Board Test a n d Other Tests MPFB Other Tests Test Group N r Series Mean SD Mean SD Wonderlic Personnel Test, Form D Male applicants for engineering posi-tions at an electric utility (Personal communication, 1964) 201 .18** M B 48.8 7.3 32.3 5.7 Arthur Stencil Design Test High school students, aged 16.5-19.5 (Magsdick, 1950) 100 ,52** — 39" 12.1 14° 4.5 Cardall Test of Practical Judgment Male inspectors in an aircraft factory (Sartain, 1945) 46 .43** — 34.5 10.5 160.1 45.4 Minnesota Engineering Analogies Test, Form F Male engineers and scientists at a large electrical company (Personal communication, 1960) 327 .25** A A 50.3 7.9 32.1 7.1 Minnesota Engineering Analogies Test, Forms E and F Male applicants for engineering posi-tions at an electric utility (Personal communication, 1964) 201 .04 M B 48.8 7.3 30.7 5.6 Measures of Numerical Ability Personnel Tests for Industry— Numerical Male applicants to an east coast chemical company (Personal com-munication, 1960-61) 216 .47** M A 41.1 10.3 16.8 6.2 Male employees in an east coast chemical company (Personal com-munication, 1960-61) 83 .55** M A 38.9 9.8 16.9 4.5 Male electrical maintenance workers at a large metropolitan public trans-portation company (Personal com-munication',' 1964) 122 .53** M A 39.0 9.9 19.2 6.3 Male apprentices in mechanical and electrical positions at several plants of a large metals manufacturer (Personal communication, 1969) 178 .38** A A or BB 44.8 7.8 22.3 4.9 Male automotive personnel at a large metropolitan public transportation company (Personal communication, 1960) 53 .35** M A 39.9 8.7 16.0 8.8 (Table continued on next page) TABLE 1 7 (confirmed) Coeff icients of Correlat ion between the Revised Minnesota Paper Form Board Test a n d Other Tests MPFB Other Tests Test Group N r Series Mean SD Mean SD Short Employment Tests— Numerical, Form 2 Male applicants for engineering positions at an electric utility (Per-sonal communication, 1964) 201 .20** MB 48.8 7.3 47.9 13.7 Measures of Verbal Ability Personnel Tests for Industry— Verbal Male electrical maintenance workers at a large metropolitan public trans-portation company (Personal com-munication, 1964) 122 .45** M A 39.0 9.9 34.6 9.7 Male apprentices in mechanical and electrical positions at several plants of a large metals manufacturer (Personal communication, 1969) 177 34** A A or BB 44.8 7.8 38.1 7.4 Male automotive personnel at a large^ metropolitan public transportation-' company (Personal communication, 1960) 53 .39** M A 39.9 8.7 30.9 6.6 Wide Range Vocabulary Test, Form B Male applicants for engineering posi-tions at an electric utility (Personal communication, 1964) 201 .10 MB 48.8 . 7-3 73.1 10.8 SRA Primary Mental Abilities: Word-Fluency Male applicants for engineering posi-tions at an electric utility (Personal communication, 1964) 201 .12 MB 48.8 7.3 44.6 11.3 Measures of Spatial Ability Revised Beta Examination, Test 4 Male prison inmates, aged 18-57 (Gurvitz, 1950) 1000 .62** A A 30.3 14.1 10.1 2.6 Minnesota Spatial Relations Test Male prison inmates with IQs of 90 and above (W. P. DeStephens, personal communication, 1950) Literates (reading above Grade 4.4 level) Illiterates (reading below Grade 4.4 level) 334 167 .61** .38** MB MB 38.2 27.8 — — — {Table continued on next page) T A B L E 7 (continued) Coeff icients of Corre lat ion between the Rev ised M i n n e s o t a Paper Form Board Test a n d O t h e r Tests MPFB Other Tests Test Group N r Series Mean SD Mean SD ' Wechsler-Bellevue Intelligence Scale, Block Design High school students, aged 16.5-19.5 (Magsdick^ 1950) 100 .61** — 39* 12.1 13" 2.7 Engineering school freshmeri, aged 17.5-21, mean age = 18.2 (Estes, 1942) 103 .40** AA 46.4 8.1 33.2 3.7 War veterans in a general medical and surgical hospital (Schultz & Knapp, 1955) 28 .63** — — — • — — Survey of Space Relations Ability War veterans in a general medical and surgical hospital (Schultz & Knapp, 1955) 31 .67** — — — — — Differential Aptitude Tests: Space Relations Male apprentices in mechanical and electrical positions at several plants of a large metals manufacturer (Personal communication, 1969) 63 ;i .54** AA or BB 42.1 7.7 54.2 21.1 Measures of Mechanical Ability - i j Bennett Test of Mechanical Com-prehension, Form AA Male applicants to a fabricated metals factory (Personal communica-tion, 1956) 111 .20* AA 36.6 11.6 38.7 9.4 • ii Male applicants for positions as apprentice foremen at a western manufacturing company (Personal communication, 1955) 69 .35** AA 40.4 9.4 44.8 9.5 Male inspectors in an aircraft factory (Sartain, 1945) tJ 46 .27 — 34.5 p 10.5 21.4 8.7 Male apprentices in mechanical and electrical positions at several plants of a large metals manufacturer (Personal communication, 1969) 179 .31** AA or BB i 44.7 7.9 45.0 6.5 Male supervisors (mostly assistant foremen) in an aircraft factory (Sartain, 1946) 40 .31* — — — — (Table continued on next page) TABLE 7 (confirmed) Coefficients of Correlat ion between the Revised Minnesota Paper Form Board Test a n d Other Tests • 1 MPFB Other Tests Test Group N r Series Mean SD Mean SD Bennett Test of Mechanical Com-prehension, Form BB Male automotive personnel at a large metropolitan public transportation company (Personal communication, 1960) 53 .39** M A 39.9 8.7 26.5 11.0 r Ii Male electrical maintenance workers at a large metropolitan public trans-portation i company (Personal com-munication, 1964) 122 .47** M A 39.0 9.9 25.5 9.6 Male draftsmen in a large nationwide electrical manufacturing company (Personal communication, 1964) 64 .43** A A 48.7 8.4 47.5 5.4 Male applicants, aged 17-26, to a large eastern manufacturing company (Personal communication, 1956) 53 .46** A A 11 41.0 11.0 22.5 10.1 Carl Hollow Square Scale Engineering school freshmen, aged 17.5-21, mean age = 18.2 (Estes, 1942) ' 103 .44** A A 46.4 8.1 117.2 10.7 O'Connor Wiggly Block Engineering school freshmen, aged 17.5-21, mean age = 18.2 (Estes, 1942) 103 .31** A A 46.4 8.1 3.8 2.1 MacQuarrie Test for Mechanical Ability Male inspectors in an aircraft factory (Sartain, 1945) 46 .31* — 34.5 10.5 58.6 11.0 O'Rourke Mechanical Aptitude Test, Form A Bennett Hand-Tool Dexterity Test H Male inspectors in an aircraft factory (Sartain, 1945) Male adults (mostly veterans) at a vocational'guidance center (Personal communication, 1946) 46 253 .09 .33**f A A 34.5 41.3 10.5 10.6 177.5 49.8 Time in Seconds 423" 84" '1 Male electrical maintenance workers at a large metropolitan public trans-portation company (Personal com--munication, 1964) 122 .24**' M A 11 39.0 9.9 393.4" 60.3" Male automotive personnel at a large metropolitan public transportation company (Personal communication, 1960) 53 .23' M A , 39.9 8.7 352.3" 70.9" (Table continued on next page) T A B L E 7 {continued) Coeff icients of Correlat ion between the Rev ised M i n n e s o t a Paper Form Board Test a n d Other Tests Test Group N MPFB Series Mean SD Other Tests Mean SD Results of a Multi-Ability Study 8 SRA Primary Mental Abilities: Reasoning Number Word-Fluency Verbal-Meaning Space Reasoning Number Word-Fluency Verbal-Meaning Space u General Aptitude Test Battery, B-1001 : h Computation " Arithmetic Reason Vocabulary Tool Matching Name Comparison Form Matching Two-Dimensional Space Three-Dimensional Space Grade 10, 255 boys and 310 girls (Mouly & Robinson, 1949) 565 Grade 12, 239 boys and 287 girls (Mouly & Robinson, 1949) 526 Grade 10, 255 boys and 310 girls (Mouly & Robinson, 1949) 565 .42** .16** .19** .26** .41** .42** .21** .16** .36** 44** .22** 2 9 * * .24** .30** .26** .49** .70** .52** AA 39.6 10.2 AA 42.0 9.6 AA 39.6 10.2 17.4 18.3 38.6 25.7 22.2 19.2 23.7 45.8 31.2 26.0 5.8 7.8 10.6 9.0 12.5 5.8 9.1 11.4 10.0 12.8 Computation Arithmetic Reason Vocabulary ., Tool Matching Name Comparison Form Matching Two-Dimensional Space Three-Dimensional Space Grade 12, 239 boys and 287 girls (Mouly & Robinson, 1949) 526 .26** .34** .30** .28** .23** .51** .70** .49** AA 42.0 9.6 (Table continued on next page) TABLE 7 {continued) ' Coefficients of Correlat ion between the Revised Minnesota Paper Form Board Test a n d Other T e s ' ; Test Group N r Series MPFB Mean ' SD Other Tests Mean SD Minnesota Clerical Test Grade 10, 255 boys and 310 girls 565 AA 39.6 10.2 Number Comparison (Mouly & Robinson, 1949) .17** 104.7 22.9 Name Comparison .26** 98.7 27.1 Grade 12, 239 boys and 287 girls 526 AA 42.0 9.6 Number Comparison (Mouly & Robinson, 1949) .21** 116.3 32.7 Name Comparison .25** 111.6 28.0 •Significant at .05 level. ••Significant at .01 level. » M e a n raw score reported to the nearest whole number. . ' ,. b These means correspond to weighted scores which were reported to the nearest whole number. Mean weighted scores of 113, 53, and 60 correspond to IOs of 112,108 and 112 respectively on the Full Scale, Verbal Scale, and Performance Scale. ' 0 Mean weighted score. d Mean raw score which is equivalent to a mean IQ of approximately 106. • Mean weighted score reported to the nearest whole number. ' The sign of this correlation was changed from negative to positive so as to indicate the true relationship between the two tests. The score on the Hand-Tool Dexterity Test is the time required to complete the test. Thus, low scores are better than high scores, and negative correlations indicate positive relationships. * In addition to the abilities listed in previous headings (e.g., numerical, verbal), the study included tests of clerical ability. h Data presented for 8 subtests expected to be most closely related to MPFB; median correlation of MPFB with 7 omitted GATB motor tests = .16 for students in both grades cn TABLE 8 Coeff icients of Correlat ion between the Rev ised M i n n e s o t a Paper Form Board Test a n d Var ious Criteria Criterion MPFB Group Students at an industrial institute (Bradley, 1958) Students in a basic ^instruction course for aviation mechanics (T. Harrell , personal communication, from 1948 manual) College students in a wartime defense training plan, mean age = 22 (Crawford, 1942) Evening college students in a wartime engineering defense training program (Moore, 1941) Full-time day college students in a wartime engineering defense program (Moore, 1941) Enrollees in engineering, science, management, defense training ( E S M D T ) courses at North Carolina State College during wartime (McGehee & Moffie, 1942) i Trainees in an aircraft company (Grimsley, 1944) N r h Description Mean SD Series Mean SD , School Success Course grades:" 46 •n A i r Conditioning, Refrigeration 3.0 0.6 M A 42.6 8.1 99 .37** Auto Mechanics, General 3.2 0.7 M A 42.5 9.8 66 .29* d Baking ' 2.8 0.7 M A 37.9 9.5 51 .35* Building Construction, Drafting, 3.1 0.7 M A 50.2 6.2 42 and Estimating .37* Building Construction, Carpentry 3.0 0.8 M A 43.9 7.3 74 .52** Electrical, General 3.1 0.8 M A 47.1 8.7 76 .23* Machine Shop, General 2.7 0.6 M A 46.7 7.0 53 .31* Mechanical Drafting, General 3.3 0.7 M A 48.7 8.7 43 .40** Printing, General 2.8 0.6 M A 44.4 9.2 79 .33** R a d i o - T V Electronics 3.0 0.9 M A 46.1 8.0 84 Course grades: .41** Mechanical Drafting and Blueprint — — Reading .35** Elements of Metalwork — • — — — 80 .56** Course grade: Machine Design and "Detail — Drafting Course grades: 85 .49** Pre-Mathematics, Mechanics, and — Strength of Materials 167 .34** Engineering Drafting — — — — — 282 Course grades: .35** Engineering Drafting — — .17** Mathematics — .14* Mechanics 1 .13* Chemistry — .17** Physics (Cooperative Physics Test) — — — — — Course grades: 22 .14 Architectural Engineering — 63 .35** Engineering Drawing — — 19 .26 Instrument Men — — — — — 165 .48** Grades in a Detail Draftsmen Train-ing Program (Table continued on next page) T A B L E 8 (continued) Coefficients of Correlat idn between the Rev ised M innesota Paper Form Board Test a n d Var ious Criteria t: ' Criterion MPFB Group N r Description Mean SD Series Mean SD Engineering school freshmen (Estes, 1942) 76 .31** Instructors' ratings in Descriptive Geometry, disregarding Drawing Technique 5.2 1.9 A A 45.0 9.7 Entering West Point cadets (French, 1955) 361 .06 b ,20* * b .53** b .31** b Course grades: Foreign Language English Military Topography and Graphics Mathematics 63.0 62.1 ' 63.5 65.4 5.8 4.1 5.0 5.9 M A 45.6 b 9.0 b Junior and senjor high school students (Hunter, 1945) 75 .45** Pupi l^ efficiency: Work samples graded on the basis of accuracy, quality of finish, and speed — — — — — Freshmen dentistry students (Thompson, 1942) " . i 35 .04 .24 Grade point average for one year of dentistry courses Combination of grade point average in dentistry courses and ratings of mechanical technique made by two laboratory instructors ' 2.4 0.8 A A i 39.3 8.8 Senior dentistry students (Thompson, 1942) 40 I'i .31* .61 Grade point average for four years of dentistry courses Combination of grade point average in dentistry courses and ratings of mechanical technique made by two technical instructors 2.3 0.4 A A 42.4 13.9 Art school freshmen, architecture majors, all male (Bryan, 1942) 75 .33** .25* .17 Course grades: Average of all art courses Design Structural Representation 78.2 78.6 78.1 5.7 9.0 6.5 A A or B B 44.8 7.8 Art school freshmen, art education majors, 61 male* and 157 female (Bryan, 1942) 218 .17** .21** .15* Course grades: Average of all art courses Design Structural Representation 82.8 82.0 82.8 4.8 7.0 6.4 A A or B B 46.7 17.7 Art school freshmen, design majors, 374 male and 341 female (Bryan, 1942) 715 .20** .20** .09** Course grades: Average of all art courses Design Structural Representation 81.4 81.0 81.2 5.3 8.1 7.9 A A or B B 43.8 8.1 (Table continued on next page) TABLE 8 (confim/ed) Coeff icients of Correlat ion between the Rev ised M i n n e s o t a Paper Form Board Test a n d Var ious Criteria •' 1 Criterion MPFB Group N r Description Mean SD Series Mean SD Fine arts students (Thompson, 1942) College freshmen, 150 male and 150 female (Alteneder, l i1940) 50 300 .18 .30** Grade point average for all courses Average grades for the first semester of college 2.9 0.5 A A A A 40.8 41.2 10.2 10.1 Male electrical and mechanical work-ers (mostly aged 25-35 with high school education) for a large metals manufacturer (Personal communica-tion, 1969) 154 .11 j Grade 1 point average" 1 in an in-company training program Job Success 3.5 0.3 A A or B B 44.9 7.9 Male inspectors in an aircraft factory (Sartain, 1945) 46 .47** i Job efficiency: The sum of two independent ratings by two instruc-tors in a refresher course for inspec-tors ' 5.9 1.4 34.5 10.5 Male draftsmen in a large nation-wide electrical manufacturing com-pany (Personal communication, 1964) 64 .22 Performance ratings: The sum of six 5-point ratings on the following qualities: Productivity, quality of work, knowledge of work, sense of responsibility, relations with others, self-control 22.0 3.4 A A 48.7 8.4 Male electrical maintenance workers at a large metropolitan public trans-portation company (Personal com-munication, 1964) 122 .24** .48** Supervisory ratings composed of the following scales: 6 personality traits, behavior in 11 areas, performance in 4 areas Age-level index : d Overall achieve- , ment level of each man " 213.8 17.7 30.2 9.1 M A 39.0 9.9 Male automotive personnel at a large, metropolitan public transportation company (Personal communication, 1960) 53 .21 Supervisors' ratings of job perform-ance 105.2 10.2 M A 39.9 8.7 .21 Age-level index: Overall achievement level of each man 13.8 8.3 Male employees in an east coast chemical company (Personal com-munication, 1960-61) 83 .35** Performance ratings by supervisors? 33.7 — M A 38.9 9.8 Female inspector-packers in a pharmaceutical supply house (Ghis-elli, 1942) 26 .57** Ratings of job proficiency by super-visors — — (Table continued on next page) T A B L E 8 [continued) Coeff icients of Correlat ion between the Rev ised M i n n e s o t a Paper Form Board Test a n d Var ious Criteri. Criterion MPFB Group N r Description Mean SD Series Mean SD Male and female inspectors in air-craft plants (Shuman, 1945a) 49 .50**' i Ratings of job success6 — — A A — — Male engine testers in aircraft plants (Shuman, 1945a) 45 .16 f Ratings of job success".. — — A A — — Male and female machine operators in aircraft plants (Shuman, 1945a) 81 .38* * f Ratings of job success8 — — A A — — Male foremen in aircraft plants (Shuman, 1945a) 99 .47* * f Ratings of job success8 ' — — A A — — Male job setters in aircraft plants (Shuman, 1945a) 25 .59* * f Ratings of job success8 — — A A — — Male toolroom learners in aircraft plants (Shuman, 1945a) ' 64 .42**' Ratings of job success8 — — A A — — Male electrical and mechanical work-ers (mostly aged 25-35 with high school education) for a large metals manufacturer (Personal communica-tion, 1969) 178 .14 Supervisors' ratings of overall job performance*1 3.2 0.8 A A or B B 44.7 7.9 Male supervisors (mostly assistant foremen) in an aircraft factory (Sartain, 1946) 40 .10 Job efficiency: The sum of the stand-ard scores of four ratings (Two different rating forms were filled out by two superiors of the supervisors studied) — Male supervisors in aircraft plants (Shuman, 1945b) 208 .39**' Ratings of job success given by superiors of the supervisors studied, on the following characteristics: Production, handling workers, con-dition and maintenance of depart-ment, general overall ability • A A Front-line supervisors eligible for promotion to foremen at a manufac-turing company (Dicken & Black, 1965) 31 .23 .27 Final salary Job level increase — — — — Male bricklayers, Wor ld War II veterans, enrolled in a commercial institute (Ferson, 1951) 150 .38** Weighted combination of instructor's performance ratings1 and oral trades questions test scores — — B B — — (Table continued on next page) TABLE 8 (confinued) Coefficients of Correlat ion between the Revised Minnesota Paper Form Board Test a n d Var ious Criteria Criterion MPFB Group Description Mean SD Series Mean SD to Male auto mechanics, World War II 87 .48** veterans, enrolled in a commercial institute (Ferson, 1951) • I Male plumbers, World War II vet- 173 .36** erans, enrolled in a commercial institute (Ferson, 1951) j Male linotype operator trainees 27 .29 (Beamer, Edmondsbn, & Strother, 1948) I Female power sewing machine opera- . 52 • .32* tors (Otis, 1938) Male engineers and scientists in de- 148 .19* velopment classifications at a large electrical company (Personal com- i munication, 1960) Male engineers and scientists in re- 116 .24** search classifications at a large electrical company (Personal com-munication, 1960) Weighted combination of instructor's performance ratings' and oral trades questions test scores Weighted combination of instructor's performance ratings' and oral trades questions test scores Objective measure of production (lines per hour minus twice the errors made) Quality of work as indicated by per-formance on a series of work samples Salary (with the influence of age removed statistically)111 Salary (with the influence of age removed statistically)* B B B B — 351.2 1726.7 448.0 2062.0 A A or B B A A A A 38.7 8.9 50.2 8.0 50.3 8.1 •Significant at .05 level. "Significant at .01 level. •Grades were converted to the following scale: A = 1;B = 2 ; C = 3 ; D = 4 ; F = 5. Since low scores are better than high scores, positive relationships would be indicated by nega-tive correlations. To show the true relationships between the MPFB and the criteria, the signs of the correlations were changed from negative to positive. b Mean and standard deviation based on original total group of 410 cadets; coefficients of correlation based on 361 of original group of cadets. 0 Grade point averages were converted to the following scale: A = 4 ; B = 3 ; C = 2. ' d This index relates chronological age and level of achievement. Age-level index = 1 0 ? L where L = weighted level according to position (level 10 down to level 3); A = age; Y = years in level. A + (Y-L) • Ratings on each of four job characteristics: quality, quantity, dependability, attitude. Sum of ratings could range fromlO (poor) to 50 (excellent). 'Biserialr. " . . " > * Ratings made by trained workers who interviewed one or more supervisors familiar with work of those being rated. h Ratings ranged from 1 (low) to 5 (high). I ' Mean biserial r for groups tested. ' Performance ratings based on quality, quantity, and job knowledge. k Criterion value for,an individual is the deviation of his income from the expected salary for his age. < CTi I68.a A P P E N D I X 6 </f*7 Sketching Technique 170. flrW RoOf^  .IVI^C/ROOf* C / 6 / 2 Thick Walls ROOM £ATH ROOM DR^VV MART I V5 1\D(V15 OAD5 ROOlVl r aw 1 JM50NS ^ 1 5r c\ O s - r \ Non-Square Style 174. DRYEA n 0 3 T 3 3 o o c_r> O D O O R O F Non-Square Style Appended Room Style Box Style 178. Han 5 Jar? Side View Three Years Old - Box Style) 184. ^ Non-Codable 3 188. Large Hall - Large Bathroom \ No Hall - Large Bathroom I V I J T * Otitis 00/71 L r>9 KrcV\ e n 1 * ^  190. Large Bathroom ^ 0 c * i PREVIOUSLY COPYRIGHTED MATERIAL IN APPENDIX 7 NOT MICROFILMED. Leaves 192-197. 191.a APPENDIX 7 191 .b Goodenough-Harris Drawing Test By Florence L. Goodenough and Dale B. Harris tame. . —< ; Boy G i r L Jchool , • ' • - _ D a t e o f Drawirvg 5 r a d e _ _ ' , „ A g e Birth Date; : _ — ' . 'other's O c c u p a t i o n — — ii. , — — . — • • — . . ..• Examiner's Notes Summary Raw Score Standard Score Percentile Rank Point Sca le Mi*"1*1 \ A / f M T I S i n Average Q u a l i t y Sca le \ A / / M T I r t f l A v e r a g e Copyright © 1963 by Harcourt, Brace 4 World, Inc., New York. All rights reserved. Printed in U.S.A. Make Your First Drawing Here Draw a picture of a man. Make the very best picture you can. Be sure to make the whole man, not just his head and shoulders. l._ 2.. 3. _ 4. _ 5. _ 4.1 42 43. 44, 45. 6._ 7.. 8._ 9.. 10._ 46. 47. 48. 49. 50. 11-12.. 13._ 14.. 15-51-52. 53= 54-5 5 , 16._ 17.. 18.. 19. _ 20. _ 56, 57. 58. 59. 60. 21. 22. 23. 24. 25.. 61. 62, 63. 64, 65. 26.. 27.. 28.. 29.. 30.. 66, 67. 68, 69= 70, 31.. 32. _ 33. _ 34.. 35.. 71-72, 73 36. _ 37. _ 38. _ 39. _ 40.. Raw Score 9 6 DRAWINCS AS MEASURES OF I N T E L L E C T U A L M A T U R I T Y T A B L E 7 Summary of Correlations Between Goodenough Scores and Scores on Other Psychological Tests PRIMARY MENTAL ABILITIES C O R R E L A T I O N S Ansbacher (1952) 100 ten-year-olds Harris (unpublished) 164 kindergarten children Yepson (1929) McElwee (1932) Williams (1935) Havighurst and Janke (1944) M c H u g h (1945) Pechoux, etaZ. (1947) Rottersman (1950) Johnson, et al. (1950) El l i s (1953) ( P M A quotients) .40 Reasoning .38 Space .37 Perception .26 Verbal Meaning .24 Number .41 Tota l test (Raw scores) .29 Verbal Meaning .17 Perceptual Speed .43 Quantitative .43 M o t o r .46 Space .46 Tota l score STANFORD-BINET 37 institutionalized mentally retarded boys, aged nine to eighteen years 45fourteen-and fifteen-year-olds, ungraded class 100 children, aged three to fifteen, subnormal to gifted 70 ten-year-olds 90 kindergarten children . 100 abnormal and delin-quent children aged five to eighteen 50 six-year-olds all mentally subnormal, epi-leptic, and brain-damaged children in a state hospital C O R R E L A T I O N S .60 (IQ values) .72 ( M A values) .80 ( M A values) .65 (IQ values) .50 (IQ values) .45 ( M A values) .41 (IQ values) .38 boys ( M A values) .26 girls ( M A values) .30 (IQ values) .48 (IQ values) A G E N 116 children in outpatient .75 4 17 psychiatric clinic, aged four .78 5 19 to nine years .69 6 20 .79 7 26 .92 8 20 .60 9 14 Reliability and Validity of the Scales T A B L E 7 (continued) 97 WECHSLER INTELLIGENCE SCALE FOR CHILDREN C O R R E L A T I O N S 50 six-year-olds Rottersman (1950) H a n v i k (1953) El l i s (1953) V .38 (IQ values) P .43 F S .47 25 psychiatric patients, aged F S .18 (rho, I Q values) five to twelve years psychiatric outpatients, aged eight to thirteen (IQ values) V P F S A G E N .77 .67 .70 8 16 .63 .59 .67 9 34 .17 .26 .24 10 20 .45 .46 .50 11 17 .50 .68 .62 12 19 .05 .15 .13 13 17 WECHSLER ADULT INTELLIGENCE SCALE C O R R E L A T I O N S Berdie (1945) 56 older, retarded adolescents .62 (Raw scores) adult mental defectives Gunzburg (1955) V .43 (IQ values) P .73 F S .63 MISCELLANEOUS TESTS C O R R E L A T I O N S Havighurst and Janke (1944) Pechoux, elal. (1947) 70 ten-year-olds 100 abnormal and delin-quent children, agod five to eighteen years Ansbacher (1952) 100 ten-year-olda Harris (1959) Spoerl (1940) (IQ values) .03 Corncll-Coxe .48 Minnesota Paper F o r m -board ( M A values) .25 boys Porteus Mazes .27 girls Porteus Mazes (Raw scores) .34 Tracing McQuarrie Test .23 Tapping of Mechanical .16 Dott ing Abi l i ty .22 (Raw scores) Raven Pro-gressive M a t -rices (1947) 30 mentally retarded chil- Examination, presumably indi-dren, tested during three vidual, not named (IQ values) successive years .56 first year .67 second year .78 third year 98 kindergarten children The Test Manual 275 1. Head present 2. Neck present 3. Neck, two dimen-sions , ' ' 4. Eyes present 5. Eye detail: brow or lashes 6. Eye detail: pupil 7. Eye detail: propor-tion 8. Eye detail: glance 9. Nose present 10. Nose, two dimen-sions 11. Mouth present 12. Lips, two dimen-sions 13. Both nose and lips in two dimensions 14. Both chin and fore-head shown 15. Projection of chin shown; chin clearly differentiated from lower lip 16. Line of jaw indi-cated 17. Bridge of nose 18. Hair I 19. Hair II 20. Hair III 21. Hair IV 22. Ears present 23. Ears present: propor-tion and position Short Scoring Guide * M A N P O I N T S C A L E 24. Fingers present 25. Correct number of fingers shown 26. Detail of fingers cor-rect 27. Opposition of thumb shown 28. Hands present 29. Wrist or ankle shown 30. Arms present 31. Shoulders I 32. Shoulders II 33. Arms at side or en-gaged in activity 34. Elbow joint shown 35. Legs present 36. Hip I (crotch) 37. Hip II 38. Knee joint shown 39. Feet I: any indica-tion 40. Feet II: ptoporlion 41. Feet III: heel 42. Feet IV: perspective 43. Feet V : d< tuil 44. Attachment of arms and legs 1 45. Attachment of arms and legs 11 46. Trunk present 47. Trunk in propor-tion, two dimen-sions 48. Proportion: head I 49. Proportion: head II 50. Proportion: face 51. Proportion: arms I 52. Proportion: arms II 53. Proportion: legs 54. Proportion: limbs in two dimensions 55. Clothing I 56. Clothing II 57. Clothing III 58. Clothing IV 59. Clothing V 60. Profile I 61. Profile II 62. Full face 63. Motor coordination: lines 64. Motor coordination: junctures 65. Superior motor co-ordination 66. Directed lines and form: head outline 67. Directed lines and form: trunk outline 68. Directed lines and form: arms and legs 69: Directed lines and form: facial features 70. "Sketching" tech-nique 71. "Modeling" tech-nique 72. Arm movement 73. Leg movement * For use only after the scoring requirements have been mastered. 294 DRAWINGS AS MEASURES OF I N T E L L E C T U A L MATURITY T A B L E Q g Table for Converting Raw Scores to Standard Scores Drawing of a Man, by Boys It AW SCORE CHRONOLOGICAL AGE IN YEARS RAW SCORE 3* 4* 5 6 7 8 9 10 11 12 13 14 15 0 68 55 53 52 51 50 49 0 1 73 61 56 54 53 52 50 1 2 77 06 59 57 55 51 52 no 51 2 3 82 70 62 60 57 56 54 62 52 3 4 86 74 65 62 59 58 55 51 54 51 4 5 91 78 68 65 62 60 57 56 55 52 5 6 95 83 71 68 64 62 5!) 57 50 53 6 7 100 87 74 70 66 63 60 OH 58 55 50 7 8 104 91 77 73 68 65 02 (10 59 56 51 8 9 109 96 80 75 70 67 63 01 00 57 53 9 10 113 100 83 78 72 00 65 o:i 02 59 54 50 60 10 11 118 104 86 81 75 71 07 01 63 60 56 52 52 11 12 122 109 89 83 77 73 69 00 05 61 57 53 53 12 13 127 113 92 86 79 75 70 07 00 63 58 55 55 13 14 131 117 95 89 81 77 72 on 08 64 60 56 50 14 15 136 122 98 91 84 79 74 70 09 66 61 58 57 15 16 140 126 101 94 86 81 75 72 70 67 63 59 59 16 17 145 130 104 96 88 83 77 73 72 68 64 60 60 17 18 149 134 107 99 90 85 79 75 73 70 65 62 62 18 19 154 139 110 102 92 87 80 70 74 71 67 63 63 19 20 158 143 113 104 94 89 82 78 76 72 68 65 64 20 21 163 147 116 107 97 90 84 79 77 73 70 66 66 21 22 168 152 119 110 99 92 85 81 78 75 71 68 67 22 23 172 15G 122 112 101 94 87 82 80 76 73 69 69 23 24 160 125 115 103 96 89 84 81 78 74 70 70 24 2.1 164 128 117 105 98 90 86 83 80 75 72 72 25 26 169 131 120 108 100 92 87 84 81 77 73 73 26 27 173 134 123 110 102 94 89 85 82 78 75 74 27 211 177 137 125 112 104 95 90 87 83 80 76 76 28 29 140 128 114 106 97 92 88 85 81 78 77 29 30 143 131 116 108 99 93 90 86 82 79 79 30 31 146 133 119 110 100 95 91 87 84 80 80 31 32 149 136 121 112 102 96 92 89 85 82 81 32 33 152 138 123 114 104 98 94 90 87 83 83 33 34 141 125 116 105 99 95 92 88 85 84 34 35 144 127 118 107 101 97 93 89 86 86 35 * These values have been calculated from samples which are not as representative as the OKC samples from 5 through 15 years. They are likely to be a little high for unselected or more adequately representative samples. They are offered as tentative guides for use with pre-The Test Manual T A B L E 32 (continued) 295 RAW SCORE CHRONOLOGICAL AGE IN YEARS 4 5 6 7 8 9 10 11 12 13 14 36 146 130 119 109 102 98 94 91 88 87 37 149 132 121 110 104 99 96 92 89 88 38 134 123 112 105 101 97 94 90 90 39 136 125 114 107 102 98 95 92 91 40 138 127 116 108 103 100 96 93 93 41 141 129 117 110 105 101 98 95 04 .42 143 131 119 111 106 102 99 96 96 43 145 133 121 113 108 104 101 98 97 44 147 135 122 115 109 105 102 99 98 45 149 137 124 116 110 106 103 100 100 46 139 126 118 112 108 105 102 101 47 141 127 119 113 109 106 103 103 48 143 129 121 114 • 111 108 105 104 49 145 131 122 116 112 109 106 105 50 146 133 124 117 113 110 108 107 51 148 134 125 119 115 112 109 108 52 150 136 127 120 116 113 110 110 53 137 128 121 117 115 112 111 54 139 130 123 119 116 113 113 55 141 131 124 120 118 115 114 56 142 133 125 121 119 116 115 57 144 134 127 123 120 118 117 58 146 136 128 124 122 119 118 59 147 137 130 126 123 120 120 60 140 139 131 127 125 122 121 61 140 132 128 126 123 122 62 142 134 130 127 125 124 63 143 135 131 129 126 125 64 145 137 132 130 128 127 65 146 138 134 132 129 128 66 148 139 135 133 130 130 67 150 141 136 134 132 131 68 142 138 136 133 132 69 143 139 137 135 134 70 145 140 139 136 135 71 146 142 140 138 137 72 148 143 141 139 138 73 149 145 143 140 139 296 I DRAWINGS AS MEASURES OF I N T E L L E C T U A L MATURITY TABLE ' . o o Table for Converting Raw Scores to Standard Scores Drawing of a Man, by Girls RAW SCORE CHRONOLOGICAL AGE IN YEARS RAW SCORE 3* 4* 5 1 6 7 8 9 10 11 12 13 14 15 0 66 58 50 50 49 0 1 70 62 53 52 51 50 1 2 74 66 56 55 53 51 2 3 78 70 59 57 55 53 50 3 4 83 74 62 60 58 55 52 4 5 87 78 65 62 60 57 54 50 5 6 91 81 68 65 62 59 55 Al 6 7 96 85 70 67 64 61 57 53 49 7 8 100 89 73 70 66 63 59 55 51 49 8 9 104 92 76 72 69 05 61 5(1 52 51 9 10 108 96 79 75 71 67 62 M 54 52 10 11 113 100 82 77 73 69 61 51) 55 54 50 11 12 117 104 85 80 75 70 00 (11 57 55 51 12 13 121 107 87 82 77 72 67 (U 58 56 53 50 13 It 126 111 90 85 79 74 69 61 60 58 54 51 14 15 130 115 93 87 82 76 71 (1(1 61 59 56 53 50 15 16 134 119 96 90 84 78 73 07 63 61 57 54 51 16 17 139 122 99 93 86 80 74 09 64 62 59 56 53 17 18 143 126 102 95 88 82 76 71 66 64 60 57 55 18 19 147 130 105 98 90 83 78 72 68 65 62 59 56 19 20 152 134 107 100 92 80 80 74 69 66 63 61 58 20 21 156 137 110 103 95 88 81 75 71 68 65 62 60 21 22 160 141 113 105 97 89 83 77 72 70 66 64 61 22 23 165 149 116 108 99 91 85 79 74 71 68 65 63 23 24 169 152 119 110 101 93 86 80 75 72 69 67 65 24 25 173 156 122 113 103 95 88 82 77 74 71' 68 66 25 26 177 160 124 115 105 97 90 83 78 75 72 70 68 26 27 164 127 118 108 99 92 85 80 77 74 72 70 27 28 168 130 120 110 101 93 87 81 78 75 73 71 28 29 171 133 123 112 103 95 88 83 80 77 75 73 29 30 175 136 125 114 105 97 90 84 81 78 76 75 30 31 139 128 116 106 98 91 86 83 80 78 76 31 32 . 142 130 118 108 100 93 87 84 81 79 78 32 33 144 133 121 110 102 95 89 86 83 81 80 33 34 147 135 123 112 104 96 91 87 84 83 81 34 35 t 150 138 125 114 105 98 92 88 86 84 83 35 • These values have been calculated from samples which are not as representative as the age samples from 5 through 15 years. They are likely to be a little high for unselected or more adequately representative samples. They are offered as tentative guides for use with pre-The Test Manual 297 T A B L E 33 (continued) RAW SCORE CHRONOLOGICAL AGE IN YEARS RAW SCORE 3 4 5 6 7 8 9 10 11 12 13 14 15 36 140 127 116 107 100 94 90 87 86 85 36 37 143 129 118 109 101 95 91 89 87 86 37 38 146 131 120 111 103 97 93 91 89 88 38 39 148 134 122 112 104 98 94 92 90 90 39 40 151 136 124 114 106 100 96 94 92 91 40 41 138 125 116 108 101 97 95 94 93 41 42 140 127 118 109 103 99 97 95 95 42 43 142 129 119 111 104 100 98 97 96 43 44 144 131 121 112 106 102 100 98 98 44 45 147 133 123 114 107 103 101 100 100 45 46 149 135 124 116 109 104 103 101- 101 46 47 151 137 126 117 110 106 104 103 103 47 48 139 128 119 112 107 106 104 105 48 49 141 130 120 114 109 107 106 100 49 50 142 131 122 115 110 109 108 108 50 51 144 133 124 117 112 110 109 110 51 52 140 135 125 118 113 112 111 111 52 53 148 137 127 120 115 113 112 113 53 54 150 138 128 121 116 115 114 115 54 55 140 130 123 118 116 115 116 55 56 142 132 124 119 118 117 118 56 57 . 143 .133.. 126 120 119 119 120 57 58 145 135 127 122 121 120 121 58 59 147 136 129 123 122 122 123 59 60 140 138 130 125 124 123 125 60 61 150 140 132 126 125 125 126 61 62 141 133 128 127 126 128 62 63 - 143 135 129 128 128 130 63 64 144 137 131 130 130 131 64 65 146 138 132 131 131 133 65 66 148 140 fl34 133^ 133 135 66 67 149 141 135 134 134 136 67 68 151 143 136 136 136 138 68 69 144 138 138 137 140 69 70 146 139 139 139 141 70 71 147 141 141 141 143 71 72 149 142 142 142 145 72 73 150 144 144 144 146 73 198 #a APPENDIX 8 c 198.b APPENDIX 8 The following example illustrates the calculation for TRE and MRE. The subject's ratio for each wall of the manual map is subtracted from the real ratio and from the mean ratio. The absolute differences are then summed to produce a total error score. Individual room scores can also be calculated. Wall Subject's Ratio Real Ratio True Ratio Error (TRE) Subject's Ratio Mean Ratio Mean Ratio Error (MRE) AE .4.58 4.14 .44 4.58 4.30 .28 AS 2, 60 2.55 .05 2.60 2.52 .08 OM 1.00 .93 .07 1.00 1.25 .25 MF .60 .57 .03 .60 .76 .16 Total Error 8.54 8.94 199. APPENDIX 8 LIST OF DISTANCE RATIOS • Real Average Male Head Female Head Others 1. AE 4.14 4.30 4.26 4.47 4.04 2. AS 2.55 2.52 2.49 2.60 2.48 3. SV 2.43 1.88 2.30 2.45 2.38 4. VW .18 .27 .26 .40 .23 5. xw 1.71 1.93 1.94 2.02 1.68 6. XE 2.73 2.64 2.62 2.70 2.55 7. AB 1.25 1.33 1.29 1.38 1.32 8. AJ 1.09 1.15 1.10 1.21 1.10 9. JL 1.25 1.33 1.27 1.33 1.39 10. LB 1.09 1.15 1.10 1.20 1.10 11. BC .64 •71 .75 .71 .62 12. BF .77 .84 .83 .85 .82 13. FG .64 .68 ,67 .71 .62 14. GC .77 .86 .88 .87 .83 15. CD 1.23 1.36 1.33 1.47 1.25 16. CO 1.18 1.37 1.39 1.38 1.37 17. OP 1.14 1.17 1.13- 1.28 1.05 18. PD 1.32 1.35 1.34 1.39 1.33 19. DE 1.02 .97 1.01 1.00 .84 20. DH .68 .78 .80 .80 .75 21. HI 1.02 .78 .80 .80 .75 22. IE .68 .76 .77 .78 .75 23. HP .64 .60 .62 .60 .58 24. PQ 1.02 1.00 1.02 1.01 .87 25. QI .64 .58 .58 .59 .59 26. JK 1.00 .92 .90 .96 .93 27, JS 1.46 1.38 1.39 1.42 1.37 28. ST 1.00 .95 .91 .99 .98 29. TK 1.46 1.39 1.39 1.43 1.38 30. TM 1.16 1.13 1.17 1.14 1.10 Real Average Male Head Female Head Others 31. MN .55 .75 .71 .81 .74 32. NR .48 .44 .44 .43 .46 33. RV .82 .90 .86 .85 .73 34. UT 1.00 1.02 1.01 1.01 1.03 35. UV •43 .51 .51 .48 .38 36. XQ 1.41 1.30 1.29 1.36 1.22 37. Q0 2.16 2.15 2.16 2.24 1.92 38. OV 1.23 1.27 1.26 1.32 1.18 39. OG .61 .56 .56 .55 .56 40. OM .93 1.25 1.21 1.32 1.18 41. MF .57 .76 .73 .84 .69 PUBLICATIONS Claus, R.U. and D.C. Rothwell, Gasoline Retailing. Vancouver: Tantalus, 1970. Claus, R.J. , W.G. Hardwick and D.C. Rothwell "Cemetaries, and urban land values", Professional Geographer, 1971, 23_, 19-21. Rothwell, D.C. and R.J. Claus, "Cross Merchandising gasoline and car wash faci l i t ies." Automotive Retailer, January 1971. Claus, R.J. , W.G. Hardwick, and D.C. Rothwell. "Car washes and gasoline retailing." Traffic Quarterly April 1971. Rothwell, D.C. "The Vancouver gasoline market." In R. Leigh (Ed.) Contemporary Geography. Vancouver: Tantalus, 1971. Rothwell, D.C. "Four sets of variables in retail location." In R. Leigh (Ed.) Contemporary Geography. Vancouver: Tantalus, 1971. Claus, R.J. , D.C. Rothwell, J . Bottomley. "Measuring the quality of a low order retail site." Economic Geographer, 48, 1972, 168-178. Rothwell, D .C , Bottomley, J . , Forbes, J.D. "Cognitive perception of distance for mental mapping." In Leigh, R. (Ed.) Malaspina  papers: Studies in human and physical geography. Vancouver: Tantalus Research Lts. , 1973. 


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