Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The emergence of class concept formation in preschool children Fryer, Margo 1974

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1974_A8 F79.pdf [ 2.27MB ]
Metadata
JSON: 831-1.0076802.json
JSON-LD: 831-1.0076802-ld.json
RDF/XML (Pretty): 831-1.0076802-rdf.xml
RDF/JSON: 831-1.0076802-rdf.json
Turtle: 831-1.0076802-turtle.txt
N-Triples: 831-1.0076802-rdf-ntriples.txt
Original Record: 831-1.0076802-source.json
Full Text
831-1.0076802-fulltext.txt
Citation
831-1.0076802.ris

Full Text

THE EMERGENCE OF CLASS CONCEPT FORMATION IN PRESCHOOL CHILDREN BY MARGARET L. FRYER B.A., University of B r i t i s h Columbia, 1970  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF  ARTS  i n the Department of Psychology  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1974  In  presenting  an  advanced  the I  Library  further  for  this  thesis  degree shall  agree  scholarly  at the U n i v e r s i t y make  that  purposes  his representatives.  of  this  written  it  for financial  of  September 6, 1974  of  Columbia,  British  gain  Columbia  shall  the requirements  f o r reference copying  by t h e Head  i s understood  Psychology  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  of  for extensive  may be g r a n t e d It  fulfilment  available  permission.  Department  Date  freely  permission  by  thesis  in p a r t i a l  that  of  I agree and this  n o t be a l l o w e d  or  that  study. thesis  o f my D e p a r t m e n t  copying  for  or  publication  without  my  Abstract  The a b i l i t y to c l a s s i f y complex v i s u a l forms was s t u d i e d three, tasks oddity of  four, based task  and f i v e year on two c l a s s e s required  the  old children.  of computer-generated  i d e n t i f i c a t i o n of the  three eight-sided polygons.  assignment  The s e q u e n t i a l  of each sequentially presented  two c l a s s e s .  No feedback was g i v e n .  developmental  change  about  4 1/2  and 5 1/2  a more s e n s i t i v e  Each subject  performed  stimuli.  set  task  the  required  s i n g l e p o l y g o n to one  The r e s u l t s  revealed  of age.  test of class  a  between  formation.  Signature  of  of  marked  The o d d i t y task appeared  concept  two  The  odd form i n a  in classification ability occurring years  in  Supervisor  to  be  TABLE OF CONTENTS  Page 1.  INTRODUCTION  1  2.  METHOD  4  3.  RESULTS  10  4.  DISCUSSION  20  5.  REFERENCES  6.  APPENDICES  . . . . . . . . . . . .  ii  27 28  List  Table I.  Summary o f a n a l y s i s responses,  Table II.  Mean number block)  Table III.  page  of variance  of number  of correct  12  included.  of oddity problems  correctly solved  (per  16  by age and by d i f f i c u l t y l e v e l .  Proportion of correct  Summary o f a n a l y s i s  Mean number  responses and most  frequently  for nine escpecially difficult  responses on the Table V.  Tables  both tasks  chosen pattern Table IV.  of  of variance  oddity  of sequential  o f number  17  problems.  of correct  19  task. problems  correctly solved  21  (per b l o c k ) by age and by d i f f i c u l t y l e v e l . Table V I .  Summary o f a n a l y s i s o f v a r i a n c e responses on the  Table V I I .  sequential  Proportion of correct and by age  (on the  22  task.  responses by v a r i a b i l i t y l e v e l  oddity  i i i  of number of c o r r e c t  task).  24  List  F i g u r e 1.  Prototypes  of Figures  and sample problems at  levels.  iv  page  three  difficulty  6  Acknowledgement  I would l i k e t o e x p r e s s my a p p r e c i a t i o n and g r a t i t u d e t o T a n n i s M. W i l l i a m s f o r t h e a s s i s t a n c e , s u p p o r t , and encouragement g i v e n t o me a t e v e r y p o i n t from t h e p r e p a r a t i o n of t h i s  thesis.  V  to the completion  The a b i l i t y t o c l a s s i f y complex v i s u a l p a t t e r n s was s t u d i e d d e v e l o p m e n t a l l y by A i k e n and W i l l i a m s  (1973).  Using a task i n which subjects  were r e q u i r e d t o i d e n t i f y one odd p a t t e r n i n s e t s o f t h r e e , they found t h a t c h i l d r e n i n Grade 5 and a d u l t s , who d i d n o t d i f f e r , were b o t h more a c c u r a t e t h a n c h i l d r e n i n Grades 1 and 3, who a l s o d i d n o t d i f f e r . e v e r , w h i l e t h e two younger age groups were s t a t i s t i c a l l y l e s s accurate  How-  significantly  t h a n t h e two o l d e r age groups, t h e a b s o l u t e d i f f e r e n c e s  were s m a l l and, t h e youngest group, Grade 1, s t i l l performed c a n t l y above chance l e v e l s .  signifi-  These r e s u l t s i n d i c a t e d t o A i k e n and W i l l i a m s  (1973) t h a t development o f t h e a b i l i t y t o p e r f o r m t h e i r o d d i t y  classi-  f i c a t i o n t a s k o c c u r s sometime p r i o r t o age s i x . I n o r d e r t o a s s e s s d e v e l o p m e n t a l change o f s t r a t e g y i n approach to t h e i r c l a s s i f i c a t i o n t a s k , A i k e n and W i l l i a m s psychophysical  analyses.  (1973) conducted s e v e r a l  They found t h a t s u b j e c t s a t a l l age l e v e l s  tended t o make t h e same e r r o r s and used t h e same p h y s i c a l f e a t u r e s f o r j u d g i n g p a t t e r n c l a s s membership.  The d a t a i n d i c a t e d t h a t t h e two  younger age groups were m e r e l y s l i g h t l y l e s s p r o f i c i e n t a t u s i n g t h e same s t r a t e g i e s used by t h e o l d e r groups. The  s t i m u l i used by A i k e n and W i l l i a m s  (1973) were e i g h t s i d e d  p o l y g o n s g e n e r a t e d from each o f two p r o t o t y p e s .  Psychophysical  analyses  of t h e i r d a t a r e v e a l e d t h a t s u b j e c t s a t a l l age l e v e l s used b o t h t h e g e n e r a l s i m i l a r i t y between p a t t e r n s and t h e i r p r o t o t y p e s  and two p a r t i -  c u l a r p h y s i c a l p a t t e r n f e a t u r e s t o j u d g e p a t t e r n c l a s s membership. o t h e r words, n e i t h e r p r o t o t y p e s t o account f o r performance.  In  n o r d i s t i n c t i v e f e a t u r e s were s u f f i c i e n t  This f i n d i n g c o n t r a d i c t s the view of  2  E.  J.  G i b s o n (1969) who has  features  is  the most  development. (1965)  argued  that  important process  To s u p p o r t  her  on v i s u a l and tactual  argument,  children  distinctive  in perceptual learning  and  she c i t e s work done by  Pick  Pick found that  facilitated transfer  formation of prototypes.  to d i s c r i m i n a t e between standard  formations  learning of  form discrimination.  discovery of distinctive features more than d i d the  the  of  She t r a i n e d  learning kindergarten  forms and s p e c i f i e d  o f them and then made t h r e e t e s t s  for transfer  The e x p e r i m e n t a l group w h i c h was g i v e n new s t a n d a r d s and which had the  same d i m e n s i o n s o f d i f f e r e n c e  s e s s i o n made fewest depended their  errors  i n the  transfer  as  those  task,  prototypes)  that while prototype  tion over time is required, important process  t e c t i o n of what reasonable other  than the  to assume  learning i s the  group  is  important When the  among s t i m u l i , as  task requires  to note task  and the  requires  more  protype the  in discrimination, will  be more  the detection of what  in classification, it  reten-  development.  that distinctive features  hand, when the  common among s t i m u l i , as  it  consideration.  is different  (i.e.,  Thus, Gibson  roles played by d i s t i n c t i v e features  task under  and  l e a r n i n g may p l a y a r o l e when  learning and  i n perceptual development,  perceptual  On the  learning  same s t a n d a r d s  made fewer e r r o r s  distinctive feature  i n perceptual  In discussing the  is  training  indicating that  The group w h i c h had the  but new t r a n s f o r m a t i o n s  (1969) argued  of  learning.  transformations  i n the  w h i c h had b o t h new s t a n d a r d s and new t r a n s f o r m a t i o n s .  totypes  of  trans-  on d i s c o v e r i n g the dimensions by which transformations  standards differed.  the  seems reasonable  deit  useful. Is to  3  assume  that prototypes w i l l  be more u s e f u l .  Pick  crimination matching task;  Aiken and W i l l i a m s  task.  surprising that  It  is  therefore  study indicated that used prototypes.  not  subjects  While the  features  classification  subjects  at  a l l age  than to  task  unanswered  by Aiken and Williams  complex v i s u a l patterns  of age.  were presented task  i s based  assignment subjects  the  ( p r i o r to age s i x )  prototype features. questions was  the a b i l i t y  to  oddity  (1973) was g i v e n to c h i l d r e n 3, forms used i n the  same s u b j e c t s .  oddity  While the  performance it  oddity the that  three. it  provides  classification of  complex v i s u a l forms.  D i r e c t comparison of the  and therefore  performance must r e f l e c t pattern  A sequential c l a s s i f i c a t i o n task using the  task  is possible  study because  i n the  4,  requires  odd form i n any group of  test of the prototype use  accurate  Thus,  A c c o r d i n g l y , the  task was i n c l u d e d i n the present  a more stringent  these  Of primary interest  of each form to one c l a s s or the other,  The s e q u e n t i a l  of  some o f the  (1973).  assumption that accurate  need only discriminate the  they  (1973)  r e l i a n c e on  the use  to answer  In a d d i t i o n , the  s e q u e n t i a l l y to on the  more than  pattern-features  Indeed,  first occurs.  employed by A i k e n and W i l l i a m s  former  l e v e l s on c e r t a i n problems.  s t u d y was designed  and 5 years  of the  the use of d i s t i n c t i v e pattern  the question of when i n development  dis-  used a c l a s s i f i c a t i o n  results  they selected  The present  classify  used a  i n the Aiken and W i l l i a m s  a c c u r a c y was p r i m a r i l y due to  information rather  left  the  to class memberships.  misled subjects  (1973)  used d i s t i n c t i v e features  study d i d use d i s t i n c t i v e features, which were unrelated  (1965)  stimuli is  same p a t t e r n  impossible  class  learning.  classes  4  employed i n the and Brown  o d d i t y task was used s u c c e s s f u l l y w i t h a d u l t s  by  Aiken  (1971).  Method Subjects Subjects attending  for  the study were three,  eight day care  Columbia.  Half  of the  and h a l f were male. had passed  changes. years,  i n metropolitan Vancouver,  last birthday i n order  and therefore  and 5 years, were tested  (S.D. 2.22 months),  7 months  their  to make the  session  One 4 year  jector malfunction.  8 months  three year olds,  four were 4 year  the number of subjects  study due to  their  inability  age l e v e l s , a g e - r e l a t e d  groups age-related  respectively. 8 of the  Five subjects  at  each age  level  were absent olds,  for and of  pro-  inattention  Of these,  five  eliminated from  task was comparable  were not l i k e l y  to be due to  ses-  were  olds and f i v e were 5 year o l d s .  to perform the  results  task.  months),  72 t e s t i n g  were eliminated for  sequential  3  A l l subjects  o l d had to be e l i m i n a t e d because  to the  months  (S.D. 2.27  (one 3 year o l d , two 4 y e a r  Fourteen subjects  or inappropriate responses  age  Twenty potential subjects  for a variety of reasons.  second testing  four  three age groups were  d u r i n g June and J u l y , w i t h a l l but  two 5 y e a r o l d s ) .  cause  4 years,  (S.D. 3.11 months),  sions occurring during the morning. eliminated  least  female  avoid obscuring developmental  The mean c h r o n o l o g i c a l ages of the  8 months  British  twelve c h i l d r e n i n each age group were  Subjects were s e l e c t e d so that at  since their  more homogeneous  centres  four and f i v e year o l d c h i l d r e n  were Be-  the across  subject  5  selection. Stimuli The s t i m u l i were eight-sided polygons computer generated prototypes to form two classes of patterns.  from two  Within each c l a s s , patterns  were generated at three levels of s i m i l a r i t y to their prototypes and thus three l e v e l s of c l a s s i f i c a t i o n d i f f i c u l t y : high.  low, moderate and  Patterns most similar to t h e i r own prototypes are easiest to  d i s t i n g u i s h from patterns of the other class.  The procedure f o r gene-  rating the patterns has been described i n d e t a i l by Aiken and Brown (1971).  The o v e r a l l p r i n c i p l e i s one of producing random changes i n  each of the prototype v e r t i c e s . Oddity task problems consisted of three patterns placed horizont a l l y on a 4" x 6" card.  Examples of problems are shown i n Figure 1.  On each problem, two patterns were from one prototype class and one was from the other c l a s s , but a l l were of the same degree of simil a r i t y to their prototype and thus were a l l of low, moderate, or high difficulty.  There were 36 problems i n t o t a l , selected from the 63  problems used by Aiken and Williams (1973) so as to include 12 at each d i f f i c u l t y l e v e l .  The correct pattern occurred equally often  i n each p o s i t i o n and equally often from each prototype c l a s s .  No  more than two problems of the same d i f f i c u l t y l e v e l occurred i n sequence. The correct pattern occurred i n the same position and was from the same class no more than three times i n a sequence.  The problems were  arranged i n three blocks of 12 t r i a l s each with four problems of each d i f f i c u l t y l e v e l i n each block.  The blocks were presented i n the  6  PROBLEMS  PROTOTYPES  low  Difficulty  4 4 ^ MOOEXATi tuffICUITY  HIGH  F i g u r e 1. P r o t o t y p e s  DlffiCUUY  V w 4  a n d sample problems a t three  [On e a c h p r o b l e m t h e s u b j e c t ' s or different were never  (e.g.,  Patterns  task  difficulty  i s t o choose t h epattern  3 , 3 , a n d2 , r e s p e c t i v e l y ) .  shown t h e prototypes.]  levels. that  i s odd  Subjects  7  three orders  of a balanced Latin Square.  In each age group,  and two females were a s s i g n e d  to each b l o c k order.  the  again at  f i r s t b l o c k was presented  of  improvement over time.  15  ( a p p r o x i m a t e l y 25%) o f t h e i r  less got  the  each o f t h e s e 15 p r o b l e m s c o r r e c t .  parable proportion of difficult  in  the present Patterns  (1973)  problems,  for the  As i n the oddity task, 12 p r o b l e m s e a c h .  level  the  oddity task, ft  tasks were eight  Each child  females  patterns.  In the  from  sequential  on a transparent  task,  slide.  in 3 blocks  two p r o b l e m s o f the  same  difficulty  W i t h i n any b l o c k , v a r i a t i o n s on each  i n the  i n a row.  three orders  f i r s t b l o c k was repeated  dif-  after  pro-  As of  the  in a  third,  trials.  received the  oddity task.  first.  included  Each block contained four problems from each  the blocks were presented  making a t o t a l o f 48  task  were  found  sided polygons  t h e r e were 36 p r o b l e m s a r r a n g e d  balanced L a t i n Square and the  the  levels  15 p r o b l e m s  o c c u r r e d e q u a l l y but no more than t h r e e times  half  that  to maintain a com-  9 of the  i n the oddity task.  l e v e l and no more than  and the  measure  difficult;  one or more age  to be e s p e c i a l l y d i f f i c u l t  sequential  occurred i n sequence.  totype  a  (1973) had found  In order  each problem consisted of a single pattern  ficulty  task as  s t u d y , w i t h t h r e e o c c u r r i n g i n each b l o c k o f 12  the stimulus samples used  of  at  males  case,  63 problems were e s p e c i a l l y  than a chance proportion of subjects  by Aiken and Williams  In each  end of the  A i k e n and W i l l i a m s  two  same b l o c k o r d e r  Task presentation  and half  the males at  The tasks were presented  for both the  sequential  order was counterbalanced, each age l e v e l r e c e i v i n g  i n separate sessions  for  with  each each  8  child.  Time between sessions  a mean o f 6.10  ranged from three  to eight  days,  with  days.  Procedure All  children were tested  from the rest  of the  Oddity Task. given the  day care  by the  same woman i n a q u i e t room away  centre.  The c h i l d was seated  following  opposite  these cards.  the  shapes  card, that  Two o f t h e s e shapes  belongs  to another,  There are  shapes  different  I want you to point  to  the one that does not Now, l e t ' s showed the  go together the  family.  the  the  squares)  same,  some c a r d s  one that does not The second, similar but not one d i f f e r e n t  one  each of  You will  see  go w i t h t h e go w i t h t h e  a  others. others,  card —  two squares  (points  (the  experimenter  and a c i r c l e ) . That's  P o i n t to  right.  These  (Experimenter points  to c i r c l e ) i s d i f f e r e n t .  to  the  two  two  This is  the  belong. t h i r d , and fourth t r a i n i n g problems consisted of  i d e n t i c a l shapes,  shape,  sisted of three  shapes.  for practice;  they belong together.  and t h i s  the  that does not  one that does not belong w i t h the others. are  on  When I show you  and one does not  one shape  shapes  belong.  look at  child  three  belong to one f a m i l y and one  I want you to look very c a r e f u l l y at two o f the  and  instructions.  I am g o i n g t o show y o u some c a r d s . of  the experimenter  s u c h as a square  such as a c i r c l e .  polygons s i m i l a r to the  the c h i l d had responded  to each of the  The f i f t h  two  and a rectangle,  and  training problem con-  experimental stimuli. training problems,  the  After experimenter  9  verbalized  the s o l u t i o n w h i l e p o i n t i n g to  Sequential Task. onto a screen,  The sequential  placed on the  About 6" d i r e c t l y i n f r o n t wooden panel.  about  gave the  shapes.  first  The c i r c l e on the  following  the  l e f t was r e d ;  who o p e r a t e d  red one.  the blue one. either  like  There are this,  look at  Now y o u p o i n t to  class)  it.  (second slide)  some new o n e s .  flat  one on the  i s what  this,  to  shows  it.  other  to this  (first  (Then, two examples o f f i r s t  slide,  see  family,  shown.)  children on t r a i n i n g t r i a l s were corrected. t h i s one you should p o i n t to  the  Each experimental session lasted  The experimenter  the  also  says,  M i s t a k e s made  red c i r c l e , because  one where you pointed to  O.K.  also  When each s l i d e i s on e x p e r i m e n t e r  " W h i c h c i r c l e do y o u t h i n k y o u s h o u l d p o i n t to now?"  the other  look  slide).  low v a r i a b i l i t y , are  looks like  look  circle,  shown; then two examples o f second f a m i l y ,  for  what  shapes  shapes you w i l l one  point  This is  shows second  the  this  kinds  I want you to  you point  A l l the or like  two d i f f e r e n t  low v a r i a b i l i t y , are  "No,  right  remote  (experimenter  (experimenter  one that l o o k s l i k e  t h i s one  the  child.  black  the projector w i t h a  Now y o u p o i n t  This  low v a r i a b i l i t y example of other I f you see  of the  instructions:  one k i n d of shape l o o k s l i k e .  like.  back-projected  diameter were n a i l e d  I f you see one that l o o k s l i k e  c i r c l e here,  shapes.  i n front  s l i d e , low v a r i a b i l i t y example of one c l a s s )  to this  Let's  s t i m u l i were  two feet  I am g o i n g t o show y o u some s h a p e s . of  appropriate  o f the c h i l d was a 6" x 4" x 1/2"  The experimenter,  control,  task  Two p l a s t i c c i r c l e s 1 1/4"  on the black panel. was b l u e .  table  the  by  says, this  shape  red c i r c l e . "  from 10-20 minutes  depending  on  10  the  speed w i t h which the  c h i l d made  choices.  Results Two s e t s o f a n a l y s e s from only the all  first  four blocks  each case  three  three  of variance were performed, blocks  (Times 1-4,  (Times 1-3)  i n c l u d i n g the  analyses were conducted:  tasks,  one f o r o n l y the o d d i t y data  data.  Only the results  (Times 1-4)  will  effects the  be d i s c u s s e d because  the data  substantial.  t h a t o c c u r r e d i n t h e T i m e 1-4  increased numbers  of task items.  from only the  first  three  and one on the  repeated  one on the data  of the data  the  from  for  In  both  sequential  between  The strengthening  of  blocks  the  two  significant  can be attributed  The r e s u l t s  blocks  data  from a l l four  differences  analyses  data  first block).  and one f o r o n l y the  of the analyses  sets of analyses were not  one on the  to  of the analyses  (Times 1-3)  are  given  of in  the Appendix. The r e s u l t s with the data  of the  from the  three  types  of analyses  are presented  combined analyses being discussed  in  order,  first.  Combined Analyses The p r o b a b i l i t y of b e i n g c o r r e c t by chance on any one t r i a l .33 f o r the  oddity task  make the data sponses  from the  and  .5 f o r the  two tasks  per block per subject  per block for that  task.  comparable,  task.  In order  was d i v i d e d by the  (oddity first,  by Sex by Age (3, 4,  5, years)  to  the number of c o r r e c t chance number  The r e s u l t i n g values were analyzed i n  analysis of variance of Order vice-versa)  sequential  was  sequential  second,  by Task (oddity,  re-  correct an or  sequential)  11  by V a r i a b i l i t y Level 25-36, of are  37-48).  (low, moderate,  high)  by Time ( t r i a l s  Conservative degrees of freedom were used  significance involving repeated measures. summarized i n Table  was s i g n i f i c a n t  than both 4 and 3 year  (F£  olds  tests  of the  analysis  24  6 . 6 1 , p_ < . 0 1 ) ,  =  were  with  significantly  (p_ < . 0 1 i n b o t h c a s e s ) ,  who  differ.  The s i g n i f i c a n t Task main effect greater o v e r a l l accuracy on the  (F  t i o n w i t h the  = 2 5 . 6 0 , p_ < . 0 1 )  analysis revealed  i n performance on the  on the  sequential  revealed  that on the  accurate  than both 4 year  who d i d n o t d i f f e r . levels,  simple effects  the  5 year  the  oddity than on the  olds  (F^  ^  5 year  conjunc-  5.54, £ <  (F£  24  H - 2 4 , p_ <  =  sequential  olds  were examined at  revealed  task  the  differences  cases), various  only  for on  task. was  significant  (F..  „ =  i n a Newman K e u l s  i n t e r a c t i o n was a l s o  69.28,  iz  levels being differentiated  (p_ < . 0 1 f o r a l l c o m p a r i s o n s  The Age by V a r i a b i l i t y  dif-  further  (p_ < . 0 1 i n b o t h  1,  p_ < . 0 1 ) w i t h a l l d i f f i c u l t y  .05).  .01)  ~ 3 1 . 7 1 , p_ < . 0 1 ) , w h o w e r e m o r e a c c u r a t e  The v a r i a b i l i t y main e f f e c t  direction  =  in  olds were s i g n i f i c a n t l y more  differences  analyses  ^  task.  A Newman K e u l s a n a l y s i s  olds and 3 year  When t a s k  (F^  reflected  t h e r e were s i g n i f i c a n t age  (F < 1 ) .  oddity task,  age  that  oddity task  task  sequential  must be i n t e r p r e t e d  s i g n i f i c a n t Age by Task i n t e r a c t i o n  A simple effects ferences  ^  1  oddity than on the  Both the Age and Task main effects  but not  for a l l  The r e s u l t s  a Newman K e u l s a n a l y s i s r e v e a l i n g t h a t 5 - y e a r - o l d s  did not  13-24,  1.  The Age main e f f e c t  more accurate  1-12,  i n the  expected  analysis).  significant  (F„  =  12  Table I.  Summary o f a n a l y s i s on b o t h o d d i t y  Source  of variance  and sequential  of number  of correct  tasks.  df  ms  1 1 2 1 2 2 2 24  .17 5.94 11.95 .02 2.13 1.96 1.81 1.81  <  D (Task) AD BD CD ABD ACD BCD ABCD D x Ss  1 1 1 2 1 2 2 2 24  11.48 .26 .40 2.48 .32 2.05 .18 .88 .45  25.60** 1 1 5.54* < 1 4.57 < 1 1.96  F (variability) AF BF CF ABF ACF BCF ABCF F x Ss  2 2 2 4 2 4 4 4 48  20.55 .15 .45 1.26 .74 .34 .91 .03 .30  G (time) AG BG CG ABG ACG BCG ABCG G x Ss  3 3 3 6 3 6 6 6 72  .07 .01 .25 .38 .90 .42 .40 .29 .37  Between  subjects  A (order) B (sex) C (age) AB AC BC ABC Ss w i t h g r p s . Within  F  1 3.28 6.61** < 1 1.18 1.08 1.00  subjects < <  69.28** 1 1.52 4.25* 2.50 1.16 3.08 < 1  <  < < <  1 1 1 1.01 2.43 1.13 1.07 < 1  responses  13  Table I  (Cont'd)  df  ms  DF ADF BDF CDF ABDF ACDF BCDF ABCDF DF x Ss  2 2 2 4 2 4 4 4 48  7.20 .46 ...17 .74 .55 .14 .41 .27 .31  DG ADG BDG CDG ABDG ACDG BCDG ABCDG DG x S s  3 3 3 6 3 6 6 6 72  .61 .58 .19 .16 .45 .28 .06 .05 .33  FG AFG BFG CFG ABFG ACFG BCFG ABCFG FG x Ss  6 6 6 12 6 12 12 12 144  .21 .13 .37 .36 .12 .23 .30 .30 .37  < <  DFG ADFG BDFG CDFG ABDFG ACDFG BCDFG ABCDFG DFG x Ss  6 6 6 12 6 12 12 12 144  .14 .34 .13 .28 .30 .31 .25 .14 .27  <  Note:  F 23.53* 1.51 < 1. 2.45 1.79 < 1 1.34 < 1  < < < < <  < < < < <  <  1.83 1.76 1 1 1.35 1 1 1 1 1 1.01 1 1 1 1 1 1 1.25 1 1.01 1.10 1.14 .90 .51  Conservative degrees of freedom were used for tests of a l l effects involving repeated measures. * i n d i c a t e s p_ < . 0 5 ; ** i n d i c a t e s p < . 0 1 .  14  4 . 2 5 , p_ < . 0 5 ) . differences (F2  24  Keuls analyses problems,  olds  2  48  =  3 year  0  '  9  » £•  0  olds, F  <  •  that  >  f o r  there were  y  4  e  a  r  o  l  d  s  »  levels 48  F 2  for  5 and 4 year  age  levels performance  and moderate  o l d s and £ < .05 f o r on moderate  than on h i g h v a r i a b i l i t y items for  3 year  olds).  significantly  Thus, at  1  6  A t a l l age  low v a r i a b i l i t y items was s i g n i f i c a n t l y greater ( £ < .01 f o r a l l age groups)  =  than both 4  3  0  (for ^2  48  =  ° . 4 6 , P_  <  F2  .01).  performance  differentiated On the  f o r  levels, accuracy  (£ <  .01  Furthermore,  5 and 4 year  on  high  at  a l l  accurate  o l d s and £ <  analysis revealing that  (F^  24  .05  were  i n the  sequential  ^g = 85.80, £ < .01; for Newman K e u l s a n a l y s e s  directions  sequential  task, the  significantly  ( £ < .01 f o r a l l  accuracy was g r e a t e r  tasks  indicated that on  on a l l v a r i a b i l i t y l e v e l s was  expected  task,  the  23.53,  =  performance  v a r i a b i l i t y l e v e l s d i f f e r e d s i g n i f i c a n t l y on both  oddity task,  oddity task,  olds,  0 1  items was s i g n i f i c a n t l y more  ( £ < .01 for  ac-  differentiated.  pattern  the  in  5 year  than on both  olds).  effects  a l l age l e v e l s , a l l v a r i a b i l i t y l e v e l s  < .01), with a simple effects  across  Simple  v a r i a b i l i t y items  3 year  and  » P_ < - ;  The Task by V a r i a b i l i t y i n t e r a c t i o n was s i g n i f i c a n t £  Newman  variability  (for -  age  moderate  significant differences  a l l age  ^g = 10.66, £ < .01).  2  and  who d i d n o t d i f f e r .  v a r i a b i l i t y at 0 1  there were  on high d i f f i c u l t y problems.  (p_ < . 0 1 i n b o t h c a s e s ) ,  also revealed  5  not  H - 2 4 , £ < .01)  =  olds were s i g n i f i c a n t l y more accurate  curacy due to pattern F  but  24  that  i n d i c a t e d that on both low and moderate  5 year  analyses  analysis revealed  i n accuracy on low (F^  6.05, £ < .01)  =  3 year  A simple effects  on low than on  comparisons). higher  15  v a r i a b i l i t y problems  (p < .01)  high d i f f i c u l t y problems was examined at than on the  and a l s o greater  (p_< . 0 5 ) .  When performance  on the  each v a r i a b i l i t y l e v e l , greater accuracy  sequential  task was found f o r  and moderate v a r i a b i l i t y problems task  on moderate than  (F^  low (F^  ^  differences  on the high v a r i a b i l i t y  None of the  effects  ^  two  on the  oh tasks oddity  = 6 6 . 6 6 , ja <  = 6 . 0 2 , p_ < . 0 5 ) , w i t h  .01)  no  problems.  involving Order,  Sex, or Time were  significant.  Oddity Task Analyses The mean number  of oddity problems  (per block) c o r r e c t l y solved  age and by d i f f i c u l t y l e v e l i s shown i n Table 2. 5 year rate  o l d s was s i g n i f i c a n t l y above chance  o n l o w (p < .01)  (p_ < . 0 5 ) v a r i a b i l i t y p r o b l e m s b u t n o t  Four year problems chance  at  olds performed (p_ < . 0 5 )  above  chance  The performance  by  of  and on  mode-  on high v a r i a b i l i t y problems.  l e v e l s on o n l y low v a r i a b i l i t y  and the performance  of 3 year  olds did not  exceed  any v a r i a b i l i t y l e v e l .  The proportion of subjects each of the nine problems and W i l l i a m s (1973)  study,  i n each age group  and the most popular p a t t e r n data  for  A i k e n and W i l l i a m s (1973)  study.  ficult  were apparently  subjects  c h i l d r e n , who tended  to make the  Number o f c o r r e c t  answering  found to be e s p e c i a l l y d i f f i c u l t i n the  given i n Table 3 along w i t h the  for older  correctly  the  Problems  o l d e r age groups  that were  in  the dif-  pre-school  choices.  responses was examined i n an  of variance of Order by Sex by Age by V a r i a b i l i t y by Time. degrees of freedom were used  are  especially  also difficult for  same w r o n g  oddity task  choice,  Aiken  analysis  Conservative  for a l l tests of significance involving  16  Table II.  Mean number block)  of oddity problems  by age  and by d i f f i c u l t y  Variability  correctly  solved  (per  level.  Level  Age Low  Moderate  High  Overall  3 years  2.08  1.72  1.25  1.69  4 years  2.31*  1.78  1.44  1.84  5 years  3.31**  2.22*  1.69  2.41  2.57  1.91  X  Note:  In relation per  block,  to  the  chance  * = _p_ < - 0 5 ;  1.46  probability **  = p_ <  .01.  of 1.33  correct  Table  III.  Proportion of correct  choices and most  nine especially difficult groups  are  chosen pattern  (Data for grades  from Aiken and W i l l i a m s ,  Proportion Problem Number  problems.  frequently  1,  3,  5,  and  4  yrs  5  yrs  adult  1973.)  Correct  Most Popular  Age 3; y r s  for  Choice  Age Gr  1  Gr  3  Gr  5  Adult  3  yrs  4  yrs  5  yrs  Gr  1  Gr  3  Gr  5  Adult  Low Difficulty 1  .25  .50  .58  .44  .48 '  .31  .19*  3  1  1  2  .25  .25  .50  .22*  .25  .31  .36  3  3  l,3  3  .17*  .25  .25  .15*  .02*  .11*  .38  2  3  4  .25  .25  .42  .39  .17*  .22*  .24  2  5  .42  .17*  .17*  .10*  .08*  .18*  .17*  6  .17*  .25  .17*  .15*  .10*  .31  7  .25  .17*  .33  .15*  .04*  8  .17*  .08*  .17*  .05*  9  .17*  .33  .50  .39  1  1  3  3  3  3  3  3  3  3  3  3  1  1  3  2  2  2  2  2  2  2  2  2  2  2  .21*  2  1  1  1  1  1  1  .07*  .05*  3  1  1  3  3  3  3  .06*  .13*  .24  2  2  2  2  2  2  3  .23  .20*  .26  2  2  l,2  2  2  2  2  Moderate Difficulty a  High Difficulty  a  i—  Note:  * indicates cl  c h o i c e made by s i g n i f i c a n t l y fewer  two p a t t e r n s  chosen by e q u a l number  of  than chance number of subjects  subjects.  (p_ <  .05).  18  r e p e a t e d measures. 4,  The r e s u l t s o f t h e a n a l y s i s a r e summarized i n T a b l e  and s e r v e t o c o n f i r m t h e r e s u l t s r e p o r t e d above f o r t h e combined  analysis. ( F ^ 24 = 1 0 . 5 , p_ < . 0 1 ) ,  The Age main e f f e c t was s i g n i f i c a n t  w i t h a Newman K e u l s a n a l y s i s i n d i c a t i n g t h a t 5 year o l d s were s i g n i f i c a n t l y more a c c u r a t e than both 4 y e a r o l d s (p_ < . 0 1 ) and 3 y e a r o l d s (p_ < . 0 1 ) , who d i d n o t d i f f e r . The V a r i a b i l i t y main e f f e c t was a l s o s i g n i f i c a n t  = 69.55,  (F^ ^  p_ < . 0 1 ) w i t h a l l d i f f i c u l t y l e v e l s s i g n i f i c a n t l y d i f f e r e n t i a t e d  (p_ < . 0 1 i n a l l comparisons).  one another i n t h e expected d i r e c t i o n  The o n l y s i g n i f i c a n t i n t e r a c t i o n was Age by V a r i a b i l i t y 3 . 7 8 , p_ < . 0 5 ) .  from  24  (F£  =  A s i m p l e e f f e c t s a n a l y s i s r e v e a l e d t h a t t h e age groups  d i f f e r e d on low (F2  24  1 7 . 7 2 , p_ < . 0 1 ) and moderate (F2  =  p_ < . 0 5 ) b u t n o t on h i g h d i f f i c u l t y problems.  24  =  ^.12,  Newman K e u l s a n a l y s e s 5 year olds  r e v e a l e d t h a t i n b o t h low and moderate d i f f i c u l t y problems,  were s i g n i f i c a n t l y more a c c u r a t e than both 4 and 3 y e a r o l d s (p_ < . 0 1 i n a l l c a s e s ) , who d i d n o t d i f f e r .  When t h e e f f e c t s of v a r i a b i l i t y  were examined a t each age l e v e l , simple e f f e c t s a n a l y s e s r e v e a l e d t h a t v a r i a b i l i t y a f f e c t e d performance F  2  48  =  4  7  '  8  3  >  P.  <  f o r 3 y e a r o l d s , F2  * 5 01  f  o  r  4  y  e  = 10.98,  ( f o r 5 year o l d s ,  a t a l l age l e v e l s a  r  °l  d  s  >  F  2  p_ < . 0 1 ) .  48  =  1 8  «  3 1  » £  <  ' '> 01  a  n  d  Newman K e u l s a n a l y s e s  i n d i c a t e d t h a t t h e a c c u r a c y o f b o t h t h e 5 and 4 y e a r age groups was s i g n i f i c a n t l y g r e a t e r on low than on b o t h moderate and h i g h v a r i a b i l i t y problems (p_ < . 0 1 f o r a l l comparisons).  The 3 y e a r age group was more  a c c u r a t e on b o t h low and moderate than on h i g h d i f f i c u l t y  problems  19  Table IV.  Summary o f a n a l y s i s o f v a r i a n c e o f number o f responses  Source  on the oddity  task.  df  ms  1 1 2 1 2 2 2 24  .01 8.33 22.40 .15 3.72 .92 1.09 2.12  1 3.93 10.57** < 1 1.76 < 1 < 1  F (variability) AF BF CF ABF ACF BCF ABCF F x Ss  2 2 2 4 2 4 4 4 48  45.65 .56 .13 2.48 2.24 .77 1.58 .30 .66  69.56** 1 1 3.78* 3.41 1.18 2.40 < 1  G (time) AG BG CG ABG ACG BCG ABCG G x Ss  3 3 3 6 3 6 6 6 72  .84 .52 .38 .50 1.50 1.06 .62 .24 .81  6 6 6 12 6 12 12 12 144  .49 .56 .80 .82 .40 .67 .72 .44 .80  Between  F  subjects  A (order) B (task) C (age) AB AC BC ABC Ss w i t h i n Within  correct  groups  <  subjects  FG AFG BFG CFG ABFG ACFG BCFG ABCFG FG x Ss Note:  < <  1.05 1 1 1 1.86 1.32 < 1 < 1 < < <  < < < < < < <  1 1 1 1.02 1 1 1 1  Conservative degrees of freedom were used for tests of a l l effects involving repeated measures. * i n d i c a t e s p_ < . 0 5 ; ** i n d i c a t e s p < . 0 1 .  20  (p_ < . 0 1 i n b o t h  cases).  Sequential Task Analyses The mean number ficulty  level is  of sequential  shown i n Table 5.  was s i g n i f i c a n t l y above but not year  the  c h a n c e o n l o w (p_ < . 0 5 )  age groups  d i d not  The number  of correct  of the  exceed chance  at  sequential  5 year  and on moderate  The performance  oddity task  of the  of the  analysis,  above for  (p_ <  4 and  c l a s s i f i c a t i o n s was  .05)  3  examined  the  the  results  combined  summarized i n T a b l e 6. serve  to confirm the  As with  findings  analysis. was s i g n i f i c a n t  (F  „, = -L ,  A Newman K e u l s a n a l y s i s  and moderate  olds  any v a r i a b i l i t y l e v e l .  task  analysis are  Only the V a r i a b i l i t y main effect p_ < . 0 1 ) .  dif-  of variance of Order by Sex by Age by V a r i a b i l i t y by  The r e s u l t s  described  s o l v e d by age and by  The performance  on high v a r i a b i l i t y items.  in an analysis Time.  problems  revealed  that performance  v a r i a b i l i t y problems was s i g n i f i c a n t l y b e t t e r  mance on h i g h v a r i a b i l i t y problems  (p_ < . 0 1 f o r b o t h  8.40,  i. H  on both  than  low  perfor-  comparisons).  Discussion The results the  of the  study provide convincing evidence  a b i l i t y to c l a s s i f y complex v i s u a l p a t t e r n s does  prior  to s i x years  takes  place between  for  present  this  of age.  the ages of about  developmental  effects,  the  formance  relative  A marked developmental  age-related  shift  levels.  change  and 5 1/2  can be found i n the  interactions  to chance  4 1/2  and the  indeed in  years.  develop accuracy Evidence  s i g n i f i c a n t age  data  that  main  concerned with  The performance  of the  3 year  perage  21  Table V.  Mean number  of sequential  problems  (per block)  correctly  s o l v e d by age and by d i f f i c u l t y l e v e l (maximum p o s s i b l e  =  four).  Variability  Level  Age  Low  Moderate  High  Overall  3  2.52  2.21  2.23  2.32  4  2.52  2.44  2.23  2.40  5  2.96*  3.04*  2.21  2.74  X  2.67  2.56  2.22  Note:  In r e l a t i o n to p e r b l o c k , **  the  chance p r o b a b i l i t y of 2.0  indicates  p < .01;  * indicates  correct p <  .05.  Table V I .  Summary o f a n a l y s i s o f v a r i a n c e o f number o f responses  Source  on the  sequential  task.  df.  ms  1 1 2 1 2 2 2 24  1.69 6.50 7.09 1.02 8.31 6.47 8.31 4.24  F (variability) AF BF CF ABF ACF BCF ABCF F x Ss  2 2 2 4 2 4 4 4 48  7.78 1.17 2.20 2.44 .09 .17 1.73 .51 .93  G (time) AG BG CG ABG ACG BCG ABCG G x Ss  3 3 3 6 3 6 6 6 72  .82 1.19 .90 1.02 2.01 .42 .42 .81 .99  <  <  1 1.21 1 1.03 2.03 1 1 1  FG AFG BFG CFG ABFG ACFG BCFG ABCFG FG x Ss  6 6 6 12 612 12 12 144  .26 .61 .29 .69 .80 .67 .55 .74 .77  <  1  Between  F  subjects  A (order) B (sex) C (age) AB AC BC ABC S_s w i t h i n Within  correct  groups  <  <  1 1.53 1.67 1 1.96 1.53 1.96  subjects  Note:  < < <  <  < <  8.40** 1.27 2.37 2.64 1 1 1.87 1  < 1 <  < < < <  1 1 1.03 1 1 1  Conservative degrees of freedom were used for tests of a l l effects involving repeated measures. * indicates p < .05; ** i n d i c a t e s p < . 0 1 .  23  group was n o t above chance on e i t h e r  task,  above chance on only low v a r i a b i l i t y items  the 4 year age group i n the oddity task,  performed and  the  f i v e year age group performed s i g n i f i c a n t l y above chance l e v e l s on low and moderate v a r i a b i l i t y items on both tasks.  both  This developmental  change i n c l a s s i f i c a t i o n a b i l i t y can also be c l e a r l y seen i n Table  7,  which gives the proportion of correct responses  at  each v a r i a b i l i t y l e v e l achieved by 3, 4,  on the  oddity task  and 5 year olds i n the  present  study along with the proportion of correct responses  achieved by  and  (1973)  6,  8,  and 10 year o l d s i n the A i k e n and W i l l i a m s  The s e q u e n t i a l task was i n c l u d e d i n the present provides a more s t r i n g e n t prototypes  test  sees the prototypes  themselves  task,  it  and the use  the oddity task.  in neither  study.  study because  of c l a s s i f i c a t i o n s k i l l s  i n c l a s s i f i c a t i o n than does  adults  The  but accurate  of  subject performance  i n the o d d i t y task might be p o s s i b l e merely through d i s c r i m i n a t i o n of the odd pattern learning.  i n each set  In the sequential task,  tern merely on the basis class.  of three,  rather  the  than through  prototype  subject must c l a s s i f y each  of his past experience with instances  pat-  of  each  That performance r e l a t i v e to chance l e v e l s was comparable on  two tasks  i n terms of the s k i l l s being tapped l i e s i n the absence  significant  effects  involving order of task presentation.  learning occurred d i f f e r e n t i a l l y i n the be l i k e l y  to vary with order of task presentation,  on which the surprising  two t a s k s ,  If  c l a s s e s w e r e b a s e d w e r e the same i n b o t h c a s e s .  that  the oddity task.  prototype  it  i s more s u r p r i s i n g that  would  prototypes It  the s e q u e n t i a l task was i n general more d i f f i c u l t Indeed,  of  then performance since the  the  5 year olds  is  not than  were  24  Table V I I .  Proportion of correct by v a r i a b i l i t y  responses on the oddity  l e v e l and by  task  age.  Variability Age  Low  3 yr  .5104  .4323  .3177  4 yr  .5729  .4427  .3229  5 yr  .8177  .5729  .4167  6 yr  .8240  .5643  .4476  8 yr  .8264  .5644  .4541  10 y r  .8960  .6041  .4930  .9035  .6398  .5038  adult  Note:  Moderate  Data f o r ages 6, and W i l l i a m s , sixty-three  8,  10 y r s and a d u l t s  1973.  are  from  These proportions are based  problems.  Proportions from the present forty-eight  High  problems.  study are based  on  Aiken on  25  able  to perform at  requires  pattern  above chance l e v e l s on the  comparisons from memory.  vide strong evidence that  was expected,  problems  (e.g.,  While i t  the results  tasks  the results  involving  suggest  prototype  that  trials progressed,  relating prototype  similar  the  study did not  ment.  Further evidence that subjects  place,  that  tended  to  they d i d indeed use  the  they tended  study were  to make the  judgstrategies  comparably  problems, and  same w r o n g c h o i c e s  clearly indicate that mastery  complex v i s u a l patterns  study used  in their  so  Williams  same b a s e s o f  i n the present exists  analyses  to c l a s s i f i c a t i o n  i n the nine p a r t i c u l a r l y d i f f i c u l t  These results classify  that  those used by older subjects  poor performance that  and  6 and 8 year o l d s i n the A i k e n and  study suggests  fact  measures  f i n d i n g that 5 year olds i n the present  (1973)  to  effects  the  however,  include psychophysical  and d i s t i n c t i v e feature  i n accuracy to the  similar  might  another.  Although the present  accuracy,  of  learning took  that the very young subjects  c a n c e l one  more  learning  is also likely,  improvement i n c l a s s i f i c a t i o n a b i l i t y and fatigue  sex  sample  1973) performance  It  the  the  time i s  occurred relatively early in both tasks. t i r e d as  pro-  assess  is possible that with a larger  including whatever  which  involving order and  as used by A i k e n and W i l l i a m s ,  of the classes,  task,  processes.  of significant effects  improve s i g n i f i c a n t l y over time, nature  cognitive  of significant effects  the absence  thought-provoking.  In summary,  the o d d i t y and sequential  same u n d e r l y i n g p e r c e p t u a l a n d / o r While the absence  sequential  (see  Table  of the a b i l i t y  o c c u r s between 4 1/2  and 5 1/2  the 7). to years  26  of  The q u e s t i o n to be answered now i s why 3 and 4 year o l d s  age.  unable that  to perform the  successfully.  t h i s change i n c l a s s i f i c a t i o n  from the preoperatory but  task  to  the  ability  concrete  It  is  tempting to  is related  operatory  to  stage of  vanced  who are more a c c u r a t e  i n terms  of Piaget's  on the  classification  developmental  stages.  task  hypothesize  advancement development,  c o n f i r m a t i o n w o u l d h a v e to come i n a s t u d y d e m o n s t r a t i n g  subjects  are  that  are more  ad-  27  References  Aiken,  L . S. and Brown, D . R.  perception 1971, Aiken,  9,  Gibson,  formation.  E. J .  York:  structure.  Perception  T. M . A developmental  Developmental  Improvement  study  Psychology,  Principles of perceptual  Appleton-Century-Crofts,  Anne D . Journal  class  of the  and Psychophysics,  279-283.  L . S. and Williams,  concept  Pick,  of pattern  A feature utilization analysis  learning  of  schematic  1973, 8_, 162-167.  and development.  New  1969.  of visual and tactual  of Experimental Psychology,  form  discrimination.  1965, J59_, 331-339.  28 APPENDIX I :  RawData  , Number o f C o r r e c t c h o i c e s (out o f a p o s s i b l e 4) Oddity Task  Subject Number  01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  36  Task Order (l=odd. 1st) 2=seq. 1st) 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2  Sex  M M M F F F M M M F F F M M M F F F M M M F F F M M M F F F ' M M M F F F  Age (in years)  Sequential  Task  Low  Mod  High  Low  Mod  High  Time 1234  Time 1234  Time 1234  Time 1234  Time 1234  Time 1234  4  4444  4  3104  2111 3322 1222 2212 2113 2112 2311 2211 1221 1223 1121 2322 2113 2222 2212 0231 2011 2122 3234 2201 3331 2221 2021 2112 3243 2233 2213 2222 2231 3213 4321 2232 2224 2213 1122 4323  1113 2232 2122 2212 1210 1010 3101 1010 1302 2112 1012 2100 2222 0220 0111 2101 2320 0211 1130 0220 2212 2131 1222 0110 3232 1222 2211 1231 1201 3113 2221 1321 2112 1122 3121 1202  1233 4444 2204 3122 3221 2312 2323 4241 2112 2344 2123 4444  4 4 4 4  2122 3344 2130 3213 3243 2130 1423 3200 3323 2222 2010 2203 4410 2213 1123 2222 2211 1322  2231 4442 1132 1012 3112 0112 0203 3442 3433 0242 3111 4444 4434 2242 2131 0420 2132 4122 4234 2222 3244 1332 3242 2123  4444  4242 3313 3432 3333  2222 2423 2222 3200 2322 2121 2332 3211 1234 3242 2322 4324 2432 3212 1122 3221 1233 3112 3332 3142 3224 1131 1232 4341 2243 0213 2232 1222 4123  4424  2334 3444 4214 4231 2333 3224  3333  1234 4444 1112 2332 1232 3244  3 3 3 3 3 3 3 3 3 3 3 3 4 4  4 4 4 4 5 5 5 5 5  1432 2121 1331 3434 2443 4233 2443  5  3434  5 5 5 5 5 5  4444  4442  3414 4334 4422  4433  4243 3333  4444  0331 3333 1222 2222 3202 4344 3114 4344 2231 3212 2231 4434 2323 2223 4433  4444  4444  2222 2332 1122 2222 1312 2234  APPENDIX 2:  Summary o f a n a l y s i s o f v a r i a n c e  of number  choices, both tasks included, for 1-12; Source Between  13-24;  25-36)  of  t i m e 1-3  correct (problems  only.  df  ms  F  subjects  A (order) B (sex) C (age) AB AC BC ABC Ss w i t h i n groups  1 1 2 1 2 2 2 24  .11 3.24 7.46 .00 1.88 1.08 .83 1.50  D (task) AD BD CD ABD ACD BCD ABCD D x Ss  1 1 1 2 1 2 2 2 24  10.75 .07 .55 2.16 .80 1.65 .22 .60 .39  27.88** 1 1.42 5.60* 2.08 4.27 < 1 1.57  F (variability) AF BF CF ABF ACF BCF ABCF F x Ss  2 2 2 4 2 4 4 4 48  14.00 .14 .57 1.16 .35 .37 .73 .11 .34  40.84** 1 1.66 3.39 1.01 1.07 2.13 < 1  G (time) AG BG CG ABG ACG BCG ABCG G x Ss  2 2 2 4 2 4 4 4 48  .11 .01 .18 .27 1.32 .60 .35 .19 .38  Within  <  < < <  1 2.17 4.98* 1 1.26 1 1  subjects  °  <  ;  <  < 1 < 1 < 1 < 1 3.49 1.58 < 1 < 1  30  APPENDIX 2  (Cont'd)  Source  df  ms  DF ADF BDF CDF ABDF ACDF BCDF ABCDF DF x Ss  2 2 2 4 2 4 4 4 48  5.92 .40 .07 .66 .19 .12 .29 .11 .33  DG ADG BDG CDG ABDG ACDG BCDG ABCDG D F x S_s  2 2 2 4 2 4 4 4 48  .67 .81 .21 .21 .34 .42 .04 .05 .34  FG AFG BFG CFG ABFG ACFG BCFG ABCFG FG x Ss  4 4 4 8 4 8 8 8 96  .20 .16 .31 .46 .07 .27 .16 .13 .34  < < <  DFG ADFG BDFG CDFG ABDFG ACDFG BCDFG ABCDFG DFG x Ss  4 4 4 8 4 8 8 8 96  .06 .29 .14 .32 .24 .43 .33 .13 .23  <  Note:  F  < < < < <  < <  < <  < < < <  <  <  17.79** 1.21 1 1.98 1 1 1 1 2.00 2.41 1 1 1.01 1.24 1 1 1 1 1 1.33 1 1 1 1  1 1.24 1 1.37 1.03 1.84 1.41 1  Conservative degrees of freedom were used for a l l tests involving repeated measures. * i n d i c a t e s p_ < . 0 5 ; ** i n d i c a t e s p_ < . 0 1 .  31  APPENDIX 3:  Summary o f a n a l y s i s o f v a r i a n c e o f number o f choices on the  Source  oddity task  o n l y , f o r t i m e 1-3  df  ms  1 1 2 1 2 2 2 24  .00 5.71 15.58 . .69 3.11 .30 .45 1.72  F (variability) AF BF CF ABF ACF BCF ABCF F x Ss  2 2 2 4 2 4 4 4 48  33.19 .60 .23 2.09 .73 .65 .96 .27 .70  G (time) AG BG CG ABG ACG BCG ABCG G x Ss  2 2 2 4 2 4 4 4 48  1.00 .74 .54 .51 1.75 1.55 .49 .26 .85  FG AFG BFG CFG ABFG ACFG BCFG ABCFG FG x Ss  4 4 4 8 4 8 8 8 96  .40 .56 .73 .99 .20 .95 .67 .39 .66  Between  only.  subjects  A (order) B (sex) C (age) AB AC BC ABC S_s w i t h i n Within  correct  groups  < <  1 3.31 9.04** 1 1.81 1 1  subjects  Note:  47.47** 1 1 2.98 1.05 1 1.37 1  < < <  < <  1.18 1 1 1 2.05 1.82 1 1  1 1 1. 1 0 1. 4 9 1 1. 44 1.02 1  Conservative degrees of freedom were used for a l l tests involving repeated measures. * i n d i c a t e s p_ < . 0 5 ; ** i n d i c a t e s p_ < . 0 1 .  32  APPENDIX 4:  Summary o f a n a l y s i s o f v a r i a n c e o f number o f choices on the  Source  sequential  t a s k o n l y , f o r t i m e 1-3  df  ms  1 1 2 1 2 2 2 24  .69 2.25 3.26 1.63 7.06 4.51 4.71 3.64  F (variability) AF BF CF ABF ACF BCF ABCF F x Ss  2 2 2 4 2 4 4 4 48  4.63 .84 2.06 2.57 .48 .49 1.91 .28 1.12  G (time) AG BG CG ABG ACG BCG ABCG G x Ss  2 2 2 4 2 4 4 4 48  .85 1.62 .34 .76 2.69 .57 .46 .37 .94  FG AFG BFG CFG ABFG ACFG BCFG ABCFG FG x Ss  4 4 4 8 4 8 8 8 96  .12 .53 .14 .89 .80 .64 .43 .17 .82  Between  F  subjects  A (order) B (sex) C (age) AB AC BC ABC Ss w i t h i n Within  correct  groups  < < < <  1 1 1 1 1.94 1.24 1.29  subjects  Note:  Conservative degrees of freedom involving repeated measures. * ** i n d i c a t e s p_ < . 0 1  <  < < <  < < < < < <  < < < < < < <  4.13 1 1.84 2.29 1 1 1.70 1  1 1.72 1 1 2.86 1 1 1 1 1 1 1.09 1 1 1 1  were used for indicates  , .05;  only.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0076802/manifest

Comment

Related Items