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An informational analysis of absolute judgments of torque Russell, David Gray 1971

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AN INFORMATIONAL ANALYSIS OF ABSOLUTE JUDGMENTS OF TORQUE BY DAVID GRAY RUSSELL B. P.E., The University of British Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION in the School of Physical Education and Recreation We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1971 S 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 deg ree at t he U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t he 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 ag ree 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 p u r p o s e s may be g r a n t e d by t he Head o f my Depar tment 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 . Depar tment of School of Physical Education and Recreation The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8. Canada Date JUNE 28th, 1971 ABSTRACT Five male Ss took part in seven experiments involving absolute judgments of stimuli selected from a continuum of torque. The first experiment required Ss to make judgments on the intensity of sixteen stimuli separated by equal intervals. The results were used to construct individual scales of equal discriminability. These scales were used to select the stimuli for the remaining six experiments in which 6, 8, 10, 12, 14 and 16 stimuli, separated by subjectively equal intervals, were used. An informational analysis was performed on the data of these experiments to determine the capacity of the kinesthetic system to transmit information derived from the inducement of torque. Maximum values of 1.680, 2.050 and 2.524 bits of transmitted information were obtained when the response was considered the output and the input variables were, respectively, the stimulus, the stimulus and subject, and the stimulus, subject and previous stimulus. These results were discussed in relation to information theory and the use of torque in-formation in the closed-loop control of movement. It was concluded that torque-derived information may be available for the control of movement but that the capacity of the kinesthetic system to transmit torque information was less than that reported for amplitude of movement. Kinesthetic after effect was cited as a possible cause of the relatively low transmission. ACKNOWLEDGEMENT I would like to express my thanks to the members of my committee, Dr. R. G. Marteniuk, Mr. R. Conry, Dr. W. G. Davenport and Mr. R. W. Schutz for their guidance and comments during the preparation of this thesis. Special acknowledgement is due to Mr. Schutz for his help with the analyses and computer programming. To my chairman, Dr. Marteniuk, 1 must express special appreciation for his continued in-spiration and his demands for academic excellence during my association with him. Most of al l, though, I express my gratitude to my wife, Ruth, and children, Neil and Susan. TABLE OF CONTENTS CHAPTER PAGE I Statement of the Problem 1 -' I ntroduction 1 - Purpose of the Study 3 - Limitations 3 - Delimitations 4 - Definition of Terms:. 4 II Review of Literature - The Role and Nature of Kinesthesis 5 - Kinesthesis and the Perception of Resistance to Movement 9 - Sensory Feedback and Closed Loop Theory 12 - Absolute Judgment and Information Analysis 18 - Scales of Equal Discriminability 22 - Summary 23 III Methods and Procedures 24 - Subjects 24 - Apparatus 24 - Experimental Design 24 - Procedures 26 - Position of Subjects at Apparatus 26 - Calculation of Torque 26 - Learning Trials 28 - Experimental Trials 28 - Analysis of Data 29 - Experiment I: Scale of Equal Dis-criminability 29 - Experiments II - Vll 29 CHAPTER PAGE IV Results and Discussion 32 - Results 32 - Scale of Equal Discriminability 32 - Information Transmission (St:R) 32 - H T (S:R) 32 - H T (P-.R) 35 - H T (St, S, P:R) 40 - Distribution of stimuli 40 - Discussion 42 V Summary and Conclusions 50 References 53 Appendices A. Treatment of Data 59 B. Individual Score Sheets 61 LIST OF TABLES iv PAGE I Input and Output Variables used in Calculating Inform- 30 ation Transfer II Information Transmitted (Bits) Between Three Input 39 Variables and Response III Mean Responses to Each Stimulus Expressed in Terms of the 40 Preceding Stimulus (Experiment II) IV Mean Responses to Each Stimulus Expressed in Terms of the Preceding Stimulus (Experiment Vll) 41 LIST OF FIGURES The Apparatus Position of Subject at Apparatus Mean Equal Discriminability Scale Information Transfer for Each Condition as a Function of the Number of Stimulus Categories Mean Information Transfer per Subject as a Function of the Number of Stimulus Categories Subjects' Mean Responses as a Function of the Stimulus Categories Used in Experiment VII Subjects' Mean Responses as a Function of the Stimulus Categories Used in Experiment VII Mean Information Transfer per Subject for Amplitude of Movement (Marteniuk, 1971) and for Torque CHAPTER I STATEMENT OF THE PROBLEM Introduction The control of skilled movement under the closed-loop model of human motor behavior depends largely on the capacity of the individual to interpret sen-sory feedback. This feedback is monitored and used to compare the actual with the intended movement. The kinesthetic sense, with the various dimensions of movement as its adequate stimuli, seems a modality ideally suited to provide this type of sensory information. Evidence from studies which deprive or distort kinesthetic afference such as those by Laszlo (1966) and Chase (1959) support the contention that kinesthesis is important to the control of skilled performance. Sensory feedback is central to a l -most all models of human performance (Welford, 1960; Chase, 1965a, 1965b). A theorectical framework for the feedback nature of kinesthetic afferent impulses has been suggested by von Hoist (1954). In that paper he suggested that response-produced afferent impulses, which he terms 're-afference' are compared with a reference level, or 'efferent copy' of the intended movement. Adams (1968) has suggested that a perceptual trace, a conditioned image of previous responses, serves as a reference level. Under Adams' theory a memory trace, which is really an S-R bond, causes the response to occur, but that the correctness of the resp-onse is determined by the comparison of the feedback from that response and the perceptual trace. In terms of either of these closed-loop models of von Hoist and Adams, the important factor is the availability of response-produced feedback in-formation. However, it has not been universally accepted that kinesthesis is a sen-2 sory modality (Howard and Templeton, 1966). Nevertheless, kinesthesis can be shown to qualify as a modality provided its sensory receptors and their afferent pathways can satisfy the requirements outlined by Smith (1969) and Eyzaguirre (1969). These requirements are that the receptors have unique anatomical loc-ations and respond to a particular form of energy, and that their afferent impulses are sentient by nature. Skoglund (1956) has found that receptors in the ligaments supporting the joints have cortical representation - a necessary property for perception. Stopford (1921) and Rose and Mountcastle (1960) have shown that unique sensory receptors capable of subserving kinesthesis arise from the joint capsule and pericapsular tissue. The involvement of these receptors in the per-ception of movement has the supporting evidence of Mountcastle and Powell (1959) who showed a 'rather precise relation' of the activity of a cortical neuron to the angle of the joint. Boyd and Roberts (1953) have demonstrated a characteristic discharge frequency of receptors for particular positions and rates of movements. Smith (1959:33) concludes: "The unique stimulus for kinesthetic receptors is movement... the receptors are mechano-receptors; responses are initiated by the deformation of their endings produced by the stretching or compression of the structures in which they are embedded." Basic to an understanding of movement control and to whether kinesthesis can be included in models such as those proposed by von Hoist (1954) and Adams (1961) is the determination of the capacity of the kinesthetic system to transmit information. The only reported study which has sought to determine the capacity of the kinesthetic system to transmit information is one by Marteniuk (1971). He reported a maximum value of 2.48 bits for amplitude of movement and concludes that this particular aspect of the kinesthetic system is at least on a par with other sensory systems in the ability to supply the central nervous system with sensory in-formation. Thus he sees cues from amplitude of movement as playing a possible role 3 in nullifying error between intended and actual movements. In terms of the present study, it is necessary to consider whether torque is an adequate stimulus for kinesthesis and thus able to transmit information with-in the kinesthetic system. While there is considerable behavioral evidence to support the notion that resistance to movement can be perceived with a fair degree of accuracy, it does not appear to have been considered an adequate stimulus for kinesthetic receptors per se. However, Howard and Templeton (1966) do consider accuracy of pressure production a type of kinesthetic judgment. Evidence showing the sensitivity of this system was presented by Jenkins (1947) who found a Weber's Ratio of .06 for the reproduction of resistances greater than 10 lbs. Shields (1970), on the other hand, obtained a Weber1 Ratio of .043 for active movement of the shoulder joint for a standard of 45°. Another line of evidence demonstrating that force and amplitude of movement cues can be used by the kinesthetic system was presented by Briggs, Fitts and Bahrick (1957) when they found that both force and amplitude cues significantly affected performance, with amplitude apparently having the greater affect. Considering the above evidence it would appear that torque can be an adequate stimulus for kinesthesis. However, to date there is very little evidence pertaining to the characteristics of this particular dimension of kinesthesis and its capacity to transmit relevant information to the CNS. Purpose of the Study The purpose of the study was to determine the capacity of the kinesthetic system to transmit information derived from the inducement of torque. Limitations The study was limited by: 1. The experimental procedures used to construct both the scale of equal discriminability and the information transmitted. 2. The accuracy of the device used to present the torque categories. 4 Delimitation The study was restricted to: 1. The specific levels of torque used in the experiments. 2. The induction of torque in the arm resultant from the extension of the elbow joint while grasping the handle of the apparatus in the right hand. Definition of Terms Torque. The effective force in producing rotation about an axis. It is measured at right angles from the axis of rotation to the line of action of that force. The unit of measurement used was the gram centimeter (gm. cm.). Scale of Equal Discriminability (ED Scale). A psychological scale on which each interval is perceived as equal by a subject even though the physical dimen-sions of these intervals may not be equal. Information (H). The amount of uncertainty associated with the outcome H of one of N events. This is usually expressed in the binary form, N = 2 or H = log2 N, when the outcome of each possible occurrence of the N events is equiprobable. When^the outcome of each occurrence of the N events is not equiprobable, H = T- P', log2 —•-; where pi is the empirical probablity of one of N events occurring. The unit of information is the binary digit or bit (Attneave 1951). Information Transmitted (HT). The information common to the stimulus categories and to a subject's response to the stimuli. CHAPTER II REVIEW OF LITERATURE The Role and Nature of Kinesthesis. Sensory feedback has been shown to be important in the control of motor performance, initially by physiologists (Mott and Sherrington, 1895) and latterly in behavioral studies by Gibbs and Baker (1952), Gibbs (1954), Chase et al. (1961), Laszlo (1966) and others. One type commonly discussed is kinesthesis as a sensory modality and thus whether this system is capable of providing sensory feedback is open to question. Smith (1969:32) has stated that if physical educators want to under-stand kinesthesis and its role in the acquisition of skill, there must be agreement on a common operational definition and a concerted effort to discover its physiological and psychological mechanisms. Of fundamental importance to the definition of kinesthesis is the question of whether it qualifies as a sensory modality. This depends, firstly, on the existence of unique sensory receptors subserving kinesthesis and, secondly, on evidence pertaining to their adequate stimulus. Eyzaquirre (1969:49) defines a sensory receptor as a "specialized structure which can be stimulated by environmental changes as well as by changes within the body .... and which .... is capable of transforming different types of energy into nerve impulses which travel through afferent nerve fibres towards the CNS .... The information provided by the sensory nerve impulses, when decoded and analysed, results in sensation." 5 CHAPTER II REVIEW OF LITERATURE The Role and Nature of Kinesthesis. Sensory feedback has been shown to be important in the control of motor performance, initially by physiologists (Mott and Sherrington, 1895) and latterly in behavioral studies by Gibbs and Baker (1952), Gibbs (1954), Chase et al. (1961), Laszlo (1966) and others. One type commonly discussed is kinesthetic feedback. However, controversy surrounds the legitimacy of kinesthesis as a sensory modality and thus whether this system is capable of providing sensory feedback is open to question. Smith (1969:32) has stated that if physical educators want to understand kinesthesis and its role in the acquisition of ski l l , there must be agreement on a common operational definition and a concerted effort to discover its physio-logical and psychological mechanisms. Of fundamental importance to the def-inition of kinesthesis is the question of whether it qualifies as a sensory modality. This depends, firstly, on the existence of unique sensory receptors subserving kinesthesis and, secondly, on evidence pertaining to their adequate stimulus. Eyzaquirre (1969:49) defines a sensory receptor as a "specialized structure which can be stimulated by environmental changes as well as by changes within the body .... and which .... is capable of transforming different types of energy into nerve impulses which travel through afferent nerve fibres towards the CNS .... The information provided by the sensory nerve impulses, when decoded and analysed, results in sensation." 5 6 Smith (1969) states that receptors subserving a sensory modality are characterised by their unique anatomical location and by their responsiveness to a particular form of energy. Perception, she says, not only involves the decoding and analysing of these 'sensory nerve impulses' but is a conscious act which implies that the receiver will be able to communicate what has been received. She goes on to state that kinesthetic receptors must provide information regarding 1. Onset and duration of movement 2. Direction of movement 3. Velocity and acceleration of movement 4. Range of movement 5. Static position of jointed segments prior to and after movement. A brief historical review will illustrate the problems associated with defining kinesthesis as a sensory modality capable of handling such requirements. Since Bell (1826) first used the term to refer to the 'sixth' or 'muscle sense' there has been considerable controversy despite the early proof of Goldscheider (1899) that kinesthesis is diarthroidal rather than muscular in nature. The involvement of the muscle spindles and tendon organs in the perception of movement has seemingly been disproveri. The pathway of the afferents of these receptors have been traced via the dorsal tracts to the cerebellum. Mountcastle, Covian and Harrison (1950) and Mountcastle (1957) have shown that direct stimulation of mamalian muscle spindles prod-uces no detectable response in the postcentral somesthetic area. Rallston (1957) provides evidence that the Golgi tendon organs do not have direct cortical representation. Skoglund (1956) has found, however, that a similar type of receptor found in the ligaments supp-orting the joints does have cortical representation and thus can be associated with perception. 7 On the other hand, the evidence that receptors in the joint cap-sule have movement and limb position as their adequate stimulus is considerable. Apart from Goldscheider (1899), and many others since, including Stopford (1921), Rose and Mountcastle (1961), and Gardner (1966), have shown that the unique sensory receptors capable of sub-serving kinesthesis arise from the joint capsule and pericapsular tissue. It is interesting to note that Stopford, in the study mentioned above initially felt that: "the recognition of a digit (finger) was obviously dependent upon the alterations in the tension or position of tendons and did not arise from any stimulation of afferent nerve terminals in the region of the joint." But, he continues, "fortunately, this source of fallacy was discovered early in the investigation." Skoglund (1956) conducted a series of detailed experiments on knee-joint innervation of the cat. On the basis of these experiments he determined the following classification of sensory receptors of the joint. Type I are slowly adapting, Golgi-type endings associated with the ligaments which work uninfluenced by the muscles, and signal the exact position of the joint. It also records the direction of the movement. Type 2, also slowly adapting are Ruffini (spray) endings which lie in the capsule and signal the direction and speed of movement. This type works under the influence of those muscles which alter the tensions of the joint capsule. Type 3 are Vater Pacini (paciniform) corpuscles of rapid adaption, which are very sensitive to quick movements, 8 independent of their direction. Skoglund (1966) considers the second and third types to be additive and to subserve acceleration. In a review of literature pertaining to joint afferent pathways, Gardner (1966) also describes three types of joint receptors: Complex non-encapsulated endings of which there are two types; Golgi-type tendon endings occurring in the ligaments and spray-type (Ruffini) endings. Secondly, complex encapsulated endings which includes modified Pacinian (Vater Pacini) corpuscles. Thirdly, free endings of which some are apparently pain receptors and some mechano-receptors. The important quality of these types of receptors is that their afferents project to the cerebral cortex; a necessary factor in perception. The involvement of these receptors in the perception of move-ment has the supporting evidence of Mountcastle and Powell (1958) who showed a 'rather precise relation of the activity of a cortical neuron to the angle of the joint'. Other evidence from the study of the cat is provided by Boyd and Roberts (1953), Andrew (1954) and Skoglund (1956). For example, Boyd and Roberts (1953) have demon-strated a characteristic discharge frequency of receptors for particular positions and rates of/ movement. Thus each receptor appears to have a limited angular range. Further, Gardner (1966) suggests that when a joint is at rest, the slowly adapting spray endings most sensitive at that position continue to discharge for long periods of time. Skoglund (1956) has provided evidence that joint receptors are accurate indicators of movement. It is apparent, therefore, that receptors are capable of accurately indicating position as well as movement. However, Howard and Templeton (1966:45) still had some doubt about the precise identification of the unique receptors subserving 9 kinesthesis: "Receptors in the joint capsule contribute to the sense of position .... but whether they are the only receptors involved is not known. It seems, on balance, doubtful whether the muscle and tendon receptors serve the passive movement sense; it is more likely that they are involved in active movement but evidence in inconclu-sive. " Nevertheless, in the absence of any conclusive evidence pertain-ing to the direct cortical representation of muscle and tendon afferents in primates it must be concluded that only the receptors of the joint capsule and pericapsular tissue can be considered to subserve the per-ception of movement and limb position. This position has been substan-tiated by Smith (1969:33) who concludes that kinesthesis is the sensory modality concerned with the perception of movement: "The unique stimulus for kinesthetic receptors is movement, more specifically movement around a diarthroidal joint. The receptors are mechano-receptors, responses are initiated by the deform-ation of their endings provided by the stretching or compression of the structures in which they are embedded." Kinesthesis and the Perception of Resistance to Movement. At no stage in the foregoing evidence has there been mentioned the perception of resistance of movement. Smith's (1969) definition above and her descript-ion of adequate stimuli for kinesthetic receptors make no reference to resistance of movement. Similarly, Howard and Templeton (1966:82) in their review of kinesthesis also fail to mention it specifically. However, there is considerable behavioral evidence to support the notion that resistance can be perceived and with a fair degree of 10 accuracy (Jenkins 1947; Orlansky 1949; Gibbs and Baker, 1952; Bahrick, Bennett and Fitts ,1955; Weiss 1955; Briggs, Fitts and Bahrick, 1957; Smith 1963; Woodruff and Helson,1965, 1967; Kerr 1967; Levy 1968; Norrie 1968, 1969). Using a pressure reproduction task in which associated movement was limited to 0.13 ins., Norrie (1969) found a constant error of 343.8 gms. for the immediate reproduction of 2000 gms. Jenkins (1947) compared performance of pilots and non-pilots on a force reproduction task. He varied the pressure to movement of stick, wheel and rudder controls from 1-50 lbs. The most relevant to this discussion are the data he obtained from the stick-type control: Ss were required to reproduce 1, 5, 10, 20, 30, 40 lbs. pressure. Jenkins calculated the difference limen for pilots for each of the standards and found that Weber's Ratio is not constant but decreases significantly as the standard increases from 1-10 lbs. (0.21 to 0.08) but holds relatively constant above 10. lbs. at about 0.06. In interpreting Jenkin's results Orlansky (1959) suggests that low pressures provide poor cues and that there is a tendency to over-exert on small forces and underexert on clarge forces. By comparison, the difference limen for active movement of the shoulder joint has been shown by Shields (1970) to range from 1.42° to 1.65° using the method of constant stimuli, and from 1.95° to 2.13° using the method of average error. The standards were 45° and 125° in each case respectively. Shields also reports Weber's Ratios. Using the method of constant stimuli, the values are .033 for a standard of 45° and .012 for 125°. Using the method of average error, the values are .043 and .012 respectively. For passive flexion of the elbow joint, Laidlow and Hamilton (1937) report a difference limen of .4°. It would seem, then, that perception of resistance to movement, is slightly superior. Gibbs and Baker (1952) used a task requiring subjects to centre a 11 spot of light on a cathode ray tube (CRT) i.e. to correct a given amount of error using both free-moving and pressure control. They showed, inter alia, that subjects under the pressure control conditions had significantly better performance. However, contrary evidence has been cited by Weiss (1954). Weiss used two sets of force-displacement conditions to determine how the accuracy of positioning responses varied as displacement and pressure was varied. In one set he kept the maximum pressure at 30 lbs. and the angular displacement of the lever was varied from 3° to 30°. In the other set, the maximum angular displacement was constant at 30° and the pressure varied from 0 to 30 lbs. The task required subjects to compensate for the displacement of a spot of light from the centre of the oscilloscope screen by moving a control lever under either of the two sets of conditions described above. From the results Weiss concluded that for non-visual positioning responses, movement provides more important cues than does the force-displacement relationship. It must be pointed out that this study by Weiss involved using 'proprioceptive' cues (Weiss's term) to correct a visually displaced spot, the position of which was held in memory. Further, Weiss's task was essentially a discrete task compared to Gibbs and Baker's tracking task. These facts could account for the difference in findings. Another possible explanation for the above disagreement was provided by Bahrick, Bennett and Fitts (1955) and confirmed by Briggs, Fitts and Bahrick (1957). In an attempt to determine the relative effect-iveness of force and amplitude cues on the performance and learning of a complex, two-dimensional task, the second of these two studies required subjects to return a target dot to the centre of a CRT by the manipul-ation of a spring centred control column, thus removing initial error. Four groups served under four conditions of amplitude and force required to oper-ate the control column. Analysis of the data led the authors to conclude that both force and amplitude cues significantly affected performance with 12 the latter apparently exerting the greater influence. This being the case, it becomes apparent that there must be per-ipheral sensory receptors capable of detecting resistance to movement. For the reasons cited above, muscle receptors must be excluded. There does, however, remain one question which must be resolved before it can be stated that the primary receptors subserving the detection of resist-ance to movement are kinesthetic in nature. It must be established that these receptors are generally more sensitive than those subserving tactile sensitivity. In an article published in 1953, Henry required twelve subjects to perform under two conditions involving pressure perception. The first condition required subjects to maintain a constant pressure on a pad which exerted varying force on the subject's hand by means of a cam and lever arrangement. The second condition required subjects to in-crease or decrease pressure against the pad in such a manner as to oppose the pressure exerted by the pad. Henry's analysis of the data showed sig-nificantly greater accuracy under the constant pressure condition. He calculated a Weber's Ratio of .061 for the constant pressure condition. According to Woodworth and Schlosberg (1954:223), Boring, Langfield and Weld have shown a Weber's Ratio of 0.013 for deep pressure and .136 for cutaneous pressure. Henry also quotes these two figures and concludes: 'The latter figure is so high that it is doubtful if cutaneous pressure is a very important contributor to the perception1 (of kinesthesis). On the basis of this foregoing evidence, it must therefore be concluded that the receptors of resistance to movement are those associated with the joints and thus qualify as kinesthetic receptors. Sensory Feedback and Closed-Loop Theory. The importance of sensory feedback to closed loop theory makes the quantification of the 13 capacities of the various sensory systems to transmit sensory information essential to the understanding of movement control. Investigations into the nature, function and importance of sensory feedback appears to have its origins in the closed-loop model of human behavior first pro-posed by Craik (1947). Craik first conceived man as an engineering system which behaves basically as an intermittent correction servo-system. Such a system consists essentially of misalignment detectors which, when activated, causes a servo-motor to be switched on. This servo-motor acts to reduce the misalignment. The following year Craik (1948) extended this concept and discussed man as the 'human operator' as an element in a control system, providing a description of man which was the basis of later models for human performance. He regarded man as a chain of processes consisting of: 1. Sensory devices which transforms misalignments into suitable physiological counterparts. 2. A computing system which responds to the misalignment input by giving a neural response calculated to be appropriate to reduce the misalignment. 3. An amplifying system to convert neural impulses at end plates to muscular action. 4. Mechanical linkages which produce, externally observ-able effects. Important in this approach is that the system can detect mis-alignment, operate to reduce it, and then monitor the results of its corrective action. In a 1961 paper, Adams compares this closed loop servo-system to human tracking behavior noting that both are "error-nulling" in nature. His analogy is essentially the same as Craik's (1948). In Adam's comparison there is a feedback loop which monitors the output of the servo-motor and relays this output to a mechanism to be converfed into input-output error which in turn is used to further control the 14 servo-motor's output. The human tracking analogy has the human operator replacing the servo-motor in the control system, i.e. the input-output error is displayed to the human operator and is used as the basis of his subsequent control action . Welford (1960) postulated a model cf the chain of processes similar to those which Craik (1948) had proposed. Welford's model was based on the single channel hypothesis which suggests that, when one signal occurs very shortly after another, the time taken to respond to the second may be longer than to the first. This suggests that the central mechanisms can process only one signal at a time. This feature is essential to the experimental concommitants of the model and derives support from Telford (1937), Vince (1948), Welford (1952, 1959). The central mechanisms of Welford's (1960) model are similar to those suggested by Craik (1948): Input is received from sensory receptors by a perceptual mechanism where it is identified, a translation mechanism which is concerned with the choice of action in relation to what is per-ceived and a central effector mechanism which activates the effector organs by impulses co-ordinated and phased to produce the chosen action. Welford suggests that a feedback loop from the effector side controls the passage of data from the perceptual to the translation stages once the response action to the previous signal has begun. Welford has thus placed the servo-system model within the human operator. The same idea is expressed by Chase (1965a, 1965b). In these papers Chase postulates an information-flow model of the organization of motor activity comprising a receptor system concerned with transducer operations and its associated input channels, mechanisms for error detection and correction concerned with central processing functions and an effector system which transmits motor output. According to Chase's model, sensory feedback occurs when there is any motor output from the nervous system and that this results in 15 afferent activity in many sensory input channels. This capacity of the system to monitor its own operation is what Welford (1968:137) terms 'the subtle interplay that takes place between action and sensory feedback'. Consideration of sensory feedback in relation to closed loop theory raises two questions: sensory information arises from the receptors of a number of sensory modalities. Does each modality have an associated feedback loop? Secondly, if this is so, is it possible to manipulate the information available to the central processes for monitoring perform-ance from the various receptors? A number of studies, including Gibbs (1954), Twitchell (1954), Chase (1958), Chase, Harvey, Standfast, Rapin and Sutton (1959), McDermid and Smith (1964) and Chase (1965a, 1965b) have considered sensory feedback from various sources and have delayed or distorted one or more feedback loops. Chase et al. (1959) had subjects clap their hands six times to the beat of a metronome. They delayed the auditory feedback by 250 msec, and found subjects tended to clap slower and to clap seven rather than six times. Subjects were also asked to say the letter 'b '. Conditions of this experiment were no delay and 244 msec, delay in auditory feedback. Under conditions of delayed auditory feedback subjects tended to increase the loudness, prolong sounds, increase the length of the pause between sounds and to repeat the sound four instead of three times. The same subjects were also given a key tapping task under the same two conditions. The dependent measures in this experiment were timing and intensity of response. The results revealed a tendency to tap harder, hold the key down longer, to increase the time betwen taps and to tap four instead of 16 three times. The results thus revealed similar tendencies for both types of task. This leads one to conclude that interferring with auditory feed-back leads to a disturbance in response. McDermid and Smith (1964) reported a study in which compen-satory reaction to displaced visual feedback was investigated by requiring subjects to negate the effects of vi'sual feedback displacement by adjust-ing the direction of response. Of importance in the present context are their findings that significant performance decrement occurred between no visual displacement and 90° to 270° displacement. Thus, not only dis-turbance of auditory, but also visual feedback interfers with motor per-formance. Laszlo (1966) reported two studies which were conducted to test the suitability of the nerve compression block as a technique in the in-vestigation of the role of kinesthesis in motor skills. Her findings suggest that a performance decrement occurs in the absence of kinesthetic feedback. The typical block syndrome was induced by inflating the sphygmomanometer attached to the uppper arm to a greater pressure than the subject's blood pressure. In one experiment prior to the induction of the block each of the six subjects was asked to tap on a morse key at his fastest rate and as evenly as possible. Following the application of the compression block and the subsequent sensory loss, he was asked to tap again. Results showed a great decrease in the number of taps for a 5 sec. period following the loss of kinesthesis compared to normal perform-ance. Further, there was great irregularity in both rhythm and the length of time the key was held depressed. Thus in addition to auditory and visual feedback disturbance, a loss of kinesthetic feedback has detrimental effects on motor performance. From these studies two things can be established: Firstly, that 17 there are a number of sensory feedback loops which appear to be modality-specific and, secondly, it is possible to manipulate the in-formation available to the central processes for monitoring performance from these sources. These sensory feedback loops appear to comprise what has been termed by Chase et al. (1961,. b) 'redundant multiple feedback loops'. In that paper, Chase and his associates demonstrated the effects of delayed and decreased sensory feedback from visual, auditory, tactile and a combination of these three and this combination together with a xylocaine-induced digital block on the performance of key-tapping tasks. These tasks involved regularity of tapping and pattern of tapping. Chase and his associates found significant changes in the performance of the pattern task which required the subjects to tap twelve sets of three taps and the regularity task which required 25 taps. Both tasks were paced by a metronome. The dependent measures were the time between the taps and the intensity (force) of the taps. In general the findings show an increased intensity of tapping and an increased time between taps during the performance of the task. Chase et al. (1959), it will be recalled, have obtained similar results with a key tapping task. In the same study, they had Ss repeat the letter 'b' a number of times and found Ss responded with increased loudness and increased time between 'b's'. They suggested that these results may reflect Ss' efforts to increase sensory feedback along undisturbed channels. One possible implication of these findings in terms of the closed-loop model of motor behavior is that a certain amount of sensory feed-back information is necessary for the central processes to adequately monitor and thus control performance. It is also possible to interpret the findings of earlier studies in 18 these terms. Of importance in this context are the studies concerned with what can be termed, in light of the above review of kinesthesis, the various dimen-sions of the kinesthetic modality. The two dimensions of specific concern are movement and resistance to movement. As reviewed previously the evidence on the influence of adding resistance to movement is divided (Gibbs and Baker, 1952; Gibbs, 1954, Weiss, 1954; Bahrick, Bennett and Fitts, 1955; Briggs, Fitts and Bahrick, 1957). It will be recalled that Briggs, Fitts and Bahrick suggested that both force and amplitude cues can contribute to the skillful execution of position-ing tasks and that the effectiveness of either type of cue is limited to the level of the other type. One possible conclusion is that the increased performance generally found is the result of the additional sensory information available. A similar conclusion can be based on the findings of studies involving in-formation analysis of multidimensional sensory input as opposed to unidimensional input. Klemmer and Frick (1953) show that subjects transmitted a maximum of 4.4 bits of information about the position of a single dot in a square matrix (two dimensions), compared to 3 bits of information about the position of a single dot on a line found by Hake and Garner (1951). Absolute Judgment and Information Analysis. The method of absolute judgment has been described by Wever and Zener (1928). Essentially, the method requires S to identify a set individually presented stimuli. Because absolute judgment does not involve any explicit standard for comparison, S is required to base his judgment on some subjective standard. The method in-volves memory and, therefore, tells little of the basic characteristics of individual sense organs, but a great deal about the relation of sensation to memory. As such it is ideally suited to study the capacity of the various sensory systems to transmit sensory information. Studies on absolute judgment (Garner and Hake, 1951; Pollack, 1952, 19 1953; Garner, 1953; Klemmer and Frick, 1953; Eriksen and Hake, 1955; Mart-eniuk, 1971) show man's capacity to transmit information to be limited, i.e. the capacity to make accurate judgments on the basis of sensory (input) inform-ation. The maximum amount of information transfer appears to vary with both the sensory modality and the number of dimensions of the stimulus input. Refer-ence to Miller's (1956) review reveals information transmitted for unidimensional stimuli to range from 1.9 bits for curvature to 3.9 bits for positions in an interval. When multidimensional stimuli are used the information transmitted increases, Miller quotes figures ranging from 2.3 bits for concentrations of salt and sucrose combined, to 4.8 bits for pitch and loudness combined. The use of information analysis in analysing absolute judgment data appears to have been first suggested by Garner and Hake (1951) and first used by Hake and Garner (1951) in the same year. Hake and Garner used information analysis because ' . ... the method gives a direct measure of the minimum number of stimuli from a set of stimuli which can transmit the maximum amount of information about some other set or event'. Their task required Ss to interpolate the position of a vertical pointer on a horizontal interval 16 inches wide. This interval re-presented one of a number of intervals of a large scale. There were two exper-imental conditions for each of five, ten, twenty, and fifty category series: A limited response condition (LR) in which S was required to make a judgment of the position of the pointer based on a scale stated by E. And an unlimited response condition (UR) in which S had to consider the interval to be divided into 100 equal units and make his judgment in relation to the number of these units from the left edge of the interval. The information transmission for LR ranged from 2.31 bits for five categories to 3.19 bits for fifty categories and for UR, from 2.29 bits to 3.41 bits respectively for the same categories. These investigators suggest the difference between conditions reflects the influence of the greater number of responses available to S for their judgments. 20 Garner (1953) conducted an absolute judgment study using a stimulus continuum based on i loudness. Garner used six Ss and required them to make judgments using each of 4, 5, 6, 7, 10 and 20 stimulus categories. The loudness continuum was from 15 db. to 110 db. The stimulus categories were based on scales of equal discriminability constructed for each S. Garner analysed his results to permit the effects of Ss' varying use of the response categories and the effects of the previous stimulus to be determined. Among Garner's results are figures for the transmission of information from stimulus to response calculated from data pooled from Ss. These results show perfect transmission at four and five categories. Transmission thereafter drops to 1.62 bits at twenty categories. When both Ss effect and previous stimulus effect are included, perfect transmission occurs at four and five categories and then falls slightly to 2.29 bits at twenty categories. Both of the above studies used a unidimensional stimulus continuum as input. Klemmer and Frick (1953), however, used a two dimensional stimulus as input. Their study was an attempt to demonstrate the application of information measurement to a simple visual perception and to discover the maximum information that can be assimilated using a particular visual code. Onto a 40 x 40 inch screen they pro-jected a white dot on a black background for .03 seconds. Two experiments com-prised the study. In the first one a single dot was projected on to the screen in a matrix of the orders varying from 3 x 3 to 20 x 20. In the second only a 3 x 3 matrix was projected and the number of dots varied from one to four. Both exper-iments were run under two conditions; with or without an internal grid. They found that the inclusion or omission of the grid had no effect. The maximum information transfer for a single dot was 4.4 bits. In their discussion Klemmer and Frick compare this with the findings of Hake and Garner (1951), who, it will be recalled, found a maximum transfer of 3.19 bits for a unidimensional display. Thus a two dimensional display yields a greater information transfer than a unidimensional dis-play for a similar visual task. 21 The only published paper related to the absolute judgment of kinesthesis is by Marteniuk (1971). In that study, Marteniuk had five Ss, blindfolded and stripped to the waist so as to limit extraneous cues, seated at a table on which was a grid calibrated in degrees. The stimulus continuum consisted of arm move-ment from zero to 120 degrees. The task required S to horizontally adduct his arm, just clear of the table, from the starting position until his hand met a block which marked the particular amplitude of movement for that trial. Upon returning his arm to the starting position S made his judgment according to the usual proced-ure for absolute judgment experiments. Marteniuk calculated the information trans-mitted for four, six, eight, ten and sixteen stimulus category conditions. The stimulus categories were based on scales of equal discriminability. Maximum information transmission of 2.48 bits occurred at sixteen categories with perfect transmission occurring only at four categories. Implicit acceptance of information analysis is not universal. MacRae (1970) suggested that information analysis has been justified on two grounds. Firstly, that it is a descriptive technique used to express the extent to which judgments reflect the state of the stimulus continuum because the method is independent of the units of measurement and the number of stimulus categories into which the continuum is divided. Secondly, the appeal of the empirical results it provides. He discusses the use of the information analysis to determine the constant, fixed channel capacity of the human processing system. He concludes with Cronbach (1955:15) that 11 Pseudo-constancies can arise because of the way measuring proced-ures are devised, or from the balancing of opposing effects". MacRae concluded from a review of the experimental results of a number of investigations including Hake and Garner (1951), Pollack (1952), Garner (1953) and Eriksen and Hake (1955) that the characteristic shape of the curves resultant from expressing inform-ation transfer as a function of the number of stimulus categories are likely the result of increasing information bias coupled with decreasing true transmission. Nevertheless, it would appear from his paper that the use of information analysis is justified provided there is an awareness of this potential bias. This bias is such 22 that as the total number of stimulus presentations decreases or the number of cat-egories becomes larger the difference between true and estimated transmission increases. It is thus important to use a large number of presentations of each of the stimulus categories. In spite of MacRae's caution, information analysis is a valuable tool for those who wish to study the capacity of the human sensory systems. As Garner (1953:373) points out: "a measure of information transmission provides a means of specifying perceptual or judgmental accuracy where absolute judgments about various categories on a stimulus continuum are required. This measure allows the deter-mination of the maximum number of stimulus categories which would be used with perfect accuracy .... However, this use of information transmission requires the assumption that the inherent judgmental accuracy is independent of the number of stimulus categories used experimentally." Scales of Equal Discriminability. Investigations in classical psychophysics have demonstrated that there is not necessarily a direct relationship between the intensity of physical stimulus and an individual's judgment of its intensity. Saffir (1947) first developed a method for correcting Ss peculiar uses of responses to a given stimulus when the stimulus is selected from a scale of physically equal intervals. Attneave (1949) developed a method based on rating scale techniques which he called the method of graded dichotomies. Attneave suggested that knowing the proportion of times S assigns a given stimulus to each of the response categories, the psychological value of the stimulus can be considered the deviate of the normal curve corresponding to that proportion. In this manner it would be possible to construct a scale of stimuli separated by subjectively equal intervals. Garner and Hake (1951) were concerned with the selection of stimuli for absolute judgment tasks. They sought to construct a psychological scale which reflected the way in which an individual perceived these stimuli. They point out that such a scale renders the stimuli equally discriminable hence the name equal discrimin-ability scale (ED Scale). Such a scale, they suggest, should make it possible, 23 in an absolute judgment task, for an individual to use each response as often as its corresponding stimulus is presented. This should minimize errors of judgment of stimulus intensity. This increased judgmental accuracy should thereby lead to increased information transfer. The effectiveness of such a technique has been dem-onstrated by Garner (1953). For stimuli selected from an ED Scale for each S as being psychologically equidistant apart the information transmitted was 1.62 bits compared with 1.53 bits when the stimuli were based on equal physical intervals. Summary: This review has sought to establish a number of points: 1. That kinesthesis is a sensory modality 2. That resistance to movement is an adequate stimulus of kinesthesis 3. That the associated tactual cues play a minor, if not insignificant, role in the perception of resistance to movement 4. That sensory feedback loops can be manipulated with sufficient degree of success so as to permit the quant-ification of their capacity to transmit sensory information 5. That information analysis used in association with absolute judgment tasks is a legitimate procedure to quantify the capacity of sensory feedback loops. CHAPTER III METHODS AND PROCEDURES Subjects Five volunteer male university students who were naive to both the task and the apparatus were paid $1.50 per hour for their services as subjects (Ss). Apparatus The apparatus (Figure I) was a device which permitted Ss to be presented with different levels of torque and is almost identical to the one described by Henry and Norrie (1968). It consisted of a vertical section of flat spring steel, anchored at the bottom. At the top of the steel strip was mounted a handgrip and at the bottom of the apparatus was an elbow pad adjustable to the forearm lengths of Ss. Linked with the upper end of the steel strip was a calibrated pointer that was displaced by the movement of the steel strip. The extent of the displacement of the pointer was proportional to the amount of force placed against the handgrip. For this study the maximum amount of force applied on the steel strip by Ss was 5,776 grams which converted to 202,160 gm.cm. of torque. At this level of torque the handgrip was displaced 12 mm. Free mounted on the upper edge of the hardboard was a microswitch. S knew he was exactly at a specific level of torque when the pointer closed the microswitch (Figure 2) since this action activated an auditory signal (a high pitched beep). This signal informed S he had reached the level of torque E wished him to induce. Experimental Design The present study consisted of seven experiments. The first experiment 24 25 26 -required each S to use sixteen different levels of torque, each of which was desig-nated by a number 1 - 1 6 . Level 1 was the lowest and was equal to 12,635 gm.cm. The other numbers (stimulus categories) consisted of equal intervals of this magnitude with Level 16 equal to 202, 160 gm.cm. Each of the remaining six experiments required Ss to use, inca similar manner to experiment one, 6, 8, 10, 12, 14 and 16 levels of torque respectively. The torque values of each number and for each experiment were derived from the ED scales constructed for each S on the basis of the first experiment. The experiments were presented to Ss in random order. Where possible, each experiment was conducted on one day. Unfortunately, this was not always possible because of the availability of Ss. The number of presentations of each stimulus category was determined by the provision that each follow every other category an equal number of times. This meant that for each of 6, 8, 10, 12, 14 and 16 categories, the number of presentations per category was 60, 64, 60, 60, 56 and 64 respectively. Procedures Position of Ss at the Apparatus. Each S, blindfolded, stripped to the waist and fitted with industrial ear protectors that reduced extraneous noise, was led into the testing cubicle. This procedure was followed to limit all extraneous cues. S was seated at the chair which was attached to the floor in a position fixed relative to the apparatus. Ss were instructed not to permit their backs to touch the chair, during the trials. S's elbow was placed on a pad and his hand on the handle of the apparatus so that his hand, wrist and forearm formed a straight line (Figure 2). The movement was one of elbow extension and special importance was attached to main-taining a constant body position during trials. Calculation of Torque. The torque was calculated by multiplying the F igure 2: Pos i t ion of subject at apparatus 28 distance from the point of contact of S's elbow on the pad to the centre of the handle of the apparatus which S grasped by the amount of force required to displace the handle. As the amount of displacement was proportional to the force required to displace the handle, the amount of torque could easily be calculated for any displacement. Since the variation in Ss1 forearm lengths was very small, the calculation of torque was generalised for all Ss to a length of 35 cm. Learning Trials. Learning trials were provided for each experiment so that S could become completely familiar with the number assigned to each stimulus category within each experiment. On the instruction "Go", S pushed on the handle until the pointer which was linked with the handle closed the microswitch and activated the auditory signal. The microswitch was placed by E so that the re-quired level of torque was presented. On hearing this signal, S permitted the handle to return to the starting position and E identified the number which des-ignated the particular stimulus category. This constituted one learning trial. Ss were presented with each of the stimulus categories in alternately ascending and descending series. The first category in each series was randomly selected to min-imize the anchor effect usually associated with lowest and highest category. This procedure was continued until both S and E agreed that further practice would result in no improvement in assigning each stimulus to its corresponding number. In no case was the number of ascending and descending series presented less than the number of stimulus categories comprising any particular experiment. Experimental Trials. The procedure for experimental trials was the same as for learning trials with one exception: On returning the handle to the starting position, S made his judgment on the number of the stimulus category which had been pre-sented. The number of the response category used by any trial could be any of the numbers associated with any of the stimulus categories which constituted the part-icular experiment, i.e. the stimulus category he judged the presented stimulus to be. E recorded S's judgment (Appendix 'M) and the procedure was repeated with the next 29 stimulus category. The intertrial interval was just sufficient to record S's response and place the microswitch in position for the next trial; approximately 10 seconds. S was instructed that he may request a rest at any time. Further, E watched S closely and suggested a rest if S showed signs of fatigue. Rest periods were of about five minutes duration. Following one of these rest periods, S was given as many learning trials as he wished before continuing with the experimental trials. Analysis of Data The independent variable was the number of stimulus categories and the dependent variable the frequency with which Ss used each response category with-in each experiment. Experiment 1: Scale of Equal Discriminability. For Experiment 1, it will be recalled that the torque continuum was divided into 16 equal units or stimulus categories, and that each category was presented 64 times so that every category followed every other category an equal number of times. Following these 1024 trials an ED Scale was constructed according to the procedure outlined by Garner and Hake (1951). This process is considered necessary by Garner (1952) because all Ss do not use the same judgmental criteria and pooling the data before deter-mining how each S uses the reference (stimulus) categories can lead to serious distortion. Further, the above authors state that the selection of stimulus cat-egories with the use of an ED Scale should lead to increased judgmental accuracy and thus maximize information transfer. Experiments II - VII. The major analysis of data was in terms of inform-ation transmission. For each of Experiments II - VII the information transmission was calculated according to Garner (1952) and by the statistical procedures outlined by McGill (1952) and Garner (1962). The details of these procedures are given in Appendix A. The various input and output variables are shown in Table I. 30 TABLE I INPUT AND OUTPUT VARIABLES USED IN CALCULATING INFORMATION TRANSFER Condition Input Variables Output Variables 1 Stimulus Res ponse 2 Stimulus, Subject Response 3 Stimulus, Subject, Previous Stimulus Response The following symbols are used in the description of the analysis of data: H - Information H T - Information transmitted S - Subject St - Stimulus R - Response P - Previous stimulus Condition 1 . Data from all Ss were pooled and Hj between Sf and R calculated according to the equation H T = H(St) + H(R) - H(St,R) (1) Condition 2. Condition 2 required the computation of HT between S and R with held constant, i.e. for each stimulus, the frequency with which each S assigned a response category was entered in cells within a S x R matrix and Hj computed accord-ing to the equation H T = H(S) + H(R) - H(S,R) (2) 31 The Hj values for each stimulus category were then summed and the average value computed. This figure gives an indication of the extent to which Ss respond with different response categories to the same stimulus. When added to the figure obtained for Condition 1 this gives the total amount of information transmitted when one has knowledge of the manner in which both the stimulus and Ss affects the response. Or, if considered in terms of the predictability of the response given certain antecedent conditions, the extent to which the know-ledge of these two factors affects the prediction of the response. Condition 3. Finally, Hf was calculated between P and R with St held constant. The procedures for this calculation are complex and are found in Appendix A. Essentially, though, data from all Ss are pooled and for each stimulus, the frequency with which each stimulus is designated a particular response when that stimulus follows each other stimuli and itself was assigned to cells within a P x R matrix and Hj calculated: H T = H(P) + H(R) - H(P,R) (3) These values for each stimulus were summed and the average value computed. This figure gives an indication of the extent to which the additional knowledge of the preceding stimulus affects the way Ss respond or adds to the predictability of the response. When added to the figures obtained from Conditions 1 and 2 the resultant Hj value indicates the extent to which the knowledge of S, St and P affects the prediction of the response. CHAPTER IV RESULTS AND DISCUSSION RESULTS Scale of Equal Discriminability Individual ED Scales were calculated and plotted from data collected in Experiment I to determine the levels of torque associated with the various stimulus categories for each of the remaining experiments. For practical pur-poses, however, only the average scale is presented in Figure 3. The use of the ED Scale can be illustrated by the following example: For Exper-iment II, when six stimulus categories were used, the level of torque assoc-iated with each of these stimulus categories would be 22,750, 50,540, 78,350, 113700, 155400, and 202,160 gm.cm. respectively. Information Transfer Information transfer (Hj) was calculated using each of stimulus, subject and previous stimulus as the input variable and the response as the output variable. Hj(St:R). When the data from all Ss are pooled and the Hj between stimulus and response calculated the bottom curve in Figure 4 was deter-mined. The maximum Hj of 1.680 bits occurs at 16 stimulus categories. Perfect transmission did not occur in any experiment. 32 ^ • I iln , , ,1 . , , I „i. I I i t 6 0 10 12 14 16 NUMBER OF STIMULUS CATEGORIES Figure 4: Information transfer for each condition as a function of the number of stimulus categories. 35 When data are not pooled and Hj between St and R is calculated for each S, the average values obtained for Experiments II to Vll are shown in Figure 5. The actual values are 1.132, 1.150, 1.204, 1.337, 1.514 and 2.31,2 bits respectively. This maximum value at 16 categories is equivalent to perfect accuracy for about 6 categories. Hj(S:R). Hj between subject and response was calculated to deter-mine the different manner in which Ss used the various response categories. The results are reflected in the difference between the lower and middle curves of Figure 4. The actual values for each experiment are given in Table II. The reason for this additional information can be seen by referr-ing to Figures 6 and 7 in which the mean response for each stimulus cat-egory is shown separately for different Ss for Experiment 11 (six categories) and for Experiment Vll (16 categories) respectively. Obviously Ss did not make the same response to the same stimulus category. It will be noted in Table II that the amount of additional Hj gained by a knowledge of Ss tends to increase as the number of stimulus categories increases. F igure 5: M e a n information transfer as a f unc t i on of the number of stimulus categor ies . 37 5 z E I STIMULUS C A T E G O R Y Figure 6: Subjects ' mean responses as a f unc t i on of the stimulus categor ies used in Exper iment II. 1 6 1 1 Z o a. m Z 4 b Z • f • A • • A z O O • • • A O E E E • A A * E A Z o O i Z E E E O O O A O E A O E 10 1 2 14 1 ( ST IMU LUS C ATEGO RY Figure 7: Subjects' mean responses as a function of the stimulus categories used in ExperimentVII. 39 TABLE II INFORMATION TRANSMITTED (BITS) BETWEEN THREE INPUT VARIABLES AND RESPONSE N umber of Stimulus Categories Input-Variables 6 8 10 12 14 16 Stimulus 1.116 1.029 1.176 1.490 1.381 1.680 Subject .192 .173 .338 .215 .349 .370 Previous Stimulus .122 .130 .225 .254 .392 .474 Stimulus, Subject Previous Stimulus 1.430 1.432 1.739 1.959 2.122 2.524 HT(P,:R). The information transfer between previous sti muli and response is shown by the difference between the middle and upper curves in Figure 4. The shape of the upper curve is essentially the same as the other two but appears slightly steeper. The actual values for these analyses, found in Table II, reveal that the amount of additional information from this source increases with the number of stimulus categories. Another way of looking at whether the previous stimulus had an effect on the response was to determine if a kinesthetic after effect was present. The analysis involved calculating the mean response for each stimulus category for Experiments II and VII. When this was done there appeared to be a relatively 40 consistent relationship between the response category used by Ss and the inten-sity of the previous stimulus as can be seen in Tables III and IV for Experiments II and VII respectively. The grand mean responses in each case respectively were 3.58 and 8.05. TABLE III MEAN RESPONSES TO EACH STIMULUS EXPRESSED IN TERMS OF THE PRECEDING STIMULUS (EXPERIMENT II) Previous Current Stimulus Stimulus 1 2 3 4 5 6 1 1.38 1.92 2.68 3.78 4.50 5.48 2 1.40 2.14 2.86 3.88 4.44 5.48 3 1.46 2.62 3.14 3.86 4.56 5.46 4 2.14 2.46 3.26 4.16 4.70 5.84 5 1.62 2.96 3.22 4.36 5.12 5.58 6 1.86 2.64 3.52 4.34 5.04 5.60 Hj(St, S, P:R). Hy from each of the three input variables is summed and is seen as the top curve in Figure 4. These values, also shown in Table II, are a measure of the predictability of R given a knowledge of St, S and P. Distribution of Stimuli. Of some interest is a comparison of Hj when the stimuli values are determined on the basis of equal intervals and when they are determined according to a criterion of equal discriminability. For 16 stimulus categories (Experiments I and VII), for stimuli placed according to physically equal intervals, HT is 1.89 bits and when selected according to ED Scales, 1.68 bits. TABLE IV MEAN RESPONSE TO EACH STIMULUS EXPRESSED IN TERMS OF THE PRECEDING STIMULUS (EXPERIMENT V I I ) ~ " '. CURRENT STIMULUS Previous Stimulus 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2.55 2.60 4.30 4.45 5.10 5.40 5.40 7.00 8.00 8.40 9.75 10.45 11.65 11.70 13.65 14.80 2 3.60 3.05 4.95 5.35 5.55 6.25 6.75 7.45 J7.95 8.80 9.30 9.95 12.25 11.35 11.95 14.50 3 4.20 3.60 4.50 5.70 6.40 6.20 6.90 7.95 8.05 9.40 9.10 10.70 10.30 10.65 12.75 13.40 4 2.75 3.90 5.55 5.40 6.25 6.85 6.35 7.85 8.70 8.90 10.00 11.05 10.80 12.15 12.85 13.25 5 3.50 5.25 5.55 4.60 6.30 7.05 7.30 7.35 9.55 10.55 11.95 10.70 11.68 11.90 12.60 13.55 6 2.90 5.40 5.80 6.50 6.30 6.75 7.05 7.90 9.60 9.75 9.85 10.15 10.80 11.70 12.25 14.80 7 3.20 5.20 5.85 6.20 7.15 7.80 7.80 8.10 8.80 9.65 9.55 10.90 11.05 12.25 11.95 14.40 8 4.40 5.30 5.80 6.55 7.50 6.70 7.30 8.65 >"9.05 10.00 9.40 11.05 11.35 10.95 12.65 14.15 9 3.60 4.95 5.80 7.40 8.30 7.45 7.50 8.05 9.05 9.35 10.90 11.15 10.60 11.40 12.95 14.40 10 4.05 4.70 5.95 7.00 6.75 7.95 8,80 8.30 9.25 9.85 10.85 12.15 12.25 12.00 13.10 14.30 11 3.05 6.80 6.95 7.20 7.80 9.10 8.00 9.25 9.10 10.50 10.75 12.60 11.80 12.70 12.40 14.00 12 3.10 4.45 6.45 7.25 7.30 8.50 8.20 8.45 10.55 9.35 12.00 12.30 12.10 13.70 12.60 14.70 13 2.80 4.15 6.35 6.00 8.20 7.70 9.35 8.25 9.70 10.65 10.65 12.15 12.20 13.30 13.95 13.80 14 3.60 4.30 6.00 7.20 7.45 8.20 8.90 8.15 10.20 11.50 11.40 11.80 12.90 12.45 14.25 14.80 15. 2.85 4.90 6.05 6.70 7.75 7.85 8.60 9.35 10.55 10.55 12.35 11.10 12.55 12.00 13.90 15.05 16 2.40 4.05 5.75 7.10 7.45 8.15 8.55 9.30 9.15 11.65 11.55 13.00 12.25 13.20 14.40 14.85 42 DISCUSSION The purpose of using ED scales is fo render stimuli selected for absolute judgment tasks discriminably equal. Use of this scale avoids the distortion inherent in results calculated from data pooled from Ss where each response category is not used with the same frequency. As a result of minimizing judg-mental error information transfer is maximized. Garner (1953) claimed to show this to hold for absolute judgment of loudness. For stimuli selected from ED scales, Hj was 1.62 bits compared with 1.53 bits when stimuli were based on equal physical intervals. In the present study, the corresponding val ues were 1.68 and 1.89 bits. Thus a reversal of Garner's (1953) results were obtained. However, the question: must be asked as to whether the difference in the two val ues reported by Garner and the difference found in the present study are meaningful differences. Perhaps, since the values are rather small, a con-clusion can be made that the ED scale has no large effect on Hj when comp-ared to the corresponding value obtained from equal physical intervals. In terms of Hj values reported in Table II, perfect transmission did not occur and thus at no stage did Ss receive sufficient information from the stimulus alone to elicit the correct response. Garner (1953) suggests that a convenient way to look at information transfer when calculated from data pooled from Ss is in terms of 'judgmental complexity1. As the number of stimulus categories increases, the task of Ss in selecting the appropriate response becomes more difficult or complex. This is so because discriminability between adjacent simuli becomes more difficult resulting, ultimately, in the inability of Ss to keep each response number associated with its appropriate stimulus category. It is also convenient to consider the input variables as predictors of the response. Thus, looking at the present results in terms of predictability of response, a knowledge of the stimulus alone was insufficient to predict the response. However, 43 perfect transmission has been reported in a number of studies including Garner (1953) for judgment of loudness and Marteniuk (1971) for judment of amplitude of movement. Both these investigators obtained an initial rise of information transfer for low judgmental complexity. In Garner's case, this rise was the result of perfect transfer at 4 and 5 categories. In Marteniuk's study, perfect transfer occurred at 4 categories but the rise was to less than perfect transfer at 6 categories. In both cases this initial rise was followed by a subsequent decline. Thus it seems likely that if experiments using fewer categories had been included in the current- study, a similar trend may have been detected. While there is, presently, no way to substantiate this possibility, it would help to account for the low information transfer in that 6 categories would be a point in the decline noted in the Garner and Marteniuk studies. Nevertheless, it is apparent from Figure 4 that the effects of the input variables or predictors of Ss' choice of response are greater as judgmental com-plexity increases. In other words, in order to predict the response, knowledge of Ss and the previous stimulus becomes increasingly important as the number of stimulus categories increases. Another interesting result obtained by inspection of Figure 4 is the fact that the curves have no tendency to asymptote. This is contrary to the findings for other modalities. For instance Pollack (1952) obtained asymptote at about 5 stimulus categories for absolute judgment of pitch and Garner (1953) at a similar level for loudness. For visual interpolation of a marker on a horizontal scale Hake and Garft'erf:" (1951) obtained asymptote at about 10 cat -egoriesJ This asymptotic phenomenon, or channel capacity, has been regarded as a measure of the limited nature of the various sensory systems of the body to trans-mit information. Garner (1962:17) suggested that the concept of channel capacity is shown to be valid for unidimensional stimuli and Miller's review (1956) has shown that this asymptote occurs at approximately 2.5 bits for unidimensional stimuli. 44' Thus, the fact that the present results do not demonstrate an asymptote on information transfer presents several points for discussion. Simply viewed, these results suggest that channel capacity of the kinesthetic system for trans-mitting information about torque occurs at beyond 16 stimulus categories. In the light of the evidence concerning other modalities this seems unlikely. How-ever, there are a number of possible explanations for the failure of the present results to asymptote and for the rise of H T up to 16 categories. The first relates to information bias. MacRae (1970) points out that information trans-mission estimates are likely to be biased on the high side when large numbers of stimulus categories are used. But, because MacRae (1970) argues for a decline in true Hj, it seems unlikely that the rise seen in Figure 4 can be totally accounted for by information bias. He would suggest that caution should be used in interpreting this,. rise because of the objections regarding pot-ential bias. It is possible, therefore, that at least some of the terminal rise in the present study is the result of information bias. The second possible reason for the terminal rise which has already been implied, is that as judgmental complexity increases, Ss depend more on input variables which are not inherent in the stimulus itself in making their response. Examples of these potential input variables are the previous stimulus and, poss-ibly, the previous response and combinations or interactions of these. Garner (1962) mathematically defines combinations of input and variables in such cases as the present. Thirdly, as judgmental complexity increases, information derived from other than torque cues may be used by Ss in determining their response. These add-itional cues could originate at a number of sources. The most obvious are amp-litude of movement and tactile in nature. In order for amplitude to be a source of usable information for the Ss of the present study, it would have to be shown that the differences in the movements of the handle of the apparatus as it was moved to induce different torques could be consciously perceived. As was des-45 cribed in the Method section above, the maximum distance Ss were required to move the handle was 12 mm. As 12 mm. converts to .29°, the difference between this maximum value and the minimum movement was less than .29°. Studies that bear on the problem of whether differences of this magnitude are above Ss' DL were one by Laidlaw and Hamilton (1937) who reported a DL of .4° for passive elbow flexion and another by Shields (1970) who showed that movement DLs ranged from 1.42° to 2.13° depending on the extent of the shoulder movement used. Thus it would appear that the difference in the move-ments involved in the present study are well below reported DLs for movement amplitude and it can therefore be concluded that movement did not contribute to the present results. In terms of whether tactual cues could be used as a source of information, Henry (1953) reported that they appear to be unimportant compared to kinesthetic cues. To support his argument he reported a Weber Ratio for resistance to move-ment of .061 and compares this to a Weber Ratio for cutaneous pressure of .136. From the above discussion, then, the reason for the obtained terminal rise in information transfer is unclear. The above evidence suggests that movement amplitude does not contribute to the present results. However, there is definitely not enough available evidence to indicate whether tactual cues are available in judgments of the type used in the present study. Taking the facts collectively, it is tentatively concluded that the terminal rise in information transfer could have been caused by a combination of information bias and supplementary information provided by the tactile sense. Even though the reported Weber's Ratio for tactile sense was less than that for torque it seems logical that for Ss in the present study to maintain a relatively accurate response with increasing judgmental comp-lexity, they were required to attend to any potential cues available to them. It is under these circumstances that tactual cues may have provided a small amount of information. 46 Behavioral evidence suggests that the difference between Marteniuk's (1971) results and those of the present study is, in fact, a real difference. Jenkins (1947) reported a Weber's Ratio of .06 for force reproduction while Woodruff and Helson (1965) report data which permits a Weber's Ratio of .06 to be calculated for torque. On the other hand, Weber's Ratios of .05 and .043 to .012 for movement have been reported by Goldscheider (1899) and Shields (1970) respectively. It seems likely, then that the capacity of the kinesthetic system to transmit information derived from torque is less than from amplitude of movement. This conclusion is consistent with the findings of Briggs, Fitts and Bahrick (1957) that while amplitude and force cues signific-antly affect performance on a tracking task, amplitude had the greater effect. Before the comparison between the present results and those of Mart-eniuk (1971) could be made, it was necessary for the data of the present study to be analysed in a manner similar to that used by Marteniuk. In essence, the Hy between stimulus and response was calculated for each S separately and then averaged (Figure 5). This procedure is in contrast to the analysis used to this point.in that they involved pooling all Ss' data before calculating information measures. As can be seen in Figure 8 the values for torque are consistently lower than those for amplitude of movement. That torque rises relatively close to amp-litude at 16 categories is probably the result of the factors already explained. Thus in the light of this comparison and the other evidence presented above it can be concluded that torque seems to provide less kinesthetic information than amp-litude. There are implications of this conclusion relative to the control of movement. First, the kinesthetic sense can provide information for the discrimination of torque on a similar basis to amplitude of movement but at a lower level. Second, if this information available to S is thought of as sensory feedback, it will be available 4 .0 j§ 3.0 < 2.0 Id 1.0 PERFECT H T ^ AMPLITUDE 8 10 12 14 16 NUMBER OF STIMULUS CATEGORIES Figure 8: Mean information transfer per subject for amplitude of movement (Marteniuk, 1971), and for torque. 48 for S to regulate skilled movement. Gibbs (1954:24) suggests that movement 'may be regulated by sense date which are always being fed back from a limb1. Almost all models of human motor behavior incorporate feedback result-ing from a response as a vital part of monitoring and control functions (von Hoist, 1954; Welford, 1960; and Chase, 1961a, 1961b). Chase, for instance, requires the perception of response-produced afference for the error detection and correction functions of his information-flow model; von Hoist requires, what he terms 'reafference' to compare with 'efference copy'. That torque can provide some in-formation concerning sensory feedback further supports Marteniuk's (1971:76) conclusion that the "inclusion of kinesthesis as a basis of correlating actual output with intended output, as for example in the model for voluntary movement suggested by von Hoist (1954), seems warranted". The final point of discussion concerns the influence of kinesthetic after effect (KAE) on the results of the present study. This influence is such that any response toca stimulus is affected by memory traces of previous stimuli and responses. Norrie (1968, 1969) reports that the overshooting evident when force reproduction follows the presentation of the standard by up to 30 sec. may be the result of KAE. Since evidence reported by Adams and Dijkstra (1966) places a 30 to 60 sec. limit on short term motor memory it would seem reasonable to conclude that KAE might occur when a second stimulus is presented within 60 sees, of a previous stimulus. In the present study the intertrial interval was approximately 10 sec. so the memory trace from the previous stimulus would still be available when a stimulus was presented. To support this viewpoint the present results show that the intensity of the previous stimulus affected Ss' current responses and this can be seen by in-spection of Tables III and IV. As an example, in Table III, when stimulus cat-egory 3 was presented and the previous stimulus was of intensity 1 the mean response was 2.68; but when the previous stimulus was of intensity 6 the mean response was 3.48. In other words, given the same stimulus, the greater the intensity the prev-ious stimulus, the higher the current response while on the other hand the lower the 49 intensity of the previous stimulus, the lower the current response. Now, because a KAE was apparent it seems that the memory trace of the previous stimulus was influencing the S's judgments. It follows that the transfer of information between stimulus and response would be reduced. In support of this, evidence from Norrie (1969) and Shields (1970) suggests that error associated with the immediate reproduction of movement is less than that associated with the immediate reproduction of force. For movement reproduction error ranges from .06% to 2.23% for 125° and 45° standards respectively. For force reproduction the value is 17.2% for a single presentation of the stimulus prior to reproduction and 6.47% for five presentations for a 2000 gm standard. Thus, since the memory trace of the previous stimulus would interfere more with judgments of torque than with judgments of movement it follows that the information transfer for movement should be greater. In fact, reference to Figure 8 shows this to be the case in that Marteniuk's (1971) results for information transfer of movement amplitude are considerably more than those values from the present study. Nevertheless, it appears unlikely that KAE can account for all this difference and it must be con-cluded the capacity of the kinesthetic system to transmit sensory information from cues associated with the perception of torque is probably less than that from the perception of amplitude of movement. CHAPTER V SUMMARY AND CONCLUSIONS The purpose of this study was to determine the capacity of the kinesthetic system to transmit information from stimuli associated with the perception of torque. Five male university student volunteers participated in seven absolute judgment experiments. In Experiment I, sixteen stimulus and sixteen response categories were used and the data used to construct an equal discriminability scale for each S. In this experiment stimuli were selected from a scale of in-tervals of equal physical dimensions. These scales were used to determine stimulus intensities for each of the remaining experiments. These latter six experiments were absolute judgment tasks with six, eight, ten, twelve, four-teen and sixteen stimulus categories respectively. For each of these latter experiments, information transfer was calculated with stimuli, subjects and previous stimuli as the input variables and S's responses as the output variable. When the data were viewed in terms of trying to predict S's response, it was found that each input variable added to the power of prediction in that inform-ation transfer from stimuli, stimuli and subjects, and stimuli, subjects and prev-ious stimuli was at a maximum of 1.680, 2.050 and 2.524 bits respectively. When information transfer was plotted against the number of stimulus categories, no tendency to asymptote was observed with a maximum transfer occurring at 16 categories. The mean information transfer between stimulus and response per subject were calculated for the two experiments consisting of sixteen stimulus categories to determine if information transfer was greater for stimuli separated by subjectively equal intervals, i.e. derived from equal discriminability scales, compared with those separated by physically equal intervals. The evidence seemed to suggest that there was very little difference in that the information transfer was 1.68 and 1.89 bits respectively. 50 51 To examine the influence that the kinesthetic after effect had on the judg-ment of stimuli, the mean response for each stimulus was calculated separately for each previous stimulus. It was found that the mean response to each stimulus category tended to increase as the intensity of the previous stimulus increased indicating that a KAE was present. The conclusions were as follows: 1. That the kinesthetic system can transmit information derived from cues associated with the inducement of torque. 2. That torque-derived sensory information/may be available for the control of movement under the terms of the closed-loop model of human behavior. 3. That the use of a scale of equal discriminability does not appear to affect information transfer from the perception of torque. 4. That kinesthetic after effect appears to affect judgments made on the intensity of a torque stimulus. Recommendations. 1. In studies involving the absolute judgment of torque, perfect transfer must be obtained to provide a base-line value for comparison of transfer in other experiments. To achieve this result experiments with 3 and 4 stimulus and response categories should be included. 2.. As the capacity of the kinesthetic system to transmit both torque and amplitude information has now been measured, further studies shouldJbe undertaken to determine if the combination of these two dimensions of kinesthesis leads to higher information transfer than either separately. 3. Some method of reducing or removing tactual cues must be found to be sure that when measuring the capacity of the kinesthetic system to transmit torque information tactual cues do not confound the results. 52 4. Further study should be made to determine if intertrial intervals of dur-ations greater than short term memory for torque increases information transfer. The assumption is made that if this is done the influence of kinesthetic after effect is controlled. 5. The procedures for calculating information transfer suggested by Garner (1953) and used in the present study require the pooling of data from Ss. Therefore, they yield only one dependent measure for each of the number of stimulus categories used, and tests of statistical significance cannot be performed on the data. Because of the resultant difficulty in interpreting results it is recommended that information transfer between the various input variables and the response be calculated for each S separately. 53 REFERENCES Adams, J . A., Human Tracking Behavior, Psychological Bulletin, 58:55-79, 1961. Adams, J. A., Motor Skills, Annual Review of Psychology, 15:181-202, 1964. Adams, J. A., Response Feedback and Learning, Psychological Bulletin, 70:486-504, 1968. Andrew, B. L., The Sensory Innervation of the Medial Ligament of the Knee Joint of the Cat, Journal of Physiology, 123:241-250, 1954. Attneave, F., A Method of Graded Dichmotomies for the Scaling of Judgments, Psychological Review, 56:334-340, 1949. Bahrick, H. P., Bennett, W. 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Gardner, E., Spingal Chord and Brain Stem Pathways for Afferents from Joints, In A. V. de Reuck and Julie Knight (Eds.), Myotatic, Kinesthetic and Vestibular Mechanisms, CIBA Symposium, London, J. and A. Churchill Ltd., 1966. Garner, W. R., An Informal Analysis of Absolute Judgment of Loudness, Journal of Experimental Psychology , 46:373-380, 1953. 55 Garner, W. R., Uncertainty and Structure as Psychological Concepts, New York: John Wiley and Sons Inc., 1962. Garner, W. R.7 and Hake H. W., Amount of Information In Absolute Judgments, Psychological Review, 58:446-459, 1951. Gibbs, C , The Continuous Regulation of Skilled Response by Kinesthetic Feedback, British Journal of Psychology, 45:24-39, 1954. Gibbs, C. B., and Baker, J . C. Free Moving versus Fixed Control Levers in a Manual Tracking Task, In A. Tustin (Ed.), Automatic and Manual Control, London: Butterworth. Scientific Publications, 1952. Goldscheider, A., UnterduchlIngen uber den Muskelsinn, Archives of Anatomy and Physiology (Lpz) 392-502, 1899. Hake, W. H. and Garner, W. R., The Effect of Presenting Numbers of Discrete Steps onca Scale of Reading Accuracy, Journal of Experimental Psycho logy 42:358-366, 1951. Henry, F. M., Dynamic Kinesthetic Perception and Adjustment, Research Quarterly, 23:176-189, 1953. Henry, F. M., and Norie, M. L. An Apparatus for Kinesthetically -Monitored Force Reproduction Tasks, Research Quarterly, 89:797-799, 1968. Hick, W. E. On the Rate of Gain of Information, Quarterly Journal of Experimental Psychology, 4:11-26, 1952. Howard, I. P.; and Templeton, W. B. Human Spatial Orientation, New York: John Wiley and Sons Publiching Co., 1966. Ch. 4. Jenkins, W. O., The Discrimination and Reproduction of Motor Adjust-ments with Various Types of Aircraft Controls, American Journal of Psychology, 60:397-406, 1947. Kerr, B. A., Weight and Velocity Factors in Kinesthetic Learing and Transfer of Training. Unpublished Doctoral Dissertation, University of Wisconsin, 1967. Klemmer, E. T., and Frick, F. C , Assimilation of Information from Dot and Matrix Patterns, Journal of Experimental Psychology, 45:15-19, 1953. 56 L-aszIo, Judith, I., The Performance of a Simple Motor Task with Kinesthetic Sense Loss, Quarterly Journal of Experimental Psychology, 17:1-8, 1966T Laidlaw, R. W. and Hamilton, M. A., A Study of Thresholds in Apperception of Passive Movement Among Normal Control Subject, Bulletin of the Neurological Institute of New York, 6:268-273, 1937. Levy, Paul, Variables Affecting the Accuracy of Limb Positioning, Unpublished Doctoral Dissertation, University of Pittsburgh, 1967. McDermid, C. and Smith, K. U., Compensatory Reaction to Angularly Displaces Visual Feedback in Behavior, Journal of Applied Psychology, 48:63-68, 1964. McGil l , W. J . , Multivariate Information Transmission, Psychometrica, 19:97-116, 1954. MacRae, A. W., Channel Capacity in Absolute Judgment Tasks: An Artifact of Information Bias? Psychological Bulletin, 73:112-121, 1970. Marteniuk, R. G., An Informational Analysis of Active Kinesthesis as Measured by Amplitude of Movement, Journal of Motor Behavior, 3:69-77, 1971. • Miller, G. E., The Magical Number Seven, Plus or Minus Two, Psychological Review, 63:81-97, 1956. Mott, F. W. and Sherrington, C S., Experiments Upon the Influence of Sensory Nerves Upon Movement and Nutrition of the Limbs, Proceedings of the Royal Society, 57:481-488, 1895. Mountcastle, V. B., Covian, M. R. and Harrison, C. R., The Central Representation of Some Forms of Deep Sinsibility, Research Bulletin Of Association for Nervous and Mental Disorders, 30:339-360, 1950. Mountcastle, V. B., Poggio, G. V. and Werner, G., The Relation of Thalamic Cell Response to Peripheral Stimuli Varied Over an Intensive Continuum, Journal of Neurophysiology, XXVI:804-834, 1963. Mountcastle, V. B. and Powell, T.P.S., Central Nervous Mechanisms Subserving Position Sense and Kinesthesis, Johns Hopkins Medical Bulletin, 108:173-200, 1959. Norrie, Mary Lou, Short-Term Memory Trace Decay in Kinesthetically Monitored Force Reproduction. Research Quarterly, 39:640-646, 1968. 57 Norrie, Mary Lou, Number of Reinforcements and Memory Trace for Kinesthetically Monitored Force Reproduction, Research Quarterly, 40:338-342, 1969. Orlansky, J . , Psychological Aspects of Stick and Rudder Controls in Aricraft, Aeronautical Engineering Review, 8:22-31, 1949. Pollack, I., Information of Elementary Auditory Displays, Journal of the Accoustics Society of American, 24:745-479, 1952. Pollack, I., The Information of Elementary Auditory Displays, II, Journal of the Accoustics Society of America, 25:765-769, 1953. Rallston, H. J . , Recent Advances in Neuromuscular Physiology, American Journal of Physical Medicine, XXXVI:94-l 19, 1957. Rose, G. E. and Mountastle, V. B., Touch and Kinesthesis, In Handbook of Physiology, Section I, Volume I, Neurophysiology, Washington, D.C: American Physiological Society, 1961. Saffir, M. A., A Comparative Study of Scales Constructed by Three Psycho-physical Methods, Psychometrika, 2:179-198, 1937. Shannon, C. E. and Wever, W., The Mathematical Theory of Commun-ication, Urbana, III: University of Illinois Press, 1949. Sheilds, K.W.D., Kinesthetic Sensitivity to Amplitude of Active Movement of the Shoulder Joint. Unpublished Masters Theses, University of British Columbia, 1970. Skoglund, S., Anatomical and Physiological Studies of Knee Joint Innervation of the Cat, Acta Physiologica Scandinavia, Supplement 124, Vol. 36, 1956. Smith, A. H., Effects of Continuous and Intermittent Feedback on Precision on Applying Pressure. Perceptual and Motor Skills, 17:883-889, 1963. Smith, Judith L., Kinesthesis: A Model for Movement Feedback, in R. C. Brown and B. J . Cratty (Eds.) New Perspectives of Man in Action, Englewood Cliffs: Prentice Hall Inc., 1969. Telford, C. W., The Refractory Phase of Voluntary and Associative Reponses, Journal of Experimental Psychology, 14:1-36, 1931. Stopford, I.S.P., Journal of Anatomy, 56:1-11, 1921. 58 Twitchell, T. E., Sensory Factors in Purposive Movement, Journal of Neurophysiology, 17:239-252, 1954. Vince, M. A., The Intermittenty of Control Movements and the Psycho-logical Refractory Periods, British Journal of Psychology, 39:149-151, 1948. Welford, A. T., The "Psychological Refractory Period" and the Timing of High-speed Performance - A Review and a Theory, British Journal  of Psychology, 43:2-19, 1952. Welford, A. T., The Measurement of Sensory-Motor Performance: Survey and Reappraisal of Twelve Years Progress, Ergonomics, 3:189-230, 1960. Welford, A. T., Fundamentals of Skill, London: Methuen, 1968. Weiss, B., The Role of Proprioceptive Feedback in Positioning Responses. Journal of Experimental Psychology, 47:215-224, 1954. Wever, E. G. and Zener, K. E., The Method of Absolute Judgment in Psychophysics, Psychological Review, 35:446-493, 1928. Woodruff, B. and Helson, H., Torque: A New Dimension in Tactile-Kinesthetic Sensitivity, American Journal of Psychology, 78: 271-277, 1965. Woodworth, R. S. and Scholsberg, H., Experimental Psychology, (Revised ed.), New York: Holt, Rhinehart and Wilson, 1954. McGi l l , W. J . , Serial Effects in Auditory Threshold Judgments, Journal of Experimental Psychology, 53:297-303, 1957. 59 APPENDIX A TREATMENT OF DATA Details for calculating scales of equal disciminability may be found in Garner and Hake (1951). Calculation of Information Transfer The following terms are used in the description of the calculations: St: Stimulus - v : Number of stimulus categories Frequency of occurrance of a specific category, Vj, i = 1,2, ...,v. S : Subject - w : Number of subjects W J : Specific subject, Wj, j = 1,2, ...,w P : Previous St - x : Number of previous stimulus categories x^: Frequency of occurrance of a specific category, x^, k = 1,2, ...,x R : Response - y : Number of response categories VL, : Frequency of occurrance of a specific cvi category, y^, h = l,2,...,y H : Information Hj: Information transfer 60 Calculation of Information Between St and R. This calculation is performed on an St x R matrix, where H(St) = log2V y H(R) =* p(h) log 2 p(h) and H(Sr,R) = ~ L X, P(ih) log2 p(ih) i = l h = l ... 1(iii) H(St) is the stimulus (input) information, H(R) is the response (output) information, and H(St,R) is the sum of HR(St), which represents input inform-ation lost in transmission and Hg (R), which represents "noise" transmitted from the system. Calculation of Hy^ (S:R). This term is referred to in the text as Hy(S:R) for reasons of conceptual simplicity, and is the information transfer between S and R with St Held constant. The calculations are performed on an S x R x St matrix i.e. an S x R matrix for each stimulus category, and the mean Hy per stimulus category computed. V HTSf(S:R) I Hy (S:R)/v ...2 where HT(S:R) H(S) + H(R) - H(S,,R) ...2(i) H(S) ...2(ii) H(R) is calculated by formula l(ii) separately for each stimulus category matrix (vi, i=l ,2, ..., v) w y and H(S,R) =-I £ p(jh) log2 p(jh) ...2(iii) p(jh) is the cell frequency divided by the matrix total for the particular stimulus category. 61 Calculations of HT s t(P:R). This term is referred to in the text as H-r(P:R) for reasons of conceptual simplicity, and is the information transfer between P and R with St held constant. The calculations are performed on a P x R x St matrix i.e. A P x R matrix for each stimulus category, and then the mean Hj per stimulus category is computed. V HTst(P:R) HT(P:R)/v ...3 where H T (P:R) = H(P) + H(R) - H(P,R) ...3(i) H(P) = log 2 x ...3(ii) H(R) =• -hE p(h) log 2 p(h) ...3(iii) and H(P,R) = - j l £ p(kh)log2 P(kh) .. .3(iv) The value, H (R), as calculated in equation 3(iii), is actually an estimate of H(R) used by Garner (1953). Garner (1962:Ch3) and McGill (1957:299, 300) gives details of multidimensional information analysis. Calculation of the actual estimate of H(R) is: H(R)= hE p(kh) log 2 p(kh)/x] ...3(iii)a Other references relating to informational analysis such as the one used in this study are Attneave (1959), Garner and McGill (1956) and McGill (1954). 62 APPENDIX B INDIVIDUAL SCORE SHEETS Q, w • 5 7 - •• Z> 5 / 7 i ! . 1 L 1 i '~> 3 f i- * 1 5 7 4-/ 4- I ' 1 / i 5 ! » B 7 •7 2 7 8 7 3; i f 6 1 5" >-! / to 7 / 1 t 7 I 7 / ? Z 9_ % 6 \ /o i. i ! 1 3 f l f • i 1 f: i si-io : f f ? 7 Io 7 /o f 7 - X G 2. 2 . 1 b 7 z 3 9 2-h 6 it / 8 4- fo t> / fo i to 3 Io f 7 / 7 1 fo 2 1 / fo 3 fo 7 ? 9 z 1 t t 7 II /' i /2 I t b 7 fo 7 3 7 2 1 lo C2- <? i ! I 1 I X i i 9 9 1 " * i 3 / i * 7 / ... 3 | / r a i •7 ! fl i 3 6 i 2. 3 v- 7 s-. 9 S 9 7 2 - f <h io •i 7 2 -c? 1 // 7 / < ^ z 3 2 .2 // CO to l / o 1 °l 7 II 1 7 1 / tfm-ui: IS 7ew'xviryu %uf rf & 5 9 1 2 7 Z 3 > 9 II H n , , i i j it CP i i > 7 ' i 1 i 2 </ • Ii 2 • . • • • . - , 1 t 9 I 3 IZ ! li 1 9 2 . fo i ! 7 a i ILL so 3 |? ? : 1 7 //-F... . . . _ „ 4 . i j 4 .. 1 ' ^ ! I/? > t \ -4-j 0 ^ .r , • -3 10 II 2 1 1 _ X 1 // 1 3 It 14- 1 10 % 5 • ll 1 I 1 1 15 II 4 9 5 \n *j 9 1* f I 11 12 13 / i? f i 3 •1: ?' / i j i It It </• it to •rl •h 7 n ? C '3 •?: 1/ i 1 if Ii i iq •-2. 7 i i • A 2- Iv 1 " , ' - v N a m e — S 6 1g.nVUDi 'V^ _ S h e e t j Kfa-rTficj: \it> Tensions 5 (tecV'fJL 11 4 , 2 II 1 4 - / f 9 i 4 - / f . ! \ 1 ' 2 1 /£> -5 12 ,, • 13 9 I f 7 . 7 13 1 » /* ll 7 3 i 5 < ? / II ! 8 • i ! ! ! 1 Q i 7 7 9 2 12 h 9 10 ii ? 2 •1 a I f 9 } tt 10 -7 6 i ! B 5 10 9 j II 3 II / / 12 Kr in i i 3 & ) f i .., 1 1 1 1 i II (, IH 1 ) ! l(o Ii-1 ii i i 8 i (o • 1 | 1 - , ~ J 1? lo 2 1 i /o ti- 2 ll / / 2 7 ' t 1 1 1 • 3 7 j i U B a II 2 i l • IL in- 7 -i i ^ 0 * 


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