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The application of statistical decision theory to a perceptual decision-making problem Papsdorf, James Daniel 1962

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THE APPLICATION OF STATISTICAL DECISION THEORY TO A PERCEPTUAL DECISION-MAKING PROBLEM JAMES DANIEL PAPSDORF A Thesis Submitted i n P a r t i a l Fulfilment of the Requirements for the Degree Of Master of Arts in the Department of Psychology We accept t h i s thesis as conforming to the standard required from candidates for the degree of MASTER OF ARTS Members of the Department of Psychology The University of B r i t i s h Columbia Aiigust, 1 9 6 2 In presenting t h i s thesis i n p a r t i a l f u lfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood 'that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of ^/^AM^Oi/-The University of B r i t i s h Columbia, Vancouver 3, Canada. Date C ^ / W ABSTRACT The object of t h i s study was to determine whether s t a t i s t i c a l d e c i s i o n theory, or a s p e c i a l a p p l i c a t i o n of i t , the theory of s i g n a l d e t e c t i o n , could he of value i n accoun-t i n g f o r the behaviour of subjects i n a perceptual d e c i s i o n -making task. The amount of information i n these tasks was v a r i e d to see i f the theory could p r e d i c t changes i n subject performance. Fi v e subjects were re q u i r e d to d i s t i n g u i s h between f i f t y percent time compressed recordings of the stimulus words "commination" and "comminution 1 1 embedded i n "white" n o i s e . Under one treatment, compression was gained by d i s c a r d i n g many small l e t t e r segments whi l e i n the other t h i s same compression value was obtained by d i s c a r d i n g a few l a r g e l e t t e r segments. I t was hypothesized that l a r g e -d i s c a r d - i n t e r v a l compression would be more detr i m e n t a l to stimulus i n t e l l i g i b i l i t y than s m a l l - d i s c a r d - i n t e r v a l com-p r e s s i o n . F i v e other subjects were asked to d i s t i n g u i s h between the two noise-embedded stimulus words which had been time-compressed s i x t y and seventy-four percent. I t was p r e d i c t e d that s i x t y percent compression would be l e s s detrimental to the i n t e l l i g i b i l i t y of the stimulus words i i than seventy-four percent compression,, Concurrently, i n both groups, an attempt was made to manipulate the degree of cautiousness or decision c r i t e r i a of a l l ten subjects. Such manipulation was attempted i n order to permit the separation of each subjects' actual sensi-t i v i t y from each's variable decision c r i t e r i o n . This manipu-l a t i o n involved varying the costs and fines associated with correct and incorrect decisions as well as the p r o b a b i l i t i e s of each stimulus word's occurrence. Large-discard-interval compression was found to be less detrimental to i n t e l l i g i b i l i t y , as inferred from subject performance, than small-discard-interval compression. This finding was contrary to the f i r s t hypothesis. Sixty percent compression, as predicted, was less detrimental to i n t e l l i g i -b i l i t y than seventy-four percent compression. It was observed that the theory of signal detection permitted separation of each subjects' s e n s i t i v i t y from his monetary degree of cautiousness. This cautiousness was also found to be accessible to manipulation. It i s suggested that since the approach of s t a t i s t i c a l decision theory detected changes i n subject per-formance i n response to varying amounts, of information, i t can be p r o f i t a b l y applied to the study of perception. ACKNOWLEDGEMENT The w r i t e r would l i k e to express h i s g r a t i t u d e to Professor M. P. Beddoes f o r the advice and encouragement received during the course of t h i s study. Thanks are also due to the Department of E l e c t r i c a l Engineering and the Nati o n a l Research Council f o r t h e i r generous f i n a n c i a l support. i TABLE OF CONTENTS C h a p t e r Page ABSTRACT i I INTRODUCTION AND STATEMENT OF THE PROBLEM 1 I I THEORETICAL AND EXPERIMENTAL BACKGROUND. 3 E a r l y H i s t o r y . . . . . . . . . . . . 3 The T h e o r y o f S i g n a l D e t e c t i o n . . . 5 (1) S t a t i s t i c a l D e c i s i o n T h e o r y . . 5 ( 2 ) The T h e o r y o f S i g n a l D e t e c t i o n 9 E x p e r i m e n t a l R e s u l t s w i t h t h e T h e o r y o f S i g n a l D e t e c t i o n 2 0 (1) The T h r e s h o l d a n d t h e V a r i a b l e C r i t e r i o n 2 0 ( 2 ) The D e t e c t i o n o f C o m p l e x S i g n a l s . . . . . 2k The Time C o m p r e s s i o n o f S p e e c h . . . 2 6 H y p o t h e s e s 27 I I I METHOD 31 S t i m u l u s M a t e r i a l . . . . . . . . . . 31 S u b j e c t s 3k I n s t r u c t i o n s 35 A n a l y s i s o f t h e D a t a 3 8 Chapter Page IV RESULTS . . . • • . . • • . . < > » . . . 39 Complex A 39 Complex B . k6 v D I S C U S S I O N . -. \ -. ; -. . '. . ; . . . " 53 APPENDICES A Stimulus M a t e r i a l . £>0 B Data of Complex A. . 64 C Data of Complex B i ' 7 1 REFERENCES 7 8 L I S T O F T A B L E S T A B L E . . . . P A G E 1 T a b l e o f E x p e r i m e n t a l T a p e s C o n s t r u c t e d 33 2 C o r r e l a t i o n B e t w e e n O b t a i n e d F a l s e A l a r m R a t e s ' a n d O p t i m a l B' V a l u e ' s - -A C o m p l e x . . . . . . . k$ 3 C o r r e l a t i o n B e t w e e n O b t a i n e d F a l s e A l a r m R a t e s a n d O p t i m a l ' B V a l u e ' s --' B C o m p l e x 5 2 LIST OF FIGURES FIGURE PAGE 1 Graphic Representation of two hypotheses 6 2 The Decision Axis i n r e l a t i o n to two hypotheses. 6 3 A lenient dec is. ion .axis versus, .a . . . s t r i c t decision axis 6 k Venn diagram of space of a l l possible observations. . .. .. ., 12 5 Graph p l o t t i n g the p r o b a b i l i t y an observation arose from a given source versus the l i k e l i h o o d r a t i o axis. . . . 12 6 Graph, p l o t t i n g the p r o b a b i l i t y an observation will^promote a correct response versus a transformed l i k e l i h o o d r a t i o axis 12 7 Theoretical ROC curves as a function of stimulus d i f f e r e n t i a t i o n 17 8 SOC curves obtained from 5°% compression, unrevised data. . . . . . . kl 9 ROC curves obtained from 5°% compression, unrevised data k2 10 ROC curves obtained from 50$. compression, revised data . . . . . . . 43 11 ROC curves obtained from 50$ compression, revised data . . . . . . . kk 12 ROC curves obtained from 6ofo and jkfo compression, unrevised data . . . . 4^-8 13 ROC curves obtained from 6of0 and "}tyj0 compression, unrevised data . . . . k9 Ik ROC curves obtained from 60$ and fkfo compression, revised data 50 15 ROC curves obtained from 60% and compression, revised data 51 C h a p t e r I INTRODUCTION AND STATEMENT OF THE PROBLEM The c e n t r a l i s s u e o f t h i s s t u d y i s w h e t h e r s t a t i s t i c a l d e c i s i o n t h e o r y c o u l d h e o f v a l u e i n p r e d i c t i n g a n d a c c o u n t i n g f o r t h e b e h a v i o u r o f s u b j e c t s c o n f r o n t e d w i t h a p e r c e p t u a l d e c i s i o n - m a k i n g s i t u a t i o n . W h i l e s t a t i s t i c a l d e c i s i o n t h e o r y h a s p r o v e n i t s w o r t h when a p p l i e d t o s i m p l e s i g n a l d e t e c t i o n s t u d i e s , t h e r e a r e v a l i d r e a s o n s f o r s u g g e s t -i n g t h a t i t w i l l be o f e q u a l e f f i c a c y i n d e s c r i b i n g t h e p r o c e s s e s i n v o l v e d i n i i e r c e p t i o n . The s a l i e n t f e a t u r e o f s t a t i s t i c a l d e c i s i o n t h e o r y i s t h a t i t r e c o g n i z e s t h e e x i s t e n c e o f , and a t t e m p t s t o m a n i -p u l a t e , t h e c r i t e r i o n t h a t i n d i v i d u a l s a d o p t i n m a k i n g d e c i s i o n s . T h i s c r i t e r i o n , w h i c h m i g h t be c o n c e p t u a l i z e d a s t h e d e g r e e o f c a u t i o u s n e s s e x i s t i n g w i t h i n a n i n d i v i d u a l , i s v a r i e d b y c h a n g i n g t h e m o n e t a r y c o s t s a n d r e w a r d s a s s o c i a t e d w i t h i n c o r r e c t and c o r r e c t d e c i s i o n s r e s p e c t i v e l y , a n d a l s o b y c h a n g i n g t h e c o m m u n i c a t e d a p r i o r i p r o b a b i l i t i e s o f s t i m u l u s o c c u r r e n c e . B e s i d e s a c k n o w l e d g i n g t h e e x i s t e n c e o f t h i s v a r i a b l e c r i t e r i o n f o r d e c i s i o n m a k i n g , s t a t i s t i c a l d e c i s i o n t h e o r y i s a l s o c o n c e r n e d w i t h t h e amount o f i n f o r m a t i o n a s u b j e c t r e c e i v e s i n t h e p r o c e s s o f a r r i v i n g a t a d e c i s i o n . I f , as 2 has heen suggested, the d i f f e r e n c e between sensation and perception i s that the l a t t e r r e q u i r e s more inf o r m a t i o n than the former, then the d i s t i n c t i o n i s at best a r b i t r a r y f o r the two may be considered to l i e along a common continuum whose c h i e f dimension i s amount of information. To j u s t i f y , i n p a r t , t h i s suggestion that sensation and perception occupy a common continuum, amount of informa-t i o n , i t would be necessary to show that the methods a s s o c i a t e d w i t h s t a t i s t i c a l d e c i s i o n theory produce an observed f l u c t u a -t i o n i n performance when the amount of informat i o n i n two otherwise equal perceptual tasks i s v a r i e d . Such a demonstra-t i o n was attempted by two d i f f e r e n t methods. Concomittantly, the d e c i s i o n axes of the i n d i v i d u a l s p a r t i c i p a t i n g , i n these experiments were manipulated by d i f f e r e n t i c a l l y rewarding and f i n i n g c o r r e c t and i n c o r r e c t d e c i s i o n s and by changing the communicated a p r i o r i p r o b a b i l i t i e s of stimulus occurrences. Chapter I I THEORETICAL AND EXPERIMENTAL BACKGROUND E a r l y H i s t o r y The frequent appearances of impatience, d i s s a t i s f a c t i o n and d i s i l l u s i o n m e n t i n the recent p s y c h o l o g i c a l l i t e r a t u r e w i t h the v a r i o u s contemporary psychophysical methods u t i l i z e d i n determining thresholds and d i f f e r e n c e l i m i n s f o r the v a r i o u s sensory m o d a l i t i e s , have prompted a number of ps y c h o p h y s i c i s t s to adopt a t h e o r e t i c a l view and experimental approach d i r e c t l y from s t a t i s t i c a l d e c i s i o n theory. The l a t t e r i s a pu r e l y mathematical theory, f i r s t propounded by Neyman and Pearson (1933) and completed i n i t s most d e f i n i t i v e form by Wald (1950). I t s focus l i e s c h i e f l y on mathematically d e s c r i b i n g the most e f f i c i e n t procedure f o r t e s t i n g hypotheses. Engineers, such as Peterson, B i r d s a l l and Fox (195^-), concerned w i t h the problem of e v a l u a t i n g the performances of radar systems i n d e t e c t i n g s i g n a l s , were quick to see the p o t e n t i a l i t y of s t a t i s t i c a l d e c i s i o n theory and the r e s u l t a n t a p p l i c a t i o n became known as the theory of s i g n a l d e t e c t i o n . P s y c h o l o g i s t s such as Tanner and Swets who were i n clo s e con-t a c t w i t h the e a r l i e r mentioned engineers, recognized the g e n e r a l i t y of the theory of s i g n a l d e t e c t i o n and proceeded to t e s t i t s a b i l i t y i n d e s c r i b i n g the behaviour of human observers i n a s i g n a l d e t e c t i o n s i t u a t i o n . (Tanner and Swets, 1 9 5 ^ 5 Tanner and Norman, 1 9 5 ^ . ) Several of the concepts b a s i c to the theory of s i g n a l d e t e c t i o n and s t a t i s t i c a l d e c i s i o n theory were a n t i c i -pated by e a r l i e r p s y c h o l o g i s t s who possessed a mathematical o r i e n t a t i o n . Boring ( 1 9 5 0 ) p o i n t s out that Fechner was q u i t e engrossed w i t h the concept of p r o b a b i l i t i e s and the p o s s i b i l i t y t hat p o t e n t i a l gambling outcomes might be expressed i n terms of s a t i s f a c t i o n u n i t s , A knowledge of such u n i t s would permit the p r e d i c t i o n of a gambler's behaviour. A s i m i l a r p r e d i c t i o n i s attempted i n s t a t i s t i c a l d e c i s i o n theory though the problem of s a t i s f a c t i o n u n i t s or u t i l i t y i s avoided by assuming that the u t i l i t y of outcomes i s l i n e a r . (Thus, winning f i f t y cents would be twice as s a t i s f y i n g as winning twenty-five cents,) Thurstone ( 1 9 2 7 a , 1 9 2 7 b ) developed a law of comparative, judgment on the assumption that while i n d i v i d u a l s can order objects or concepts along any d e f i n e d dimension, the c o r r e l a t i o n between successive orderings i s never p e r f e c t but f l u c t u a t e s . The observed f l u c t u a t i o n s form the b a s i s of h i s psychometric s c a l e and can be found to have t h e i r counterpart i n s t a t i s t i c a l d e c i s i o n theory where a v a r y i n g d e c i s i o n c r i t e r i o n promotes the d e t e c t i o n of s i g n a l s p r e v i o u s l y missed. 5 T h e T h e o r y o f S i g n a l D e t e c t i o n (1) S t a t i s t i c a l D e c i s i o n T h e o r y S t a t i s t i c a l d e c i s i o n t h e o r y a t t e m p t s t o i d e n t i f y t h e b e s t s t r a t e g y o n e m i g h t a d o p t i n a s i t u a t i o n w h e r e a l a r g e n u m b e r o f s u c c e s s i v e d e c i s i o n s m u s t b e m a d e . T h e " b e s t " s t r a t e g y c o u l d b e s p e c i f i e d i n s e v e r a l d i f f e r e n t w a y s , s u c h a s a t t e m p t i n g t o m a x i m i z e t h e n u m b e r o f c o r r e c t d e c i s i o n s . S i n c e i n t h i s s t u d y t h e m o n e t a r y v a l u e s o f d e c i s i o n o u t c o m e s a r e m o s t i m p o r t a n t , t h e s t r a t e g y i n s u r i n g t h e m a x i m u m f i n a n c i a l o u t c o m e i s d e f i n e d a s t h e " b e s t , " T h e d e c i s i o n s i t u a t i o n i s t y p i c a l l y c o n c e p t u a l i z e d a s r e q u i r i n g a n i n d i v i d u a l t o c h o o s e f r o m o n e o f t w o h y p o t h e s e s o n t h e b a s i s o f i n f o r m a t i o n p r e v i o u s l y g i v e n h i m a n d i n f o r m a -t i o n o b t a i n e d f r o m o b s e r v a t i o n o f t h e d e c i s i o n s i t u a t i o n . T h e t w o h y p o t h e s e s , H y p o t h e s i s A a n d H y p o t h e s i s B , a r e r e p r e s e n t e d b y t h e t w o n o r m a l c u r v e s o f F i g . 1. T h e o r d i n a t e r e p r e s e n t s t h e p r o b a b i l i t y t h a t s e n s o r y i n f o r m a t i o n a r i s i n g f r o m t h e m a n y , d i f f e r e n t , p o t e n t i a l o b s e r v a t i o n s o f t h e d e c i s i o n s i t u a t i o n w i l l p r o m o t e a c o r r e c t r e s p o n s e . T h e a b s c i s s a r e p r e s e n t s a m a t h e m a t i c a l t r a n s f o r m a t i o n o f t h e i n f o r m a t i o n w i t h i n t h e s e o b s e r v a t i o n s . T h e c r i t e r i o n a n i n d i v i d u a l a d o p t s f o r d e c i d i n g w h e t h e r t h e i n f o r m a t i o n o b t a i n e d o n a g i v e n o b s e r v a t i o n c o m e s f r o m t h e p o s s i b l e n u m b e r o f o b s e r v a t i o n s o n H y p o t h e s i s A o r - 6 -RROBABIL ITY OF A C O R R E C T I D E N T I F I C A T I O N o b s e r v a t i o n s on hypo thes i s A FIG. I S E N S O R Y INFORMAT ION o b s e r v a t i o n s on h y p o t h e s i s DECIS ION AXIS .. mean of h y p o t h e s i s ^ yes FIG. 2 mean of ^/hypothes is A L E N I E N T STR ICT decision axis dec is ion axis i i i i i i i i i no I yes. no yes F IG .3 7 from those of Hypothesis B, i s v i s u a l i z e d as a l i n e p e r p e n d i c u l a r to the a b s c i s s a , as i n F i g . 2. The d e c i s i o n a x i s i s assumed to he a v a r i a b l e one, and s t a t i s t i c a l d e c i s i o n t h e o r y attempts to determine i t s f i n a n c i a l l y i d e a l p o s i t i o n under a set of g i v e n c o n d i t i o n s . For example, suppose the task of the observer was to decide whether the i n f o r m a t i o n gained from a p a r t i c u l a r o b s e r v a t i o n d i d or d i d not a r i s e from Hypothesis A. I f the su b j e c t had r e c e i v e d p r i o r i n f o r m a t i o n to the e f f e c t that the p r o b a b i l i t y of Hypothesis A o c c u r r i n g i n any one d e c i s i o n s i t u a t i o n was equal to the p r o b a b i l i t y of Hypothesis B occur-r i n g i n any one s i t u a t i o n , then the d e c i s i o n a x i s would l i e midway between the means of the two d i s t r i b u t i o n s ( F i g . 2 ) . Any o b s e r v a t i o n the i n d i v i d u a l had judged to f a l l to the r i g h t o f the a x i s would promote a "Yes, i t was Hypothesis A" response, w h i l e anything he f e l t had f a l l e n to the l e f t of the a x i s would evoke a "No" response. This would be the i d e a l o p e r a t i n g p o s i t i o n f o r the d e c i s i o n a x i s i f the subj e c t had been informed that a c o r r e c t "Yes" or "No" was as e q u a l l y rewarded as an i n c o r r e c t "Yes" or "No" was punished by a f i n e . Unequal a l t e r a t i o n of the c o s t s and f i n e s a s s o c i a t e d w i t h c o r r e c t and i n c o r r e c t d e c i s i o n s serves to move the d e c i -s i o n a x i s . Thus f i n i n g an i n c o r r e c t "Yes" more, while keeping the other p a y o f f m a t r i x v a l u e s constant and equal, should move the d e c i s i o n a x i s to p o s i t i o n (a) i n F i g . 3. V/hile the 8 proportion of correct affirmations f a l l s ( i . e . the area under the curve of Hypothesis A and to the right of the decision axis decreases) so does the number of incorrect affirmations (the areas under the curve of Hypothesis B and to the right of the d e c i s i o n axis also decreases). The subject has become more cautious and i s less w i l l i n g to say "Yes." If the payoff matrix were again constant so that correct and incorrect decisions were equally rewarded and f i n e d but the p r o b a b i l i t y of Hypothesis A occurring i n any one decision s i t u a t i o n was equal to . 9 , then the decision axis would move to the far l e f t (position (b) i n F i g . 3 ) . Since nine out of ten observations are promoted by the occur-rence of Hypothesis A, there i s l i t t l e need for adopting extreme v i g i l a n c e and one would be f i n a n c i a l l y prudent to say "Yes" almost every time. Thus the basic concepts of s t a t i s t i c a l decision theory are a c t u a l l y quite simple. Information a r i s i n g from observations of two hypotheses can be ordered along a given dimension and moving along t h i s dimension, i s a decision axis whose p o s i t i o n i s determined by the costs and rewards associa-ted with incorrect and correct decisions as well as by the p r o b a b i l i t y of the occurrence of each hypothesis. The major d i f f i c u l t y s t a t i s t i c a l decision theory meets when applied to problems requiring, for example, the detection of an auditory signal from a noisy background, resides i n adopting a single 9 dimension on which the o b s e r v a t i o n s a r i s i n g from both a s i g n a l source and a n o i s e source can be ordered. T h i s problem i s d e a l t w i t h i n the next section,, (2) The Theory of S i g n a l D e t e c t i o n In a p p l y i n g s t a t i s t i c a l d e c i s i o n t h e o r y to the behaviour of i n d i v i d u a l s i n a s i g n a l - d e t e c t i o n s i t u a t i o n , i t was assumed t h a t the sensory mechanisms i n v o l v e d were prim-a r i l y communicative i n c h a r a c t e r . Decision-making would then be a c e n t r a l p r o c e s s , r a t h e r than p e r i p h e r a l , and would be based upon a p r i o r i i n f o r m a t i o n as w e l l as the sensory d a t a of an o b s e r v a t i o n . Somewhat more s p e c u l a t i v e (Green, i960) was the assumption t h a t the sensory communication channels were "noisy" or imperfect and thus they "corrupted" the i n f o r m a t i o n a r r i v i n g at the c e n t r a l decision-making areas. Although Swets and B i r d s a l l (1956) f e l t t h a t t h i s "noise" assumption has s t r o n g n e u r o l o g i c a l support, of equal importance, and, pro-ducing the same r e s u l t , i s the assumption that the p e r c e p t u a l system of the observer i s of a scanning nature and thus the i n f o r m a t i o n obtained i n s u c c e s s i v e o b s e r v a t i o n s of the same s i t u a t i o n i s v a r i a b l e i n amount and p a r t i c u l a r emphasis. In the l i m i t i n g and c l a s s i c form of the s i g n a l -d e t e c t i o n paradigm, an i n d i v i d u a l must decide whether, w i t h i n a d e l i n e a t e d i n t e r v a l , a s i g n a l may be a pure tone embedded i n "white" n o i s e s i m i l a r to s t a t i c or i t may be a f a i n t l i g h t 10 f l a s h e d a g a i n s t a w e l l - i l l u m i n a t e d or "noisy" background. I t might even c o n s i s t of the odour of a p a r t i c u l a r type of per-fume which must he d e t e c t e d i n a room f u l l of heavy smoke. To g r a p h i c a l l y i l l u s t r a t e any of these s i t u a t i o n s , as was done w i t h the two hypotheses i n F i g . 1, i s d i f f i c u l t , f o r the graph i s two-dimensional while an a u d i t o r y s i g n a l , f o r example, w i t h such a t t r i b u t e s as p i t c h , volume, d u r a t i o n , phase, e t c . has, consequently, many dimensions. In a d d i t i o n , though both the n o i s e and s i g n a l - p l u s - n o i s e , d i s t r i b u t i o n s must occupy the same a x i s , i t i s not tenable to assume that n o i s e and s i g n a l - p l u s - n o i s e occurrences are c h a r a c t e r i z e d by an equal number of a t t r i b u t e s . Consequently, i n order to j u s t i f y the o r d e r i n g o f both c l a s s e s of o b s e r v a t i o n s on a s i n g l e a x i s or continuum, the concept of l i k e l i h o o d r a t i o ( ) was i n t r o d u c e d . For any g i v e n o b s e r v a t i o n , based on e i t h e r a n o i s e or s i g n a l - p l u s -n o i s e occurrence, there i s a p o i n t , Y, i n m u l t i d i m e n s i o n a l space, which a c c u r a t e l y d e s c r i b e s i t . For t h i s p o i n t Y, t h e r e i s a p r o b a b i l i t y v a l u e that i t arose from a s i g n a l - p l u s -n o i s e occurrence — pSN, and another p r o b a b i l i t y value that i t arose from a n o i s e p r e s e n t a t i o n — pN. I f the former p r o b a b i l i t y i s d i v i d e d by jfche l a t t e r , a l i k e l i h o o d r a t i o r e s u l t s . The r a t i o g i v e s the l i k e l i h o o d t h a t p o i n t Y arose from a s i g n a l - p l u s - n o i s e occurrence r e l a t i v e to the p r o b a b i l -i t y that i t arose from n o i s e a l o n e . Since such a r a t i o i s a 11 r e a l , nonzero number, i t has a true dimension of magnitude. Thus a l l observations may be ordered along t h i s one dimension regardless of the number of attributes required to specify them. Observations a r i s i n g from a noise source and those o r i g i n a t i n g from a signal-plus-noise source are represented as X's and O's, respectively, on the Venn diagram of F i g . The diagram may be considered a d r a s t i c s i m p l i f i c a t i o n of the space of a l l possible observations. The d i s t r i b u t i o n s of the observations are not separate but overlap s l i g h t l y , suggesting that c e r t a i n observations have much i n common with both classes of stimulus occurrence. Those far removed from the centre of the diagram may be considered as being very d i s t i n c t and clear observations of t h e i r respective stimulus events. P l o t t i n g a l l observations on a l i k e l i h o o d r a t i o axis against the p r o b a b i l i t y they arose from t h e i r respective stimulus, classes gives a clearer indi c a t i o n of these r e l a t i o n s h i p s . In F i g . 5 the dashed l i n e represents the observations r e s u l t i n g from the occurrence of noise alone. Moving from l e f t to r i g h t , the l i k e l i h o o d that such an obser-vation resulted from noise alone decreases. With reference to the Venn diagram of F i g . 5, noise-alone observations located at the extreme l e f t are quite separate from the signal-plus-noise observations and they would be expected to have a low l i k e l i h o o d r a t i o . Movement to the right decreases F I G . 4 x X K • k X * x ? ft* • * x * 5 * l T * * x • • •• . • o t • O x " O X o o o x Venn, diagram of noise obser--vation(x) and signal plus noise observation (o) plotted in multi dimensional space.-Probability, an- r I observation arose from noise from . signal+noise— F I G . 5 *—Likel ihood Ratio »•' Probability an r| observation will promote a correct response F I G . 6 noise observation , signal plus noise observations -10 0 +10 Likelihood •10 0 *I0 Transformed 13 the "purity" of these observations, thus increasing the value of the l i k e l i h o o d r a t i o . A similar argument applies to the signal-plus-noise observations, mutatis mutandis,1, which are represented by a s o l i d l i n e i n F i g . 5 . The point at which the two l i n e s cross in F i g . 5 i s the area of greatest confu-sion, for here the l i k e l i h o o d r a t i o s of the two classes of observations are equal. This point occupies a pos i t i o n , on the Venn diagram of F i g . k, halfway between the average observations, as indicated by the two crosses, of the two observation classes. This average observation represents that p a r t i c u l a r observation which occurs most frequently for each stimulus c l a s s . As one moves away from t h i s average, the density or frequency of occurrence of the appropriate class of observa-tions decreases. These mean observations occupy a point i n multidimensional space and consequently can be located on the l i k e l i h o o d r a t i o axis. About these two values the other observations must be di s t r i b u t e d . Since the d i s t r i b u t i o n s are assumed to be normal i n order to simplify mathematical computations, a mathematical transformation of the l i k e l i h o o d r a t i o axis must be undertaken. The p r o b a b i l i t y that a given observation w i l l promote a correct response i s a function of the p r o b a b i l i t y that that observation arose from that stimulus class ( i . e . the correct class) and of the frequency with which that Ik o b s e r v a t i o n o c c u r s . Thus a n o b s e r v a t i o n l y i n g f a r t o t h e l e f t o f F i g . k h a s a h i g h p r o b a b i l i t y o f o c c u r r i n g f r o m a n o i s e s o u r c e ( a n d t h u s a l o w . 1 i k e l i h o o d r a t i o v a l u e ) b u t t h e f r e q u e n c y w i t h w h i c h i t o c c u r s i s v e r y s m a l l . The p r o d u c t o f t h e s e two v a l u e s , w h i c h g i v e s t h e p r o b a b i l i t y t h a t t h e p a r t i c u l a r o b s e r v a t i o n w i l l p romote a c o r r e c t r e s p o n s e , i s v e r y s m a l l . As t h e f r e q u e n c y o f a n o b s e r v a t i o n i s i n c r e a s e d b y moving t o w a r d s t h e mean o f t h e n o i s e c l a s s , t h e p r o b a b i l i t y t h a t i t o c c u r r e d f r o m a n o i s e s o u r c e d e c r e a s e s . HoAvever, t h e l a t t e r d e c r e m e n t i s n o t as g r e a t as t h e f o r m e r i n c r e m e n t and t h e p r o d u c t o f t h e s e two v a l u e s g i v e s a l a r g e r p r o b a b i l i t y t h a t t h e o b s e r v a t i o n w i l l promote a c o r r e c t r e s p o n s e . M o v i n g t o t h e r i g h t o f t h e n o i s e d i s t r i b u t i o n c e n t r e d e c r e a s e s t h e f r e q u e n c y o f an o b s e r v a t i o n ' s o c c u r r e n c e , as w e l l as t h e p r o b a b i l i t y t h a t i t o r i g i n a t e d f r o m a n o i s e s o u r c e , a n d a g a i n t h e p r o d u c t o f t h e s e two v a r i a b l e s i s v e r y s m a l l . P l o t t i n g t h e s e p r o d u c t s f o r t h e o b s e r v a t i o n s o f b o t h c l a s s e s a g a i n s t t h e l i k e l i h o o d r a t i o a x i s , w h i c h h a s b e e n t r a n s f o r m e d t o a n o r m a l d e v i a t i o n s c a l e , p r o d u c e s t h e two n o r m a l c u r v e s o f F i g . 6. The s u b j e c t f a c e d w i t h a s i g n a l - d e t e c t i o n s i t u a t i o n i s v i e w e d as u t i l i z i n g t h e l i k e l i h o o d r a t i o as a s u b j e c t i v e y a r d s t i c k f o r m aking h i s d e c i s i o n s . I f he h a s b e e n i n f o r m e d t h a t t h e p r o b a b i l i t y o f t h e s i g n a l - p l u s - n o i s e o c c u r r i n g i s e q u a l t o t h e p r o b a b i l i t y o f n o i s e a l o n e o c c u r r i n g , pSN = pN, 15 and i f the d e c i s i o n outcomes are a l l equal (a constant payoff m a t r i x ) , the, subject should o r i e n t h i s d e c i s i o n a x i s on the l i k e l i h o o d r a t i o a x i s at a p o i n t midway between the means of the two d i s t r i b u t i o n s . Any observation he judges to have a l i k e l i h o o d r a t i o gre.ater than t h i s value w i l l evoke one response and any value judged l e s s than i t w i l l promote the opposite response. With the d e c i s i o n a x i s at t h i s p o i n t , he w i l l be maximizing h i s expected earnings. I f the payoff m a t r i x i s a l t e r e d and/or the p r o b a b i l i t i e s a s s o c i a t e d with, s i g n a l occurrence are changed, the d e c i s i o n a x i s i s assumed to r e o r i e n t i t s e l f a p p r o p r i a t e l y . The e f f e c t s of manipulating t h i s d e c i s i o n axis are conveniently summarized by Receiver Operating C h a r a c t e r i s t i c (ROC) curves. C o n s i d e r a t i o n of any one of the ROC curves, l y i n g above the diagonal i n F i g . 7, shows the p r o b a b i l i t y of responding w i t h a c o r r e c t c o n f i r m a t i o n (pSNly) as a f u n c t i o n of responding w i t h an i n c o r r e c t c o n f i r m a t i o n (pNly) under a set of f i x e d stimulus parameters (and where the t a s k i s to say "Yes" when the s i g n a l i s p r e s e n t ) . Any one curve i s gen-erated by moving a v a r i a b l e d e c i s i o n c r i t e r i o n along a l i k e l i h o o d a x i s underlying two observation d i s t r i b u t i o n s (as i n F i g . 6) and measuring the proportions of c o r r e c t and i n c o r r e c t a f f i r m a t i o n s l y i n g to the r i g h t of the d e c i s i o n a x i s . For example, the curve c l o s e s t to the diagonal was generated by moving such an axis along the l i k e l i h o o d r a t i o 16 a x i s of the two d i s t r i b u t i o n s i n the i n s e t of F i g . 7 . The d i s t a n c e d between the means of the two d i s t r i b u t i o n s i s measured i n terms of the d e v i a t i o n u n i t and thus: M S N - M N d = CT Here d i s equal to 1 and f o r such a d i s t a n c e , a d e f i n i t e HOC curve e x i s t s , as p l o t t e d . As the d i s t a n c e between the two d i s t r i b u t i o n s i n c r e a s e s , d i f f e r e n t i a t i o n between the two c l a s s e s o f st i m u l u s events i s f a c i l i t a t e d and the ROC curves move up to the l e f t ( F i g . 7 ) . The d e v i a t i o n d i s t a n c e s between the means of the two d i s t r i b u t i o n s u n d e r l y i n g each of these ROC curves are noted. The importance of these ROC curves i s that they show the i n f l u e n c e of a v a r i a b l e c r i t e r i o n on the p o s i t i v e response r a t e and a l s o give a pure measure of the p s y c h o l o g i c a l d i s t a n c e between the two stimulus c l a s s e s . I n any experiment one needs on l y p l o t the obtained v a l u e s o f pSNly and pNly and f i t them w i t h the a p p r o p r i a t e ROC curves. Since each ROC curve has a p a r t i c u l a r d v a l u e , we have a pure measure of the s e n s i t i v i t y of the s u b j e c t or of the p s y c h o l o g i c a l d i s t a n c e between the two stimulus events. Besides i n d i c a t i n g the s e n s i t i v i t y and c o n t r o l l i n g the c r i t e r i o n v a r i a b i l i t y of a s u b j e c t , the the o r y of s i g n a l -L7--F IG,7 R O C c u r v e s , obtained by. moving a va r i ab le c r i t e r i o n t h rough two , n o r m a l d is t r ibut ions . T h e ; g rea te r the disTonce between their m e a n s , the greater the value of. d , and - the f u r t h e r -displaced to. J .he _l.ef.t__are,' t h e " . R O C c u r v e s . 18 detection can determine the optimal value of the l i k e l i h o o d r a t i o on which to locate the decision axis for a given set of experimental conditions. This value of the l i k e l i h o o d r a t i o , denoted by B, w i l l maximize the expected value of a decision s i t u a t i o n and for any decision s i t u a t i o n with f i x e d decision outcomes and signal c h a r a c t e r i s t i c s . = P(N) ( v y > B + K M. A) P(SN) <V S N J L + K S N > B ) where p(N) i s the communicated a p r i o r i p r o b a b i l i t y of N occurring. where p(SN) i s the communicated a p r i o r i p r o b a b i l i t y of SN occurring. where V N B i s the reward value of a correct i d e n t i f i c a t i o n of noise. where A i s the fine value of an incorrect i d e n t i f i c a t i o n of noise. where Vg-^  A is the reward value of a correct i d e n t i f i c a t i o n of S N . and where Kg N fi i f the fine value of an incorrect i d e n t i f i c a -t i o n of S N . B so weights the values, costs and p r o b a b i l i t i e s associated with decision outcomes that the best strategy, one minimizing r i s k while maximizing potential outcome, i s defined. The optimum strategy a subject should have 19 adopted i n order to maximize h i s expected outcome i n a given d e c i s i o n s i t u a t i o n i s determined by p l o t t i n g the two stimulus d i s t r i b u t i o n s w i t h a d e v i a t i o n d i s t a n c e between the means of the d i s t r i b u t i o n s equal to the d va l u e of the obtained ROC curve. B i s l o c a t e d on the l i k e l i h o o d r a t i o a x i s at t h a t p o i n t where the v e r t i c a l d i s t a n c e between the l i k e l i h o o d r a t i o a x i s and the n o i s e d i s t r i b u t i o n , d i v i d e d by the v e r t i c a l d i s t a n c e between the l i k e l i h o o d r a t i o a x i s and the s i g n a l -p l u s - n o i s e d i s t r i b u t i o n , g i v e s a q u o t i e n t equal to the c a l -c u l a t e d B. A simpler d e t e r m i n a t i o n o f the optimum s t r a t e g y u s u a l l y d e f i n e d i n terms of the maximum number of i n c o r r e c t a f f i r m a t i o n s a l l o w a b l e , i s found by drawing a l i n e , w i t h s l o p e equal to B, tangent to the determined ROC curve. The p o i n t where the l i n e touches the curve d e f i n e s the optimal " f a l s e alarm" or i n c o r r e c t a f f i r m a t i o n r a t e . Thus, i t has been shown how the theory of s i g n a l d e t e c t i o n can both d e s c r i b e the behaviour of an i n d i v i d u a l f a c e d w i t h a decision-making s i t u a t i o n and p r e d i c t what h i s optimum d e c i s i o n s t r a t e g y should be. While d, the measure of s e n s i t i v i t y , was a r r i v e d at on the b a s i s of observed behaviour, v a r i o u s i n v e s t i g a t o r s have attempted to p r e d i c t what the i d e a l v a l u e of d should be, independent of the s e n s i t i v i t y of the observer. T h i s aspect o f the theory i s c a l l e d the t h e o r y of i d e a l observers (Green, i960) and a comparison of the observed d w i t h the i d e a l d, p r o v i d e s an 20 e f f i c i e n c y measure of the sensory processes involved. The ideal value of d i s defined i n terms of the phase, time and power spectrum of the s i g n a l . To comply with this d e f i n i t i o n a simple s i g n a l , such as a pure tone, which can he measured on the above attributes, must be chosen and since i n t h i s study complex sounds, which do not lend themselves to these measurements, were u t i l i z e d as the signal, a measure of the ideal d was not attempted. Experimental Results with the Theory of Signal Detection (1) The Threshold Concept and the Variable C r i t e r i o n One of the e a r l i e r reports i n the l i t e r a t u r e to present experimental evidence megating the u t i l i t y of the threshold concept was by Smith and Wilson (1953). While they constructed a s t a t i s t i c a l theory of decision, i t d i f f e r s i n certain important aspects from that presented here. A strong s i m i l a r i t y however exists i n th e i r i m p l i c i t assumption that a variable decision c r i t e r i o n determines those signals which w i l l be detected and those which w i l l be missed. Two d i f f e r e n t confidence attitudes were induced within subjects required to detect an auditory signal i n noise. One group was t o l d to affirm the signal's presence whenever they f e l t i t had occurred (a l i b e r a l attitude) while the other was to assert the signal's occurrence only when they were certa i n i t had occurred (a conservative a t t i t u d e ) . 21 In conventional psychophysics a measure of "true" s e n s i t i v i t y i s supposedly obtained by a correction technique which u t i l i z e s the number of "f a l s e p o s i t i v e s " (incorrect affirma-tions of signal present) to weight the correction procedure. If the threshold concept were v a l i d , then the performance of the " l i b e r a l " group, when corrected for "false p o s i t i v e s , " should coincide with that of the "conservatives." As i t was found to s t i l l be s i g n i f i c a n t l y better, Smith and Wilson con-cluded that the threshold concept was, at best, i n need of substantial r e v i s i o n . Since the theory of signal detection precluded the existence of a threshold, much of the early experimentation was primarily designed to test t h i s assumption. The threshold, i n i t s c l a s s i c a l formulation, i s that value of stimulus intensity which promotes a correct detection or recognition response f i f t y percent of the time the stimulus i s presented. Thus, stimuli of i n t e n s i t i e s below t h i s value should be impossible to order and they should generate an ROC curve whichcrosses the right hand corner of the graph where .pSNly = pNly =1. In other words, no d i f f e r e n t i a t i o n would be achieved. Tanner and Swets (195^ ) report two experiments which suggest that subjects are not only capable of ordering observations on "below-threshold" signals but also of ordering the l i k e l i h o o d r a t i o values of noise alone as the theory of 22 s i g n a l d e t e c t i o n p r e d i c t s . In the f i r s t experiment, the s u b j e c t s were r e q u i r e d to d e t e c t the presence or absence of l i g h t s i g n a l s , c o n s i s t i n g of four d i f f e r e n t degrees of i n t e n s i t y , f l a s h e d a g a i n s t a u n i f o r m l y i l l u m i n a t e d screen. V a r i o u s p a y o f f matrices and p r o b a b i l i t i e s of s i g n a l occurrence were i n t r o d u c e d i n order to manipulate the s u b j e c t s ' d e c i s i o n axes. In s p i t e of the extremely low i n t e n s i t i e s of the s i g n a l s r e l a t i v e to the w e l l - i l l u m i n a t e d background, the o b t a i n e d ROC curves of the three s u b j e c t s d i d not cross the upper r i g h t hand corner o f the graph. S i m i l a r r e p o r t s have been obtained with the d e t e c t i o n of a u d i t o r y s i g n a l s i n n o i s e , (Tanner, Swets and Green, 195&) thus adding s u b s t a n t i a l support to the p o s i t i o n that the t h e o r y of s i g n a l d e t e c t i o n adopts i n d i s r e g a r d i n g a t h r e s h o l d concept when c o n s i d e r i n g the s e n s i t i v i t y of sensory m o d a l i t i e s . In e v a l u a t i n g a s u b j e c t ' s performance i n a complex decision-making s i t u a t i o n , the rank c o r r e l a t i o n between the computed v a l u e s of B f o r each set of stimulus c o n d i t i o n s and the corresponding observed " f a l s e alarm" r a t e s i s determined. A h i g h c o r r e l a t i o n i n d i c a t e s a s u b j e c t has v a r i e d h i s d e c i s i o n a x i s a p p r o p r i a t e l y . In the f i r s t of the two v i s u a l experiments mentioned above (Tanner and Swets, 195*0 the c a l c u l a t e d B v a l u e s ranged from .25 to 3 . 0 0 . S u b j e c t i v e l y , these v a l u e s might be c o n s i d e r e d to d e f i n e a degree of c a u t i o n concerning 23 the occurrence of an incorrect "Yes" which ranges from " f a i r l y l i b e r a l " to "moderately conservative." The rank c o r r e l a t i o n c o e f f i c i e n t s between the calculated values of B and the observed f a l s e alarm rates were . 7 0 , »k6 and . 7 1 for the three subjects. Except for the second c o e f f i c i e n t , i t would seem that the subjects were capable of appropriately a l t e r i n g t h e i r decision axis. In the second v i s u a l experiment (Tanner and Swets, 195M the four subjects had t h e i r respective B.0C curves drawn and the appropriate d values determined for the detec-t i o n of l i g h t flashes held at one i n t e n s i t y value. By the methods referred to above, the appropriate false alarm rate for each subject was determined and communicated to that subject. He then resumed the detection procedure. At i t s termination, the rank c o r r e l a t i o n between the calculated B values and the associated f a l s e alarm rate was determined. The information concerning the optimum false alarm rates pro-moted c o e f f i c i e n t s of .9^ , . 9 7 , . 8 6 and . 9 8 for the four subjects. A c o e f f i c i e n t of . 6 8 , here and in the other v i s u a l experiment, i s s i g n i f i c a n t at the ,01 l e v e l of c o n f i -dence. The higher c o e f f i c i e n t s were not only the result of the communicated optimum fals e alarm rate but also due to the fact that the B values extended over a wider range, from . 1 6 to 9 . 0 0 . Nevertheless, further support i s given by th i s study to the concept of a variable decision axis. In addition, Swets, Tanner and B i r d s a l l (196l) refer to a 1956 experiment where the co r r e l a t i o n between the.calculated B values and observed f a l s e alarm rates for the detection of an auditory signal i n noise, was equal to 1 , 0 .for each of two observers. This perfect c o r r e l a t i o n was achieved even, though neither subject had been informed of his optimum f a l s e alarm rate, (2) The Detection of Complex Signals There has been a surprising reluctance to apply the conventional framework of the theory of signal detection to the recognition of complex sounds and words in noise. Part of the caution i s due to an understandable desire to f i r s t describe the detection of simple tones and other sensa-tions before proceeding with more complex combinations and patterns. In addition, many re s u l t s , such as the detection of d, obtained from the application of the theory of signal detection, compare well with those obtained from other psychophysical methods such as the forced choice technique (Swets, Tanner and B i r d s a l l , 1961). Consequently, several investigators have u t i l i z e d the l a t t e r technique to describe more accurately the s t a t i s t i c a l nature of the auditory recognition process. A complex tone may be presented i n one of several experimental i n t e r v a l s and the subject i s required to indicate i n which i n t e r v a l the complex occurred. However, as no attempt i s made to control the individual's c r i t e r i o n 25 for selecting any p a r t i c u l a r interval,,much of the precision of the theory of signal detection i s l o s t . Thus i n thi s study an attempt was made to determine the e f f i c a c y of the conventional theory of signal detection i n describing the behaviour of subjects required to d i f f e r e n -t i a t e between two complex words embedded i n noise. It i s true that Egan (1955) and others have u t i l i z e d the convention-a l approach i n the recognition of di f f e r e n t words, but th e i r emphasis has been on the confirmation or rej e c t i o n of a response already made. From these f i r s t and second order responses, response-response BOC curves are dram and the ch a r a c t e r i s t i c s of conununication networks are investigated. The conventional BOC curve, however, i s a stimulus-response one and thus no attempt i s made in thi s study to investigate any relationships with further confirmations or rejections of these responses. It i s hoped that the curves constructed from the performances of the subjects i n t h i s experiment, w i l l i l l u s t r a t e the eff e c t of a variable c r i t e r i o n on the recognition of two complex words as well as detect the ef f e c t s of varying the amount of information associated with these words. Should t h i s be the case, the generality and p r e d i c t a b i l i t y of the theory of signal detection w i l l have been s i g n i f i c a n t l y increased. 26 The Time Compression of Speech The stimulus material i n t h i s study consisted of the auditory presentation of two words which had heen markedly shortened i n duration, or time, compressed, by the random removal of internal sound segments. The e f f e c t s of removing segments of speech sounds on the i n t e l l i g i b i l i t y of that speech was f i r s t studied by M i l l e r and L i c k l i d e r (1950). The segments were removed by a high speed on-off switching of the presentation apparatus. Though segments were removed (when the switch was on-"off')) there was no speed-up i n the t o t a l duration of the word. It was found that even f i f t y percent removal of a word, had l i t t l e effect on i n t e l l i g i -b i l i t y . In 1953 Garvey manually removed segments of recorded tape and s p l i c e d the remaining lengths together. The tape was appropriately speeded-up i n order to return the speech p i t c h to i t s proper l e v e l , thus achieving true time compres-sion. Garvey's results confirmed those of M i l l e r and L i c k l i d e r , v i z , removal of up to f i f t y percent of the duration of a word ( f i f t y percent time compression) was not markedly detrimental to i n t e l l i g i b i l i t y . In 195^  Fairbanks, E v e r i t t and Jaeger reported the invention of a machine capable of time compressing speech, thereby eliminating the task.of tediously measuring, removing and s p l i c i n g tape segments. The machine permits very precise compression, operations, so that both the duration of segments 27 retained and discarded can be independently manipulated. The net e f f e c t of t h i s control is that a given compression value can be obtained by several combinations of the sampling and discard i n t e r v a l s . Fairbanks and Kodman (1957) found that with th i s machine, compression of up to f i f t y percent had l i t t l e e f fect on the i n t e l l i g i b i l i t y of a large number of common words. However, compression of f i f t y percent obtained by the discard of a few large segments was more detrimental to i n t e l l i g i -b i l i t y than the f i f t y percent compression obtained by the removal of many short segments. In addition, seventy-five percent compression was found to be more detrimental to i n t e l l i g i b i l i t y than s i x t y percent compression, the size of the discard i n t e r v a l i n each case being r e l a t i v e l y constant. Hypotheses The results of the three speech compression studies reviewed above strongly suggest that the amount of information within a word far exceeds the amount required for recognition. It might be contended that the redundancy of information serves to more accurately define that point i n multidimensional space which the word could be considered to occupy. While the concept of the l i k e l i h o o d r a t i o served to permit the ordering of d i f f e r e n t stimuli on the same continuum, no mathematical error i s made i f one considers the 28 l i k e l i h o o d r a t i o to he equivalent to an information measure. Thus, the greater the distance, on the l i k e l i h o o d r a t i o axis, between the means of two d i s t r i b u t i o n s , the greater i s the amount of information available to d i s t i n g u i s h between them. If the d i s t i n c t i o n between sensation and perception i s that the former requires less information than the l a t t e r , then the d i s t r i b u t i o n s of the two curves i n a sensation experiment may be assumed to l i e further to the l e f t on a l i k e l i h o o d r a t i o axis than the two d i s t r i b u t i o n s of a perception experi-ment. In any event, the d i s t i n c t i o n i s quite a r b i t r a r y arid one i s quite j u s t i f i e d , as Swets, Tanner and B l r d s a l l (1961) have suggested i n assuming that the signal detection studies previously reported were in fact perceptual studies and that the theory of signal detection applies quite appropriately to decision-making i n a perceptual s i t u a t i o n . Whatever the role that amount of information plays i n the theory of signal detection, i t was assumed that the two stimulus words u t i l i z e d i n t h i s study could be plotted i n multidimensional space and ordered on a l i k e l i h o o d r a t i o axis. The psychological distance between the two d i s t r i b u -tions of t h e i r observations was assumed to be a function of the amount of information inherent i n them. Certain hypotheses follow from these assumptions and t h e i r v e r i f i c a -t i o n forms the basis of the experimental study undertaken. Since Fairbanks and Rodman (1957) found that f i f t y 29 percent compression w i t h a large d i s c a r d i n t e r v a l was more det r i m e n t a l to i n t e l l i g i b i l i t y than f i f t y percent compression w i t h a small d i s c a r d i n t e r v a l , an ROC curve obtained by r e q u i r i n g the d i f f e r e n t i a t i o n of two words time compressed f i f t y percent w i t h a l a r g e d i s c a r d i n t e r v a l should l i e c l o s e r to the graph's diagonal than an ROC curve obtained from an i d e n t i c a l task but w i t h compression obtained through small segment removal. A l a r g e d i s c a r d i n t e r v a l , i t was hypothe-s i z e d , would remove l t i r g e r segments of those v i t a l word p o r t i o n s necessary f o r i n t e l l i g i b i l i t y . Small segment removal, i t was f e l t , would remove only small p o r t i o n s of the v i t a l segments, thereby being l e s s detrimental to i n t e l l i -g i b i l i t y . In the former case the p s y c h o l o g i c a l d i s t a n c e , d, between the observation d i s t r i b u t i o n s would be s h o r t , h i n d e r i n g d i f f e r e n t i a t i o n and consequently producing an ROC curve l y i n g c l o s e to the d i a g o n a l . In the l a t t e r , the p s y c h o l o g i c a l distance should be greater, generating an ROC curve s i t u a t e d f u r t h e r to the l e f t . Fairbanks and Kodman al s o reported that s e v e n t y - f i v e percent compression was more detr i m e n t a l to i n t e l l i g i b i l i t y than s i x t y percent compression, w i t h the d i s c a r d i n t e r v a l h e l d constant, ROC curves generated by r e q u i r i n g the d i f f e r e n t i a t i o n of the two stimulus words should l i e f u r t h e r to the l e f t when they are compressed by s i x t y percent and c l o s e r to the diagonal when they are compressed by seventy-30 four percent, the s i z e s of the d i s c a r d i n t e r v a l being equal i n each case 0 Seventy-four percent compression should r e s u l t i n a greater removal of information than s i x t y percent com-p r e s s i o n , and consequently the observation d i s t r i b u t i o n s of the two seventy-four percent compressed words should l i e c l o s e r than the observation d i s t r i b u t i o n s of the two s i x t y percent compressed words. Chapter I I I METHOD The present i n v e s t i g a t i o n c o n s i s t e d of two separate experiments, which, f o r purposes of e x p o s i t i o n , are r e f e r r e d to as A complex and B complex. In the former, the framework of the theory of s i g n a l d e t e c t i o n was a p p l i e d to the d i f f e r -e n t i a t i o n of stimulus words time compressed by f i f t y percent w i t h the d i s c a r d i n t e r v a l v a r i e d . In the l a t t e r , the theory of s i g n a l d e t e c t i o n was a p p l i e d to the r e c o g n i t i o n of s t i m u l u s words which were time compressed by s i x t y and seventy-four p e r c e n t w h i l e the d i s c a r d i n t e r v a l was h e l d r e l a t i v e l y c o n s t a n t . Stimulus M a t e r i a l Three, 200 item, l i s t s of the stimulus words "commiiiation" and "comminution" Ave re randomly c o n s t r u c t e d . In one l i s t , "commination" appeared 100 times, thus pCA = . 5 . I n the other t A v o , the A v o r d 11 commination" o c c u r r e d 20 a n d 180 times, thus pCA = .1 and pCA = .9 r e s p e c t i v e l y . (Refer to Appendix A f o r the orders of the stimulus A v o r d s ) The l i s t s were then read out by the examiner, at the r a t e of one A v o r d per 10 seconds, and recorded on a Roberts 990 tape r e c o r d e r A v i t h tape speed set at 3-3/^" per second. A r e l a t i v e l y con-s t a n t v o i c e l e v e l Avas maintained by o b s e r v i n g the f l u c t u a t i o n s 32 of the r e c o r d e r ' s V.U. meter. These three tapes, w i t h p r o b a b i l i t i e s of "commination 1 1 equal to .5, .1, and .9 were u t i l i z e d to form the s t i m u l u s tapes of Complex A and Complex B. A V a r i Voc speech compression machine, S e r i a l No. 19979, r e c e i v e d the a p p r o p r i a t e l y speeded playbacks of the above mentioned tapes and compressed them a c c o r d i n g to the s p e c i f i c a t i o n s of Table 1. The output of the V a r i Voc, which c o n s i s t e d of the compressed st i m u l u s words, was taken up by a Wollensack r e c o r d e r w i t h tape speed set at 3-3/^ " per second. This tape, which c o n s i s t e d o f the compressed sti m u l u s words, was t r a n s f e r r e d to the Roberts 99°. The output of t h i s r e c o r d e r was then "mixed" w i t h that from an E i c o r r e c o r d e r p l a y i n g a tape of "white" n o i s e by a Wollensack Mixer, and the.combined outputs were taken up by the Wollensack w i t h a tape speed of 3-3/^ ". In t h i s manner each of t h e . s t i m u l u s elements were embedded i n "white" n o i s e . The n o i s e , generated by t u r n i n g up the g a i n of a F e r r i o g r a p h Recorder and having, the machine r e c o r d the n o i s e generated by i t s own tubes, was r e l a t i v e l y " f l a t " from 50 to 25OO cps, i n d i c a t i n g t h a t a l l of the f r e q u e n c i e s common to the speech spectrum were e q u a l l y r e p r e s e n t e d and thus meeting the e s s e n t i a l c r i t e r i o n f o r "white" n o i s e . The s i g n a l - t o -n o i s e r a t i o ( g i v i n g the a u d i t o r y s t r e n g t h of the compressed TABLE 1 TABLE OF EXPERIMENTAL TAPES CONSTRUCTED COMPLEX A COMPLEX B Treatment A -50% Compression w i t h a l a r g e d i s c a r d i n t e r v a l pCA = . 5 , Tape B pCA = . 5 , Tape D pCA = . 5 , Tape F pCA = .1, Tape P pCA = . 9 , Tape Q Treatment B -50$> Compression w i t h a s m a l l d i s c a r d i n t e r v a l pCA = . 5 , Tape A pCA = o5, Tape C pCA = . 5 , Tape E pCA = .1, Tape N pCA = . 9 , Tape 0 Treatment A -6of0 Compression w i t h a constant d i s c a r d i n t e r v a l pCA = . 5 , Tape I pCA = . 5 , Tape H pCA = . 5 , Tape J pCA = .1, Tape R pCA = _9> Tape S Treatment B 7WJ0Compress i o n w i t h a constant d i s c a r d i n t e r v a l pCA = „5, Tape K pCA = . 5 , Tape L pCA = . 5 , Tape M pCA = .1, Tape T pCA = . 9 , Tape U 34 w o r d s r e l a t i v e t o t h e a u d i t o r y s t r e n g t h o f t h e n o i s e ) was a p p r o x i m a t e l y -12 <;d'b a n d was c o n t r o l l e d b y t h e m a n i p u l a t i o n o f t h e m i x e r d i a l s . The l o w v a l u e o f t h e s i g n a l - t o - n o i s e r a t i o was s e l e c t e d t o i n s u r e t h a t p e r f e c t d i f f e r e n t i a t i o n b e t w e e n t h e two s t i m u l u s w o r d s c o u l d n o t o c c u r . E a c h t a p e c o n s i s t e d o f 10 b l o c k s o f 20 s i g n a l s , g i v i n g t h e 200 s i g n a l s a s m e n t i o n e d a b o v e . A p a u s e o f 10 s e c o n d s d u r a t i o n e x i s t e d b e t w e e n e a c h s i g n a l p r e s e n t a t i o n . The p r e s e n t a t i o n c o n s i s t e d o f t h r e e s e c o n d s o f n o i s e f o l l o w e d i m m e d i a t e l y b y t h e c o m p r e s s e d s i g n a l embedded i n t h e n o i s e . A t t h e e n d o f a b l o c k o f 20 s i g n a l p r e s e n t a t i o n s , a p a u s e o f 14 s e c o n d s l a p s e d b e f o r e a v o i c e w a r n e d t h e s u b j e c t t h a t t h e n e x t b l o c k was a b o u t t o commence. S u b j e c t s The 10 m a l e s u b j e c t s r a n g e d i n age f r o m 18 t o 29, h a d a t l e a s t one y e a r o f U n i v e r s i t y , a n d were a l l o f s a t i s -f a c t o r y h e a r i n g a b i l i t y . They w e r e c o n t a c t e d t h r o u g h t h e u n i v e r s i t y employment o f f i c e a n d w e r e i n f o r m e d t h a t t h e e x p e r i m e n t w o u l d r e q u i r e a t l e a s t 10 h o u r s o f t h e i r t i m e . T h e i r p a y , t h e y w e r e w a r n e d w o u l d be c o n t i n g e n t o n t h e i r p e r f o r m a n c e , b u t i n t h e e v e n t t h e y made a n y t h i n g o v e r $ 1 0 . 0 0 , t h i s amount w o u l d be f o r f e i t e d . I f t h e i n d i v i d u a l a g r e e d t o p a r t i c i p a t e i n t h e e x p e r i m e n t u n d e r t h e c o n d i t i o n s c i t e d , a t i m e was a r r a n g e d f o r t h e f i r s t s e s s i o n . 35 I n s t r u c t i o n s When the su b j e c t a r r i v e d he was randomly a s s i g n e d to Complex A or Complex B, w i t h the r e s t r i c t i o n that 5 s u b j e c t s were r e q u i r e d f o r each experiment. As each complex c o n s i s t e d of two d i f f e r e n t treatments of the stim u l u s words, the order i n which a s u b j e c t r e c e i v e d them was a l s o randomly determined. Random assignment of the three tapes having pCA = .5 ( r e f e r to Table 1) to the three d i f f e r e n t p a y o f f m a t r i c e s a s s o c i a t e d with t h i s p r o b a b i l i t y r a t i o was a l s o made f o r each s u b j e c t under each treatment c o n d i t i o n . (Refer to Appendices B and C f o r the tape sequence f o r each s u b j e c t ) The s u b j e c t was then informed t h a t the focus of the experiment was to see how w e l l i n d i v i d u a l s c o u l d make d e c i s i o n s . He was t o l d t h a t he would be presented v i a e a r -phones, w i t h r e c o r d i n g s of 11 comminat i o n " and "comminution" embedded i n n o i s e , and t h a t h i s t a s k would be to determine the presence or absence of "commination" and to communicate h i s d e c i s i o n by a v e r b a l "Yes" or "No" r e s p e c t i v e l y . The meaning of the pa y o f f matrix t o be a s s o c i a t e d w i t h h i s f i r s t experimental tape was e x p l a i n e d i n e x t e n s i v e d e t a i l to each s u b j e c t . Each was a l s o informed of the meanings of the p r o b a b i l i t y statements. Thus, i f pCA = ,5, 100 of the 200 stimulus words to be presented would be "commination" and 100 would be "comminution.". The p o s s i b i l i t y 3 6 that any one st i m u l u s word would he "commination" was equal to the p r o b a b i l i t y that i t would be "comminution," It was hoped that the s u b j e c t s would be capable of u t i l i z i n g t h e i r past performance i n t h e . d e c i s i o n s i t u a t i o n to guide t h e i r behaviour i n the p r e s e n t . Consequently, a , b a t t e r y operated l i g h t d i s p l a y , w i t h the monetary valu e s a s s o c i a t e d . w i t h the p a y o f f m a t r i c e s mounted on s i x opalescent discs,.was c o n s t r u c t e d . A corresponding set of buttons v/as operated by the experimenter and a s l i g h t push on a button served to cause the a p p r o p r i a t e l i g h t b u l b to f l a s h , thereby i l l u m i n a t i n g the adjacent d i s c . Not o n l y was the monetary co s t or v a l u e o f the d e c i s i o n thereby g i v e n to each s u b j e c t , but knowledge of t h i s s o r t a l s o served to inform him of what the a c t u a l stimulus p r e s e n t a t i o n had been. . A 10 minute p r a c t i c e s e s s i o n was giv e n each s u b j e c t i n order to f a m i l i a r i z e him w i t h both the nature of the sti m u l u s p r e s e n t a t i o n s and the method whereby he would be g i v e n immediate knowledge of h i s performance. The experiment then commenced. Each s u b j e c t was informed t h a t he had a $1.00 b a n k r o l l to h i s c r e d i t , p r i o r to the commencement of,ea c h tape and t h a t he c o u l d add to i t or s u b t r a c t from i t depending on h i s performance. He was t o l d to so make h i s d e c i s i o n s that he c o u l d leave the e x p e r i -mental room w i t h as much money as p o s s i b l e . In a d d i t i o n , a 37 copy of the p a y o f f m a t r i x and the p r o b a b i l i t y of stimulus occurrence a s s o c i a t e d w i t h each tape was p l a c e d before each s u b j e c t f o r constant r e f e r e n c e . In the f i r s t tape f o r each of the two stimulus treatments of Complex A and Complex. B, the m a t r i x was a constant one with, a l l v a l u e s and f i n e s equal to one cent and the p r o b a b i l i t y of "commination 1 1 equal to .5 ( r e f e r to Appendices B and C f o r , t h e m a t r i x sequences). In the second tape the p r o b a b i l i t y of "commination" was equal to .5 a g a i n . However, an i n c o r r e c t "Yes" was f i n e d f i v e cents w h i l e the other m a t r i x v a l u e s were i d e n t i c a l w i t h the f i r s t tape. In the t h i r d tape, the p r o b a b i l i t y of "commination" was a g a i n .5 and the m a t r i x v a l u e s equal to one cent, except f o r an i n c o r r e c t "Yes" which was now f i n e d nine c e n t s . In the f o u r t h and f i f t h tapes the pay o f f m a t r i c e s were agai n con-s t a n t and i d e n t i c a l w i t h the f i r s t tape, but the p r o b a b i l i t y of "commination" was set at .1 and .9 r e s p e c t i v e l y . The f i r s t experimental s e s s i o n l a s t e d approximately an hour and was devoted s o l e l y to the f i r s t tape. A short f i v e minute break was allowed halfway through t h i s tape. In the la-ter experimental s e s s i o n s , the sub j e c t was allowed to complete up to three tapes i n s u c c e s s i o n , w i t h a p p r o p r i a t e r e s t i n t e r v a l s . Each s u b j e c t thus r e q u i r e d at l e a s t f o u r s e s s i o n s i n order to complete the t e n tapes of the assig n e d complex. 38 A n a l y s i s o f The D a t a F rom t h e r e s p o n s e r e c o r d s o f e a c h s u b j e c t t h e p r o b a b i l i t y o f r e s p o n d i n g w i t h a " Y e s " t o " c o m m i n a t i o n " — p C A l y , a n d t h e p r o b a b i l i t y o f r e s p o n d i n g w i t h a " Y e s " t o " c o m m i n u t i o n " — p C U l y , was c a l c u l a t e d f o r e a c h s u b j e c t o n a l l t e n t a p e s . To v e r i f y t h e a s s u m p t i o n t h a t t h e o b s e r v a -t i o n d i s t r i b u t i o n s o f t h e s t i m u l u s w o r d s were n o r m a l , i t was n e c e s s a r y t o show t h a t when t h e ab o v e o b t a i n e d v a l u e s a r e p l o t t e d on d o u b l e n o r m a l p r o b a b i l i t y p a p e r , t h e y a r e b e s t f i t t e d w i t h a s t r a i g h t l i n e r u n n i n g p a r a l l e l t o t h e d i a g o n a l o f t h e g r a p h . ( S w e t s , T a n n e r & B i r c l s a l l , 1961). S u c h . p l o t s w e r e c o n s t r u c t e d a n d t h e o b t a i n e d l i n e s a l s o gave a r e a d y v a l u e o f d. To t e s t t h e h y p o t h e s e s c o n c e r n i n g amount o f i n f o r m a t i o n a n d t h e p o s i t i o n o f t h e SOC c u r v e , t h e c u r v e s w e r e p l o t t e d f r o m t h e same d a t a b u t o n a g r a p h o f e q u a l -i n t e r v a l u n i t s . F i n a l l y , t o d e t e r m i n e t h e e f f i c i e n c y w i t h w h i c h i n d i v i d u a l s m a n i p u l a t e t h e i r d e c i s i o n a x i s , a r a n k o r d e r c o r r e l a t i o n was c o m p u t e d f o r t h e B v a l u e s a s s o c i a t e d w i t h e a c h s t i m u l u s c o n d i t i o n a n d f o r t h e o b s e r v e d f a l s e a l a r m r a t e c o r r e s p o n d i n g t o t h a t c o n d i t i o n . C h a p t e r I V RESULTS C o m p l e x A The d a t a p o i n t s o b t a i n e d f r o m t h e d e c i s i o n b e h a v i o u r o f t h e f i v e s u b j e c t s a s s i g n e d t o C o m p l e x A ( r e f e r t o A p p e n d i x B) were p l o t t e d on t h e f i v e d o u b l e n o r m a l -p r o b a b i l i t y g r a p h s i n F i g . 8. The s i x t h g r a p h g i v e s t h e a p p r o p r i a t e a v e r a g e s o f t h e s e p o i n t s . F i t t i n g s t r a i g h t l i n e s t o t h e d a t a p o i n t s o f t h e i n d i v i d u a l g r a p h s was n o t a t t e m p t e d b e c a u s e o f t h e w i d e v a r i a n c e s i n d a t a p o i n t s . H o w e v e r , i n t h e a v e r a g e d g r a p h t h e d a t a p o i n t s w e r e b e s t f i t t e d w i t h two ROC l i n e s e a c h c o m p a r a t i v e l y p a r a l l e l t o t h e d i a g o n a l . Thus t h e a s s u m p t i o n o f e q u a l v a r i a n c e s f o r t h e two o b s e r v a t i o n d i s t r i b u t i o n s was n o t n e g a t e d . I n s p e c t i o n o f t h e d a t a p o i n t s on a l l s i x g r a p h s o f F i g . 8 s u g g e s t e d a r e s u l t c o u n t e r t o t h e p r i m a r y h y p o t h e s i s o f C o m p l e x A, v i z . t h a t l a r g e - d i s c a r d - i n t e r v a l c o m p r e s s i o n w o u l d be more d e t r i m e n t a l t o i n t e l l i g i b i l i t y t h a n s m a l l -d i s c a r d - i n t e r v a l c o m p r e s s i o n . The d v a l u e o f t h e ROC l i n e ( o r c u r v e ) p r o d u c e d b y l a r g e - d i s c a r d - i n t e r v a l c o m p r e s s i o n i s .50 i n t h e a v e r a g e d g r a p h w h i l e t h a t p r o d u c e d b y s m a l l -d i s c a r d - i n t e r v a l c o m p r e s s i o n i s . ii-6. Thus t h e l a t t e r was more d e t r i m e n t a l t o i n t e l l i g i b i l i t y r a t h e r t h a n f a c i l i t a t i v e . In F i g . 9 the same da t a p o i n t s are p l o t t e d on an e q u a l - i n t e r v a l p r o b a b i l i t y graph. The averaged graph shows th a t the BOC curves are not onl y v e r y c l o s e to each other, but not too f a r d i s t a n t from the chance d i a g o n a l . The l a t t e r d i s t a n c e suggested that the S/N r a t i o was somewhat too low. I t was e l e v a t e d to an extent by removal of a l l stimulus p r e -s e n t a t i o n s which were c o r r e c t l y p e r c e i v e d o n l y once or never at a l l . The r e v i s e d d a t a p o i n t s are p l o t t e d on the graphs of F i g s . 10 and 11. Note, that i n the averaged graph of F i g . 10 the two ROC curves are s t i l l p a r a l l e l to the d i a g o n a l , i n d i c a -t i n g that the removal of the h a r d l y d i s t i n g u i s h a b l e s t i m u l i has not a l t e r e d the two d i s t r i b u t i o n s s i g n i f i c a n t l y . In. a l l of the graphs of F i g s . 10 and 11 the da t a p o i n t s l i e f u r t h e r up and to the l e f t . The r e l a t i v e p o s i t i o n s of the two curves remain the same, as shown i n the averaged graphs of F i g s . 10 and 11. The d v a l u e f o r the ROC curves obtained v i a l a r g e - d i s c a r d - i n t e r v a l compression i s now 1.2 w h i l e that f o r the s m a l l - d i s c a r d - i n t e r v a l compression i s now 1.0 5. These val u e s are approximately double what they were w i t h the u n r e v i s e d d a t a . The rank-order c o r r e l a t i o n between the c a l c u l a t e d B v a l u e s a s s o c i a t e d w i t h each p a y o f f m a t r i x and stimulus p r o b a b i l i t y and the corresponding " f a l s e alarm" r a t e s — pCUly — are gi v e n i n Table 2. A l l c o e f f i c i e n t s f o r r e v i s e d and u n r e v i s e d data are equal to .9 at the l e a s t . A - 4 1 - r pcq l y . pcaly F I G . 6 . Compar i son of the R O C curves obtained from.: 5 0 % c o m p r e s s i o n . S m a l l d i s c a r d i n t e r v a l = « L a r g e .» » . B • , U n r e v i s e d D a t a . -42-0 I -2 -3 -4 -5 -6 7 -8 -9 i-0 0 1 2 -3-4 5 6 7 Q S 10 pculy pculy 0 \ -2 -3-4 -5 -6 7 -8 9 10 pculy •I -2 -3 -4 -5 -6 7 -8 -9 10 pculy d=-50 •I 2 -3 4 -5 6 7 -8 9 pculy •46 •I -2 -3 4 -5 6 7 -8 -9 pculy F I G . 9 . Compar i son of the R O C c u r v e s ob t a i ned f r o m 1 5 0 % c o m p r ' n . S m a l l d i s c a r d , i n t e r v a l = o L a r g e <• « • U n r e v i s e d D a t a -43-pcjuly pculy FIG.10 Compar ison of the R O C curves obtained f r o m : 5 0 % c o m p r ' n . S m a l l d i s c a r d i n t e r v a l - • . - „ ' ' ' • ' ' L a r g e " • R e v i s e d D a t a . - 4 4 -V i i — > — i — . 1 < i i I 0 I 2 -3 -4 -5 -6 7 -8 -9 1-0 pculy 0 I 2 -3-4 -5 6 7 -8 9 10 pculy 0 I 2 3 4 -5 6 7 -8 -9 10 0 I -2 3 -4 -5 6 7 -8-9 10 pculy pcu ly ' FIG.If. Compar i son of the R O C c u r v e s ob t a i ned from•• 5 0 % c o m p r ' n . S m a l l d i s c a r d i n t e r v a l = o L a r g e » = • , R e v i s e d Data.. TABLE 2 CORRELATION BETWEEN OBTAINED FALSE ALARM RATES AND OPTIMAL B VALUES A COMPLEX Unrevised R e v i s e d Subject S.D.I. L.D.I. S.D.I. L.D.I. B.I. 1.00+++ . 9 0 + . 9 0 + . 9 0 + B.L. 1,00+++ 1 . 0 0 + + + 1 . 0 0 + + + 1 . 0 0 + + + T.O. . 9 5 + + . 9 0 + . 9 5 + + . 9 0 + M.P. 1 . 0 0 + + + . 9 0 + 1 . 0 0 + + + . 9 0 + R.W. 1 . 0 0 + + + . 9 0 + 1 . 0 0 + + + . 9 0 + +P . 0 5 ++p . 0 5 +++P .1 (a) C o r r e l a t i o n by Spearman's Rank C o r r e l a t i o n Method. k6 c o e f f i c i e n t of .9 i s s i g n i f i c a n t at the l e s s than .05 l e v e l of c o n f i d e n c e . Complex B The h y p o t h e s i s of Complex B, that seventy-four percent compression would he more d e t r i m e n t a l to i n t e l l i g i -b i l i t y than s i x t y percent compression, was supported. F i g . 12 c o n t a i n s the i n d i v i d u a l and averaged data p o i n t s p l o t t e d on d o u b l e - n o r m a l - p r o b a b i l i t y graphs. The ROC curves which c o u l d best f i t the averaged data p o i n t s are r e l a t i v e l y s t r a i g h t and p a r a l l e l to' the d i a g o n a l , suggesting that the v a r i a n c e s of the two stimulus p o p u l a t i o n s are normal and equal. The d v a l u e f o r the ROC curve o r i g i n a t i n g from s i x t y p e rcent compressed stimulus m a t e r i a l has a value of .35; w h i l e t h a t o r i g i n a t i n g from the d i f f e r e n t i a t i o n of seventy-four percent compressed m a t e r i a l has a d v a l u e of ,25* P l o t t i n g the same data p o i n t s on equal i n t e r v a l p r o b a b i l i t y paper produces the ROC curves of F i g . 13. As i n Complex A, the s e p a r a t i o n between the two curves i s q u i t e small and the d i s t a n c e from the d i a g o n a l n e g l i g i b l e . R e v i s i o n of the d a t a , as i n Complex A, produces d a t a p o i n t s which are s i t u a t e d f u r t h e r up and to the l e f t , as i n F i g . I** and 15. The two s t r a i g h t ROC curves of the averaged graph i n F i g . Ik again show that t h i s r e v i s i o n has not served to a l t e r the v a r i a n c e s of the two d i s t r i b u t i o n s appreciably. The d values of the two HOC curves on the averaged graph of F i g . 1 5 are equal to . 7 3 and . 6 8 for s i x t y percent and seventy-four percent compression respectively. These are approximately double the values of the unrevised data. The rank co r r e l a t i o n of the B values associated with each set of experimental conditions and the corresponding observed "f a l s e alarm" rates are given for each subject i n Table 3 . No c o e f f i c i e n t f a l l s below 9 . 0 and, a c o e f f i c i e n t of this value i s s i g n i f i c a n t at the less than . 0 5 l e v e l of confidence. 4 8 -pculy pcaly •I 2 4 -6 -8 pculy pcaly -2 vm I I i i I I I i i — i — i — j •01 I 2 -4-6 -8 ' 9 9 pcu l y •99, •01 -2 -1 0 1 2 l I 1 1 1/ -°o / */* -r I I - M M 6.D. I I i i _ . •01 -I -2 -4 -6 -8 pculy 2 I 0 - f -2 9 9 pcaly 01 •I -2 4 -6 -8 pculy ' • < i I I I I I 1 L 01 I 2 4 6 - 8 •99 pculy FIG.J 2. Compar i son of the R O C curves obtained f r o m : 6 0 and 7 4 % compr'n 6 0 % compress ion = . . ' 7 4 % U n r e v i s e d D a t a . - 4 9 -pculy pcu ly F|G.13. Compar i son of the R O C c u r v e s o b t a i n e d f r o m 1 6 0 a n d 7 4 % c o m p r ' n 6 0 % compress ion = * 7 4 % " B • U n r e v i s e d - D a t a . - 5 0 -•2-1 0 1 H-2 •01 •I -2 -4 -6 8 pculy pcdy J L I I I I I I I •I -2 4-6 -8 pculy -2 99 pcaly 01 •I -2 -4 -6 -8 pculy -2 §9 Pcaly. t 4 i i i • l i l t i i L •01 •I 2 -4-6 -8 pcu l y 99 ' I I I i I I I I L L 99 •01 -I 2 4-6 -8 pculy FIG. 14 Compar ison of the ROC curves obtained from : 6 0 8» 7 4 % compr'n. 6 0 % c o m p r e s s i o n = ° 7 4 % ii = •• R e v i s e d D a t a . -51 -0 -I -2-3 4 -5 6 7 -8 9 10 pculy I 2 -3 4 -5 -6 7 -8 9 10 pculy •I -2 -3 -4 -5 -6 7 -8 -9 pculy 0 I 2 -3 4 -5 6 7 -8 -9 IO pculy F IG . 15.Compar ison of the R O C 6 0 % compress ion 3 • 74 % „ pculy c u r v e s ob t a i ned f r o m 1 6 0 8t 7 4%comprh R e v i s e d D a t a . TABLE 3 CORRELATION BETWEEN OBTAINED FALSE ALARM RATES AND OPTIMAL B VALUES B COMPLEX Un r e v i s e d R e v i s e d Subject 60f0 Comp. 7^0 Comp. 6of0 Comp. 7h°j0 Comp. cc. 1 . 0 0 + + + 1 , 0 0 + + + 1 . 0 0 + + + 1 . 0 0 + + + S.D. 1 . 0 0 + + + . 9 0 + 1 . 0 0 + + + 1 . 0 0 + + + B.L. 1 . 0 0 + + + 1 . 0 0 + + + . 9 0 + . 9 0 + R,P« 1 , 0 0 + + + . 9 0 + . 9 0 + 1 . 0 0 + + + G.W. . 9 0 + 1 . 0 0 + + + . 9 0 + 1 . 0 0 + + + +p . 0 5 ++p . 0 5 +++p . 0 1 (a) C o r r e l a t i o n by Spearman's Rank C o r r e l a t i o n Method, Chapter V DISCUSSION The n e g a t i o n of the hypothesis of Complex A, t h a t w i t h the compression r a t i o h e l d constant, a l a r g e d i s c a r d i n t e r v a l i s more d e t r i m e n t a l to i n t e l l i g i b i l i t y than a small d i s c a r d i n t e r v a l , i s not, i n r e t r o s p e c t , too d i f f i c u l t to account f o r . The d u r a t i o n of the s i g n i f i c a n t speech sounds, the "a" and "u" of "commination" and "comminution," are r e l a t i v e l y s h o r t i n comparison w i t h the d u r a t i o n of the l a r g e d i s c a r d i n t e r v a l . Consequently, these sounds were o f t e n missed or o n l y p a r t i a l l y shortened i n the compression procedure, w h i l e the other p o r t i o n s o f the words were s e v e r l y e x c o r i a t e d . Since the s u b j e c t s were r e q u i r e d to l i s t e n o n l y f o r the complex sounds of "a" and "u," the f a c t t h a t the remainder of the corresponding words were s e v e r e l y a l t e r e d f a i l e d to hamper the r e c o g n i t i o n of these two sounds. With r e f e r e n c e to the r e s u l t s of Fairbanks and Kodman ( 1 9 5 7 ) , t h e i r s t i m u l u s words v a r i e d w i d e l y i n sound so t h a t f o r accurate r e c o g n i t i o n i t was necessary to hear something from a l l s e c t i o n s of the word. A small d i s c a r d i n t e r v a l i n s u r e d t h a t a l l s e c t i o n s would be represented w hile compression w i t h the l a r g e d i s c a r d i n t e r v a l meant t h a t c e r t a i n important p o r t i o n s would be l e f t out. In t h i s study, the "a" and "u" sounds were always present a f t e r s m a l l - d i s c a r d - i n t e r v a l 5k compression but they were always compressed and a l t e r e d somewhat, while with l a r g e - d i s c a r d - i n t e r v a l compression such was not the ca,se, thereby i n s u r i n g , over a large number of p r e s e n t a t i o n s , b e t t e r i n t e l l i g i b i l i t y f o r l a r g e - d i s c a r d -i n t e r v a l compression. One of the more serious drawbacks of the theory of s i g n a l d e t e c t i o n , i s that no s t a t i s t i c a l t o o l e x i s t s f o r determining,the s i g n i f i c a n c e of d value or the d i f f e r e n c e between two d v a l u e s . Consequently, the v a l i d i t y of the obtained ROC curves must be judged by i n s p e c t i o n r a t h e r than by an o b j e c t i v e s t a t i s t i c a l technique. The extensive variances of the r e v i s e d and unrevised data p o i n t s i n a l l the i n d i v i d u a l graphs of Complex A and Complex B suggest that many v a r i a b l e s were not adequately c o n t r o l l e d . Part of the variance i s due to the d i f f e r e n t i a l s e n s i t i v i t y of the subject. A measure of the average s e n s i t i v i t y of the s u b j e c t s , as shown i n the averaged graphs, s i g n i f i c a n t l y reduced t h i s variance and gives a more obvious i n d i c a t i o n of the e f f e c t s of v a r y i n g amounts of i n f o r m a t i o n on i n t e l l i g i b i l i t y . Serious e r r o r variance may have a l s o been introduced because of the manual c o n t r o l of the S/N r a t i o , d i s r u p t i v e e n v i r o n -mental changes i n the experimental room and gross f l u c t u a -t i o n s i n the a t t i t u d e s and f a t i q u e l e v e l s of the s u b j e c t s . Since these e r r o r s tend t o . c a n c e l each other out when combined, the averaged graphs are probably the purest 55 indication of the effects of the manipulated experimental variables. . In spite of these c r i t i c i s m s , the data points of the individual and averaged graphs of both complexes con-s i s t e n t l y indicate r e l a t i v e differences in i n t e l l i g i b i l i t y for the d i f f e r e n t -experimental treatments. With increased compression, d decreases i n magnitude. With the unrevised data, f i f t y percent compression gave d values of . 5 0 and ,k6 for the large and small discard intervals respectively. Si x t y percent compression gave a d value of . 3 5 while seventy-four percent compression promoted a d value of . 2 5 . In the revised data these values are doubled, but the r e l a t i v e order i s the same. This ordering occurred despite the fact that two d i f f e r e n t groups were u t i l i z e d and adds further support to the argument presented e a r l i e r that the difference between . observation means on a l i k e l i h o o d r a t i o axis may be considered a function of amount of information. F i f t y percent compres-sion, v i a either method, does not remove as much information as s i x t y percent compression, and consequently, d i f f e r e n t i a -t i o n of f i f t y percent compressed material i s less d i f f i c u l t than d i f f e r e n t i a t i o n of s i x t y percent compressed material. The ROC curves of both complexes, as plotted on the equal i n t e r v a l p r o b a b i l i t y paper, show that the rate of " h i t s " — pCAly, i s a function of the "false alarm" rate — pCUly. Or, from a d i f f e r e n t perspective, the detection and 5 6 r e c o g n i t i o n of the stimulus words were f u n c t i o n s of the c r i t e r i o n the s u b j e c t adopted and not o n l y of h i s s e n s i t i v i t y . M a n i p u l a t i o n o f the c r i t e r i o n , by changing the p r o b a b i l i t i e s of s i g n a l occurrence and the v a l u e s and co s t s of d e c i s i o n outcomes, serves to permit the s e p a r a t i o n of t h i s v a r i a b l e from the s e n s i t i v i t y of the s u b j e c t s . Thus, f u r t h e r support i s g i v e n to those p s y c h o p h y s i c i s t s who i n s i s t t h a t c o n t r o l of the d e c i s i o n c r i t e r i o n must be maintained. Because of i n d i v i d u a l d i f f e r e n c e s i n the understanding and r e c e p t i o n o f experimental i n s t r u c t i o n s , the best way to i n s u r e t h i s c o n t r o l i s to manipulate the c r i t e r i o n so t h a t i t s i n f l u e n c e on the d e t e c t i o n of s i g n a l s can be separated from the " t r u e " s e n s i -t i v i t y of the s u b j e c t . There i s no doubt that the s u b j e c t s i n t h i s study possessed a v a r i a b l e d e c i s i o n a x i s . The c a l c u l a t e d B v a l u e s ranged from .11 to .90, d e s c r i b i n g a s u b j e c t i v e c a u t i o n -continuum extending from v e r y " l i b e r a l " to v e r y " c o n s e r v a t i v e . When a rank c o r r e l a t i o n between these v a l u e s and the observed " f a l s e alarm" r a t e s was computed f o r each s u b j e c t , the lowest c o e f f i c i e n t was .9. Such a va l u e i s s i g n i f i c a n t at the l e s s than .05 l e v e l of c o n f i d e n c e . Thus c r i t e r i o n m a n i p u l a t i o n d i d occur when the p a y o f f and p r o b a b i l i t y c o n d i t i o n s of the experiment were v a r i e d . I t would appear that i n d i v i d u a l s are capable of a p p r o p r i a t e l y weighing these f a c t o r s when making d e c i s i o n s . The h i g h c o r r e l a t i o n obtained a l s o adds f u r t h e r 57 s u p p o r t t o t h e c o n c e p t o f t h e l i k e l i h o o d r a t i o h e i n g u s e d a s a f o r m o f s u b j e c t i v e y a r d s t i c k . O b s e r v a t i o n s f a l l i n g b e l o w t h e p o i n t w h e r e t h e d e c i s i o n a x i s c r o s s e s t h i s y a r d s t i c k p r o -m ote one c l a s s o f d e c i s i o n , w h i l e o b s e r v a t i o n s o r d e r e d a b o v e t h i s a x i s e v o k e a s e c o n d c l a s s o f r e s p o n s e s . The o b t a i n e d c o e f f i c i e n t s compare f a v o u r a b l y w i t h t h o s e o b t a i n e d b y S w e t s , T a n n e r a n d B i r d s a l l (1961). I n t h e c a s e where t h e ab o v e a u t h o r s i n a v i s u a l d e t e c t i o n s t u d y d i d . n o t i n f o r m t h e i r s u b j e c t s o f what t h e a p p r o p r i a t e f a l s e a l a r m r a t e s h o u l d b e , t h e c o e f f i c i e n t s f o r t h r e e s u b j e c t s f e l l b e l o w t h o s e o b t a i n e d f o r t h e t e n s u b j e c t s i n t h i s s t u d y . O n l y when a n o t h e r f o u r s u b j e c t s i n a s l i g h t l y d i f f e r e n t v i s u a l d e t e c t i o n e x p e r i m e n t w e r e i n f o r m e d o f t h e a p p r o p r i a t e f a l s e a l a r m r a t e s , d i d t h e c o e f f i c i e n t s a p p r o x i m a t e t h e v a l u e s o b t a i n e d h e r e . H o w e v e r , i n a n a u d i t o r y d e t e c t i o n e x p e r i m e n t , t h e ab o v e a u t h o r s o b t a i n e d c o e f f i c i e n t s o f 1.0 f o r some two s u b j e c t s who w e r e n o t i n f o r m e d o f t h e i r o ptimum f a l s e a l a r m r a t e s . T h u s , : t h e r e s u l t s o f t h i s s t u d y a r e q u i t e i n a c c o r d w i t h o t h e r e x p e r i m e n t a l f i n d i n g s . A l t h o u g h t h i s h i g h c o e f f i c i e n t may b e due i n p a r t t o t h e i n s t r u c t i o n s t h a t t h e s u b j e c t s h o u l d s o c h o o s e h i s d e c i s i o n s t h a t he w o u l d l e a v e t h e e x p e r i m e n t a l room w i t h a s much money as p o s s i b l e , i t i s q u i t e p l a u s i b l e t o c o n t e n d t h a t t h e s u b j e c t w o u l d h a v e done so e v e n i f he h a d n o t b e e n so i n s t r u c t e d , a s most o f them w e r e n o t i n g o o d f i n a n c i a l s t a n d i n g 58 a t t h e t i m e . I t s h o u l d h e p o i n t e d o u t a t t h i s p o i n t , t h a t one s u b j e c t i n p a r t i c u l a r — G. D. ( s e e A p p e n d i x C ) , made no a t t e m p t t o s i g n i f i c a n t l y v a r y h i s " f a l s e a l a r m " a n d d e t e c t i o n r a t e s e v e n when a " f a l s e a l a r m " was f i n e d a s much as f i v e a n d n i n e c e n t s . W h e t h e r he f o u n d t h e g a m b l i n g v a l u e o f a d e c i s i o n t o be more s a t i s f y i n g t h a n t h e c o s t o f a f a l s e a l a r m i s d i f f i c u l t t o s a y . I n a n y e v e n t , s u c h a d e c i s i o n - m a k i n g s i t u a t i o n a s t h i s may b e o f v a l u e i n p r o b i n g a n d m e a s u r i n g c e r t a i n p e r s o n a l i t y c h a r a c t e r i s t i c s s u c h as d e g r e e o f c a u t i o n o r r e s i s t a n c e t o p r e s s u r e . No a t t e m p t h o w e v e r , was made t o i n v e s t i g a t e t h e s e s u b j e c t v a r i a b l e s . T h u s , t h e r e s u l t s o f t h i s s t u d y s t r o n g l y i n d i c a t e t h a t t h e a p p l i c a t i o n o f s t a t i s t i c a l d e c i s i o n t h e o r y , o r i t s s p e c i a l v a r i a n t , t h e t h e o r y o f s i g n a l d e t e c t i o n , t o p e r c e p t u a l d e c i s i o n - m a k i n g s i t u a t i o n s , i s b o t h j u s t i f i e d a n d p r o d u c t i v e . The t h e o r y was a b l e t o d e t e c t i n f o r m a t i o n d i f f e r e n c e s i n t h e s t i m u l u s m a t e r i a l b y e x a m i n a t i o n o f t h e s u b j e c t s . ' r e s p o n s e s . B y m a n i p u l a t i n g t h e s u b j e c t s ' d e c i s i o n a x e s , t h e e f f e c t s o f t h e i r d e c i s i o n c r i t e r i o n c o u l d b e s e p a r a t e d f r o m t h e i r a c t u a l s e n s i t i v i t y . T h u s , a s a p s y c h o p h y s i c a l t e c h n i q u e , s t a t i s t i c a l d e c i s i o n t h e o r y o r t h e t h e o r y o f s i g n a l d e t e c t i o n w o u l d a p p e a r l i k e l y t o b e more w i d e l y u s e d i n t h e f u t u r e . W h e t h e r t h e s e t h e o r i e s h a v e a n y t r u e c o r r e s p o n d e n c e w i t h t h e a c t u a l s e n s o r y a n d p e r c e p t u a l p r o c e s s e s s t i l l r e m a i n s t o be shown. C e r t a i n l y t h e f i n d i n g s o f n e u r o p h y s i o l o g y t h a t 59 the s e n s i t i v i t y of receptor organs i s not constant hut a f u n c t i o n of c e n t r a l i n f l u e n c e , would a l l o w f o r v a r y i n g observations of the "same" stimulus s i t u a t i o n . The s u r v i v a l value and f a m i l i a r i t y of s t i m u l i might be considered as corresponding to the payoff m a t r i x and the p r o b a b i l i t y of s t i m u l i occurrence. To permit p r e d i c t i o n on the b a s i s of these concepts would f i r s t r e q u i r e t h e i r measurement and i n the case of humans, great i n c o n s i s t e n c i e s and problems then a r i s e . Studies of gambling behaviour suggest that the u t i l i t y of money i s not l i n e a r . Moreover, i f A i s judged more d e s i r -able than B, a,nd B more d e s i r a b l e than C, t h i s does not mean that the observer w i l l n e c e s s a r i l y judge A more d e s i r a b l e than C. In a d d i t i o n , s u b j e c t i v e or personal p r o b a b i l i t i e s have not been found to equal o b j e c t i v e or a c t u a l p r o b a b i l i t i e s (Edwards, 195*4-). Consequently, u n t i l more inf o r m a t i o n i s a v a i l a b l e , i t would appear more s c i e n t i f i c a l l y d e f e n s i b l e to make s t a t i s t i c a l d e c i s i o n theory, or the theory of s i g n a l d e t e c t i o n , t o o l s of psychophysical i n v e s t i g a t i o n before p o s t u l a t i n g them as substantive t h e o r i e s of p e r c e p t i o n or human behaviour. A P P E N D I X A S T I M U L U S M A T E R I A L 6 l ORDER OF STIMULUS WORDS FOR TAPES HAVING THE PROBABILITY OF COMMINATION EQUAL TO . 5 SET SET SET SET SET SET SET SET SET SET 1 2 3 k 5 6 7 8 9 10 A U u U u A A A u A U U A A u A U U u U U A A U A u U u u A U A A A u u A A u U A A A A A A A U u U U U A U A A U u A U A U U U U A u A A A U U u A A A A A A u U A A A U U A U A u A A U U A U TJ A U u U A U U U U U A A A A A u A U u A A A A A u u A A TJ A U U k A U A A A A U U U A A U u U A A A A A u A U A A U U U U U U U A U A A A A u A A U A A U U U U A U A u A A A u A A U U A u U A U u A U A U A 6 2 ORDER OF STIMULUS WORDS FOR TAPES HAVING THE PROBABILITY OF COMMINATION EQUAL TO .1 SET SET SET SET SET SET SET SET SET SET 1 2 3 k 5 6 7 8 9 1 0 A U U U u u u A A u U U U u u u A U U u U A U u u u U U U u U U U u u u U u u A u U U u u A U A u U U A u u A u u u u A u U u u U u U u A U u u u u U A U u U u u u u u u u U u U u u u u u u U u u U u u u u u u U u u U u u u u u u u A u u A A u u u u u u u u U u u u u u u u u u U u u u u u u A u u U u u u u u u A u u u u u u u u u u u u u u u A u u u u u u u u u u u u u U u u u A u u u u u U u u u OSDER OF STIMULUS WORDS FOR TAPES HAVING THE PROBABILITY OF COMMINATION EQUAL TO , 9 SET SET SET SET SET SET SET SET SET SET 1 2 3 k 5 6 7 8 9 1 0 A A A A A A A A A A A U A A A U U A A A A A A A A A A U A A U A A A A A A A A A A A A A U U A A U U A A A A A A A U A A A U A A A A A A A A U A A A A A A A A A A U A A U A A A A A A A A A A U A A A A A A A A A A .'A U A A A A A A A A A A U A . A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A U A A A A A U A A A A A A U A A A A A A A P P E N D I X B Data of Complex A 5 0 $ Compression SUBJECT B . I . D i s c a r d I n t e r v a l Tape pCA - M a t r i x U n r e v i s e d p C A l y , p C U l y R e v i s e d p C A l y , p C U : S m a l l A .5 +1,-1 .56,^31 .65, .28 S m a l l E .5 +1,-5 . 2 7 , .10 .^5, .09 Smal 1 C .5 +1,-9 . 2 5 , .08 .^3,.01 S m a l l N .1 +1 ,-1 .25,.0/+ .50, .05 S m a l l 0 .9 +1,-1 .90, .70 .90, .38 L a r g e D .5 +1,-1 . ^ , . 2 7 .57,.19 L a r g e B .5 +1,-5 .36,.Ok .71, .0^ L a r g e F .5 +1,-9 .15,.07 .25, .03 L a r g e P .1 +1,-1 .15, .03 .38, .0ir L a r g e Q .9 +1,-1 .93,-75 .98, .68 SUBJECT B..L B i s c a r d I n t e r v a l Tape pCA M a t r i x Unrevised pCAly,pCUly Revised pCAly,.pCU: Small A .5 +1, -1 .58,.,; 60 .73,. .58 Small, E +1 ,.-5 ..52, M .80,.46 Smal 1 C ..5 +1,-9 .,30 ,,.22 .55 ,..,20 Small N a +1 ,-1 ao,.8.05 .20,; o05 Small 0 ..9 +1,-1 ..95 ,..90 ..95 ,,..75 Large B .5 +1 , - l . .69,. 63 .,88 , .57 Large F *5 +1,-5 a 7, ,;15 .27, a 5 Large B .5 +1,-9 .08,.06 „21, a,06 Large P a +1 , - l a5, 0o4 Large Q .9 +1 , - l .95, .90 .98, .78 67 SUBJECT D i s c a r d I n t e r v a l Tape pCA M a t r i x Unrevised pCAly,.pCUly Revised pCAly,pCU] Smal 1 C .5 +1,-1 . 6 5 , . 5 3 . 8 6 , . 5 3 Small A .5 +1,-5 o 3 9 , . 2 7 . A 8 . . 2 3 Small E .-5 +1,-9 . 1 3 , - 0 5 . 2 3 , , 0*4-Smal 1 N .1 +1,-1 . 1 5 , . 0 3 . 3 0 , . 0 3 Small 0 ,9 +1,-1 . 9 2 , . 8 5 . 9 0 , . 8 8 Large D .5 +1,-1 .57,:M . 7 6 , . 2 k Large F .5 +1,-5 . 2 9 , . 1 0 . 5 0 , . 1 0 Large B .5 +1,-9 . 0 9 , . 0 1 . 2 2 , . 0 1 Large P a +1,-1 .15,.0*+ . . 3 8 , . 0*4-Large Q . 9 +1,-1 . 9 0 , . 8 5 .90,.78 S U B J E C T T . O . D i s c a r d I n t e r v a l T a p e p C A M a t r i x U n r e v i s e d p C A l y , p C U l y R e v i s e d p C A l y , p C U l ; L a r g e F ".5 +1,-1 .60,V33 .82,.33 L a r g e D .5 +1,-5 .33,.16 .42,,08 L a r g e B .5 +1,-9 .17,.02 .39,.02 L a r g e P a +1,-1 .10,,0^ ,25,.oip L a r g e Q .9 +1,-1 .98,.95 .98,.89 S m a l l A .5 +1,-1 V 6 9 , . 5 8 .81,.57 S m a l 1 C .5 +1,-5 .07,.03 a3,.oi S m a l l E .5 +1,-9 .10,.00 .18,.00 S m a l l N a +1,-1 .00,.00 .00,.00 S m a l l 0 .9 +1,-1 1.00,1.00 1.00,1.00 SUBJECT R D i s c a r d I n t e r v a l Tape pCA M a t r i x Large B .5 +1,-1 Large D .5 +1,-5 Large F .5 +1,-9 Large P .1 +1,-1 Large Q .9 +1,-1 Smal 1 E .5 +1,-1 Small C .5 +1,-5 Small A .5 +1,-9 Smal 1 N .1 +1,-1 Small 0 .9 +1,-1 w. U n r e v i s e d pCAly,pCUly R e v i s e d pCAly,pCUly .73,.68 .66,.69 .85,'; 60 .51,.38 .82,.38 .to), .13 1.00,.0^ .95,.85 * • - . .93,.67 .67,.60 .82,.60 M , M .80,'.42 .37,.13 .48,. 12 .30,.08 .60,.08 .93,.90 .93,.75 70 AVERAGES e D i s c a r d I n t e r v a l pCA M a t r i x Unrevised pCAly . pCUly Revised pCAly pCUly Small .5 * +1, -1 .63 .52 •77 .51 Small .5 . +1, -5 .35 .26 .53. :zk Smal 1 .5 +1, -9 .23 . .10 .38 .08 Smal 1 .1 +1, - l .16 .. '.ok ...32. . a0i}-Smal 1 .9 . +1, -1 .9^  .89 .9^  .75 Large .5 +1, -1 .61 . .k? .'69. . , .kk Large .5 • +1, -.5 .36 .23 :'.55. . .19 Large .5 +1, -9 .20 . .11 .38 . .10 Large .1 - +1, 1 """ JL. .-19 .06 .^8 . »ok Large .9 ., +1, -1 .95 : . .86 .96 .76 A P P E N D I X . C Data of Complex B 60<fo and 7kf0 Compress 72 SUBJECT C.C. Unr e v i s e d R e v i s e d Compression Tape pCA M a t r i x pCAly,pCUly pCAly,pCUly 7*4 K .5 + 1 , -1 .59 .58 .68 .60 7W/0 M .5 +1, _ —J .^ 9 .49 .70 >7 7^jo L .5 +1, -9 .to* .36 .56 .33 7kfo T .1 +1, -1 .25 .09 .63 .09 7^/o U .9 + l , -1 .91 .85 .91 .73 6of0 J .5 +1, -1 M .30 .60 .29 6of0 H .5 +1, -5 .26 .28 .3^  .25 60$ I .5 +1, -9 .20 .5^  .17 6of0 R .1 +1, -1 .25 .09 .56 .09 6of0 S »9 +1, -1 .92 .80 .92 .50 73 SUBJECT C.D. U n r e v i s e d R e v i s e d Compression Tape pCA M a t r i x pCAly,pCUly pCAly.pCUly 6cf0 I .5 +1, : - l .5.6 .60 .65 .57 60$ H .5 +it -5 .64 .5^  .7^- .5^  6of0 J .5 +1, -9. .60 .43 .7^  6o<?o R .1 +1, -1 .15 .13 .33 .13 6ofo S •9. +1, -1 .9,0 .85 .90 .75 7M° M •5 +1, -1 .5,0 >7 .89 K .5 +1, -5 .ko .4-8 .kk .32 ?Lpfo L .5 +1, -9 .38 .35 M . 2 8 7ty T .1. +1, -1 .15 .05 .38 .05 7kio U • 9 . +l, -1 .9^  .85 .9^  .73 SUBJECT B.L. Unrevised Revised Compression Tape pCA M a t r i x pCAly,pCUly pCAly,pCUly 6ofo I .5 +1, -1 .52 .40 .65 .37 6of0 H .5 +1, -5 .37 .17 .47 .13 6of0 J .5 +1, -9 .14 .47 .14 6of0 R .1 +1, -1 .20 .07 .44 .07 60io S .9 +1, -1 .90 .85 .90 .63 L .5 +1, -1 .53 .60 .70 .58 M .5 +1, -5 .40 .33 , .60 .32 7^fo K .5 +1, -9 .31 .22 .44 .20 7^fo T .1 +1, -1 .15 .05 .38 .05 7Mo U .9 +1, -1 .88 .65 .88 .36 75 SUBJECT R.P. U n r e v i s e d R e v i s e d Compression Tape pCA M a t r i x pCAly.pCUly pCAly,pCUly K .5 + 1, - l M 0 6o .^5 7^o M .5 +1, - 5 .28 '.28 : M .18 7ty L .5 +1, -9 .19 .20 .25 .16 7^jo T .1 +1, -1 .05 .10 .13 .10 7^o U .9 +1, -1 .91 .95 .95 .91 6o<?0 H .5 +1, - l .61 .55 •'.71* .53 6o$ J .5 +1, - 5 .25 .12 .35 .11 6o$ I .5 +1, - 9 .18 .13 .10 60$ R .1 +1, - l .10 .05 .22 .05 6o$ S .9 +1, - l .95 .80 .95 .50 76 SUBJECT G.W. Unr e v i s e d R e v i s e d Compression Tape pCA M a t r i x p C A l y ? p C U l y pCAly,pCUly 6of0 I .5 -1 .56 .51 .72 .75 6of0 J .5 +1, -5 .20 .10 .32 .10 6Q<?o H ,5 + l , -9 .21 .05 .25 .05 6of0 R .1 +1, -1 .05 .07 .11 .07 6of0 S .9 + 1 > - I 1.00 .95 1.00 .88 7^h L .5 +1, -1 .65 .51 .69 .62 714 K • .5 +1, .14 .11 .22 .10 7ty M ,5 +1, -9 .08 .05 .10 .04 T .1 -1 .00 .02 .00 .02 7kf0 U .9 + 1 > -1 . .98 1..00 .,98 1.00 77 Compression pCA 60fo .5 6o<?0 .5 6o$ .5 6o$ . l 6ofo .9 7^ .5 .5 7^ .5 7&/o .1 7^ .9 AVERAGES . Unrevised M a t r i x pCAly pCUly +1, -1 .56 .51 +1, .38 .25 +1, -9 .35 .19 +1, -1 .25 .08 +1, -1 .93 .85 +1, -1 .5^  .53 +1, -5 .3^  .3^  +1, -9 .28 .2^  +1, -1 .12 ,06 +1, -1 .92 .85 Revised pCAly. pCUly .67 .50 \hh .23 .45 .18 .33 .08 .93 .65 .71 .54 ,i*<8 .28 .36 .20 .28 .06 .93 .75 REFERENCES B o r i n g , E. G. A h i s t o r y o f e x p e r i m e n t a l p s y c h o l o g y . (2nd e d . ) . New Y o r k : A p p l e t o n C e n t u r y - C r o f t s , 1950. 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J . a'cous. Socj Amer.. 1953, ^5, 102-108. G r e e n , D. M. P s y c h o a c o u s t i c s a n d d e t e c t i o n t h e o r y . J . a c o u s t . S o c . Amer., i960, 32, 1189-1205. M i l l e r , G. A., a n d L i c k l i d e r , J . C. R. The i n t e l l i g i b i l i t y o f i n t e r r u p t e d s p e e c h . J . a c o u s t . S o c . Amer., 1950, 22, 167-I73. Meyman, J . , a n d P e a r s o n , E. The t e s t i n g o f s t a t i s t i c a l h y p o t h e s e s i n r e l a t i o n t o p r o b a b i l i t i e s . P r o c . C a m b r i d g e P h i l . S o c . , 1933, 29, 4-92-510. P e t e r s o n , W. W., B i r d s a l l , T. G., and F o x , W. C. The t h e o r y o f s i g n a l d e t e c t a b i l i t y . I n s t . R a d i o E n g r s . T r a n s . P r o f e s s i o n a l G r o u p o n I n f o r m a t i o n  T h e o r y , 1954, PGIT-4, 171-212. S e n d e r s , V. L. Me a s u r e m e n t a n d S t a t i s t i c s . New Y o r k : M a c M i l l a n . , 1958. S m i t h , M., a n d W i l s o n , E d n a A. A m o d e l f o r t h e a u d i t o r y t h r e s h o l d and i t s a p p l i c a t i o n t o t h e m u l t i p l e o b s e r v e r . P s y c h o l . M o nogr., 1953, 67, No. 9 (Wole No. 359). 79 Swets, J. A., Tanner, W. P., J r . , and B i r d s a l l , T. G. Decision processes in perception. Psychol. Rev., 1961, 68, 301-3*10. Tanner, W. P., J r . , and Norman, R. T. The human use of information I I . Signal detection for the case of an unknown signal parameter. Inst. Radio Engrs. Trans. Information Theory. 195^ , PGIT-*l, 222-226. Tanner, W. P., J r . , and Swets, J. A. A decision-making theory of v i s u a l detection. Psychol. Rev.. 195**, 61, *M)1-*K)9. Tanner, W. P., J r . , Swets, J. A., and Green, D. M. Some general properties of the hearing mechanism. Techn. Rep. No. 30, E l e c t r o n i c Defense Group, University of Michigan, 1956. Thurstone, L, L, A law of comparative judgement. Psychol. Rev., 1927, 3^ , 273-286. (a) Thurstone, L..L. Psychophysical analysis. Amer. J. Psychol., 1927, 38, 368-389. (h) Wald, A. S t a t i s t i c a l decision functions. New York: Wiley, 1950."" 

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