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UBC Theses and Dissertations

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 T h e s i s Submitted i n P a r t i a l F u l f i l m e n t o f the Requirements  f o r the Degree Of  Master of A r t s i n the Department of Psychology  We accept t h i s t h e s i s as conforming to the s t a n d a r d r e q u i r e d from c a n d i d a t e s f o r the degree of MASTER OF ARTS  Members of the Department of Psychology The U n i v e r s i t y of B r i t i s h Aiigust, 1 9 6 2  Columbia  In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. f o r extensive  I f u r t h e r agree that permission  copying of t h i s t h e s i s f o r s c h o l a r l y purposes may  granted by the Head of my Department or by h i s  be  representatives.  I t i s understood 'that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  Department of  ^/^AM^Oi/-  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 3, Canada. Date  C ^ / W  ABSTRACT The  o b j e c t of t h i s s t u d y was  to determine whether  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 , or a s p e c i a l a p p l i c a t i o n of i t , the t h e o r y o f s i g n a l d e t e c t i o n , c o u l d he of v a l u e i n account i n g f o r t h e behaviour making t a s k .  The  of s u b j e c t s i n a p e r c e p t u a l d e c i s i o n -  amount o f i n f o r m a t i o n i n these t a s k s  was  v a r i e d t o see i f the t h e o r y c o u l d p r e d i c t changes i n s u b j e c t performance. F i v e s u b j e c t s were r e q u i r e d t o d i s t i n g u i s h between f i f t y percent  time compressed r e c o r d i n g s of the  words "commination" and noise.  "comminution  Under one t r e a t m e n t ,  11  stimulus  embedded i n "white"  compression was  gained  d i s c a r d i n g many s m a l l l e t t e r segments w h i l e i n the t h i s same c o m p r e s s i o n v a l u e was l a r g e l e t t e r segments.  I t was  by other  o b t a i n e d by d i s c a r d i n g a hypothesized  few  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 d e t r i m e n t a l t o stimulus 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 com-  pression. F i v e other s u b j e c t s were asked t o d i s t i n g u i s h between the two noise-embedded s t i m u l u s words w h i c h had been time-compressed s i x t y and s e v e n t y - f o u r p r e d i c t e d that s i x t y percent  percent.  I t was  compression would be l e s s  d e t r i m e n t a l t o the i n t e l l i g i b i l i t y of the s t i m u l u s words  ii  than seventy-four  percent  Concurrently, to  compression,,  i n both groups, an attempt was  manipulate the degree of cautiousness  of a l l ten s u b j e c t s . order to permit tivity  Such m a n i p u l a t i o n  or d e c i s i o n c r i t e r i a was  attempted i n  the s e p a r a t i o n of each s u b j e c t s ' a c t u a l s e n s i -  from each's 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 .  l a t i o n i n v o l v e d v a r y i n g the costs and c o r r e c t and  made  f i n e s associated with  i n c o r r e c t d e c i s i o n s as w e l l as the  of each stimulus word's  T h i s manipu-  probabilities  occurrence.  L a r g e - d i s c a r d - i n t e r v a l compression was l e s s 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 ,  found to be  as i n f e r r e d from s u b j e c t  performance, than s m a l l - d i s c a r d - i n t e r v a l compression. f i n d i n g was  c o n t r a r y to the f i r s t h y p o t h e s i s .  compression, as p r e d i c t e d , was bility  than seventy-four  S i x t y percent  l e s s d e t r i m e n t a l to  percent  compression.  t h a t the t h e o r y of s i g n a l d e t e c t i o n p e r m i t t e d  This  intelligi-  I t was  observed  s e p a r a t i o n of  each s u b j e c t s ' s e n s i t i v i t y from h i s monetary degree of cautiousness. a c c e s s i b l e to It  T h i s cautiousness  was  a l s o found to be  manipulation. i s suggested that s i n c e the approach of  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 d e t e c t e d changes i n s u b j e c t  per-  formance i n response to v a r y i n g amounts, of i n f o r m a t i o n , i t can be p r o f i t a b l y a p p l i e d to the study of p e r c e p t i o n .  ACKNOWLEDGEMENT  The w r i t e r would l i k e t o express h i s g r a t i t u d e to P r o f e s s o r M. P. Beddoes f o r t h e advice and encouragement r e c e i v e d d u r i n g t h e course of t h i s study.  Thanks are a l s o  due t o the Department of E l e c t r i c a l E n g i n e e r i n g and the N a t i o n a l Research support.  i  C o u n c i l f o r t h e i r generous f i n a n c i a l  T A B L E OF  CONTENTS  Chapter  Page ABSTRACT  I  II  i  I N T R O D U C T I O N AND  STATEMENT  OF  THE P R O B L E M  1  T H E O R E T I C A L AND E X P E R I M E N T A L BACKGROUND.  3  Early History. The  Theory of S i g n a l Detection  5  . . .  (1)  Statistical  (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  D e c i s i o n Theory.  Experimental Results of S i g n a l Detection (1)  The  with  The D e t e c t i o n Signals.  9  the Theory 20 20  o f Complex . . . .  Time C o m p r e s s i o n o f S p e e c h  . . .  Hypotheses  2k 26 2  7 31  METHOD Stimulus  5  .  The T h r e s h o l d a n d t h e Variable Criterion  (2)  III  3  . . . . . . . . . . .  Material. . . . . . . . . .  31  Subjects  3k  Instructions  35  Analysis  3  of the Data  8  Chapter  IV  Page  RESULTS . . . • • . . • • . . < > » . . .  39 39  Complex A Complex B D I S C U S S I O N  v  .  -.  \  -.  ;  -.  .  '.  .  ;  .  .  .  .  k6  "  53  APPENDICES A  Stimulus Material.  B  D a t a o f Complex A .  .  64  C  D a t a o f Complex B  i '  7  1  7  8  REFERENCES  £>0  LIST  OF  TABLES  TABLE  .  Experimental  Tapes  .  .  1  Table  2  Correlation Alarm Rates' A Complex  Between Obtained False a n d O p t i m a l B' V a l u e ' s - . . . . . . .  Correlation Alarm Rates B Complex  Between Obtained False and Optimal' B Value's --'  3  of  .  Constructed  PAGE  33  k$  5  2  L I S T OF FIGURES  FIGURE  PAGE  1  Graphic Representation of two hypotheses  6  2  The D e c i s i o n A x i s i n r e l a t i o n to two hypotheses.  6  3  A l e n i e n t dec is. i o n .axis versus, .a s t r i c t d e c i s i o n axis  k  Venn diagram of space of a l l p o s s i b l e observations. . ..  5  . . .  .. .,  6 12  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 a x i s . . . .  12  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 ratio axis  12  7  T h e o r e t i c a l ROC curves as a f u n c t i o n 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, r e v i s e d data . . . . . . .  43  11  ROC curves obtained from 5 0 $ compression, r e v i s e d data . . . . . . .  kk  12  ROC curves obtained from 6ofo and jkfo compression, unrevised data . . . .  ^4-8  13  ROC curves obtained from 6of and "}tyj compression, unrevised data . . . .  k9  ROC curves obtained from 60$ and fkfo compression, r e v i s e d data  50  ROC curves obtained from 6 0 % and compression, r e v i s e d data  51  6  0  0  Ik 15  Chapter  I N T R O D U C T I O N AND  The statistical and a  accounting  decision signal ing  pulate,  with by  could  PROBLEM  i s whether  of subjects  i n predicting confronted  While  there  be o f e q u a l  are v a l i d  with  statistical  i t s w o r t h when a p p l i e d reasons  to  simple  f o r suggest-  efficacy i n describing the  i n iierception.  of s t a t i s t i c a l  the existence  the criterion  that  criterion,  of cautiousness  by changing  decision  o f , and attempts  i n d i v i d u a l s adopt which might  theory to mani-  i n making  be c o n c e p t u a l i z e d  as  e x i s t i n g w i t h i n an i n d i v i d u a l , i s  t h e monetary  i n c o r r e c t and c o r r e c t  changing  study  situation.  salient feature  This  OF THE  he o f value  i t recognizes  degree  varied  studies,  involved  decisions. the  has proven  i tw i l l  The that  of this  decision-making  detection  processes  issue  f o r the behaviour  theory  that  STATEMENT  decision theory  perceptual  is  central  I  costs  decisions  t h e communicated a p r i o r i  and rewards  associated  r e s p e c t i v e l y , and a l s o p r o b a b i l i t i e s of  stimulus  occurrence.  Besides criterion also  acknowledging the existence  f o r d e c i s i o n making,  concerned with  receives  statistical  of arriving  variable  d e c i s i o n theory  t h e amount o f i n f o r m a t i o n  i n the process  of this  a  subject  at a decision.  I f , as  i s  2  has heen s u g g e s t e d , t h e d i f f e r e n c e between s e n s a t i o n and p e r c e p t i o n i s t h a t t h e l a t t e r r e q u i r e s more i n f o r m a t i o n t h a n the former, t h e n t h e d i s t i n c t i o n i s a t best a r b i t r a r y f o r t h e two may be c o n s i d e r e d  t o l i e a l o n g a common continuum whose  c h i e f d i m e n s i o n i s amount o f i n f o r m a t i o n . To  j u s t i f y , i n p a r t , t h i s suggestion  that  sensation  and p e r c e p t i o n occupy a common continuum, amount o f i n f o r m a t i o n , i t would be n e c e s s a r y t o show t h a t t h e 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 t h e o r y produce an o b s e r v e d f l u c t u a t i o n i n performance when t h e amount o f i n f o r m a t i o n i n two otherwise  equal p e r c e p t u a l  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,  t h e d e c i s i o n axes o f t h e 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 t h e s e e x p e r i m e n t s were m a n i p u l a t e d by d i f f e r e n t i c a l l y r e w a r d i n g 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 t h e communicated 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  occurrences.  Chapter I I THEORETICAL AND EXPERIMENTAL BACKGROUND Early History The  f r e q u e n t appearances o f i m p a t i e n c e ,  dissatisfaction  and d i s i l l u s i o n m e n t i n t h e r e c e n t 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 t h e v a r i o u s contemporary p s y c h o p h y s i c a l methods utilized  i n d e t e r m i n i n g t h r e s h o l d s 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 s e n s o r y m o d a l i t i e s , have prompted a number o f p s y c h o p h y s i c i s t s t o adopt a t h e o r e t i c a l v i e w and e x p e r i m e n t a l 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 t h e o r y . l a t t e r i s a p u r e l y mathematical Neyman and Pearson  The  t h e o r y , f i r s t propounded by  (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 f o c u s l i e s c h i e f l y on m a t h e m a t i c a l l y  d e s c r i b i n g t h e most e f f i c i e n t procedure  for testing  hypotheses.  E n g i n e e r s , such as P e t e r s o n , B i r d s a l l and F o x (195^-), concerned  w i t h t h e problem o f e v a l u a t i n g t h e performances o f  r a d a r systems i n d e t e c t i n g s i g n a l s , were q u i c k t o see t h e potentiality  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 and t h e r e s u l t a n t  a p p l i c a t i o n became known as 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 . P s y c h o l o g i s t s such as Tanner and Swets who were i n c l o s e cont a c t w i t h t h e e a r l i e r mentioned e n g i n e e r s , r e c o g n i z e d t h e g e n e r a l i t y o f 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 and proceeded t o  test i t s a b i l i t y  i n d e s c r i b i n g the b e h a v i o u r of human  observers i n a s i g n a l detection s i t u a t i o n . 195^5  Tanner and Norman,  (Tanner and  195^.)  S e v e r a l of the c o n c e p t s b a s i c to the t h e o r y 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 t h e o r y were  p a t e d by e a r l i e r p s y c h o l o g i s t s who orientation.  Boring  Swets,  (1950)  of antici-  possessed a mathematical  p o i n t s out t h a t Fechner was  e n g r o s s e d w i t h the concept of p r o b a b i l i t i e s and the  quite  possibility  t h a t p o t e n t i a l gambling outcomes might be e x p r e s s e d 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 p e r m i t  t h e p r e d i c t i o n of a gambler's b e h a v i o u r .  A similar prediction  i s attempted i n 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 though the problem o f 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 a v o i d e d by assuming t h a t  the u t i l i t y of outcomes i s l i n e a r .  (Thus, w i n n i n g f i f t y  w o u l d be t w i c e as s a t i s f y i n g as w i n n i n g t w e n t y - f i v e Thurstone  (1927a,  1927b)  developed a law  cents  cents,) of  comparative, judgment on the assumption t h a t w h i l e i n d i v i d u a l s can order  o b j e c t s or concepts a l o n g any d e f i n e d d i m e n s i o n ,  c o r r e l a t i o n between s u c c e s s i v e fluctuates.  The  orderings  i s never p e r f e c t  the but  o b s e r v e d f l u c t u a t i o n s form the b a s i s of h i s  p s y c h o m e t r i c s c a l e and can be found t o have t h e i r i n 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 where a v a r y i n g  counterpart  decision  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 m i s s e d .  5  The  Theory  of  Signal  S t a t i s t i c a l  (1)  Detection  Decision  S t a t i s t i c a l the  best  number  strategy  of  strategy as  could  attempting  Since are  in  this  most  outcome  be to  decision  one  successive  Theory  might  adopt  decisions  specified maximize  theory  in  the  in  must  attempts a  several of  values  important,  the  strategy  insuring  as  the  decision  situation  individual  on  the  of  information previously  by  from  hypotheses, the  the  two  probability  different, w i l l  curves  that  potential  promote  a  mathematical  choose  observation  Hypothesis  normal  A  of  of  the  ways,  such  decisions. outcomes  maximum  financial  response. of  the  The  the  of  two  hypotheses  him  and  informa-  decision  information of  conceptualized  one  given  The  1.  observations  transformation  from  and H y p o t h e s i s Fig.  sensory  correct  the  large  "best"  decision  typically  an  obtained  to  is  requiring basis  of  a  "best,"  as  two  correct  monetary  defined  The  different  the  The  tion  made.  study  is  identify  s i t u a t i o n where  be  number  to  B,  situation. are  ordinate arising decision  abscissa  The  represented represents  from  the  many,  situation  represents  information within  a  these  observations.  The whether from  the  the  c r i t e r i o n  information  possible  number  an  individual  obtained of  on  a  adopts given  observations  for  deciding  observation  on Hypothesis  comes A  or  -6-  RROBABILITY A  CORRECT  OF  IDENTIFICATION  o b s e r v a t i o n s on hypothesis A FIG. I  SENSORY  INFORMATION  observations hypothesis  D E C I S I O N A X I S .. mean of hypothesis^  FIG.  yes  m e a n of ^/hypothesis A  2  LENIENT decision axis  STRICT d e c i s i o n axis  i iii i i i i i no I y e s . no y e s  FIG.3  on  7  from those  o f H y p o t h e s i s B, i s v i s u a l i z e d  perpendicular axis  t o the abscissa,  to determine  under a s e t o f g i v e n  For to  a s i n F i g . 2.  i s assumed t o he a v a r i a b l e  theory attempts  decision decision  position  conditions.  example, s u p p o s e t h e t a s k o f t h e o b s e r v e r was  had r e c e i v e d  prior  I f the  information to the e f f e c t i n a n y one  to the p r o b a b i l i t y  i n a n y one s i t u a t i o n ,  from a p a r t i c u l a r  f r o m H y p o t h e s i s A.  of Hypothesis A occurring  s i t u a t i o n was e q u a l ring  The  its financially ideal  observation d i d or d i d not a r i s e  probability  line  o n e , and s t a t i s t i c a l  d e c i d e whether t h e i n f o r m a t i o n g a i n e d  subject  as a  that the  decision  of Hypothesis B occuraxis  would l i e  midway b e t w e e n t h e means o f t h e two d i s t r i b u t i o n s  (Fig. 2).  Any  to the  observation the i n d i v i d u a l  right  of the axis  response, while the  axis  ideal had  had judged t o f a l l  w o u l d promote a " Y e s , i t was H y p o t h e s i s A"  a n y t h i n g he f e l t  had f a l l e n  w o u l d evoke a "No" r e s p o n s e .  operating position  been informed that  Unequal with correct axis. other  the  decision  i f the subject equally  "Yes" o r "No" was p u n i s h e d  by a f i n e .  a l t e r a t i o n o f t h e c o s t s and f i n e s  associated  and i n c o r r e c t  decisions  payoff matrix values axis  axis  " Y e s " o r "No" was a s  Thus f i n i n g a n i n c o r r e c t  the  to the l e f t of  T h i s w o u l d be t h e  f o r the decision  a correct  rewarded as an i n c o r r e c t  sion  then the d e c i s i o n  to p o s i t i o n  s e r v e s t o move t h e d e c i "Yes" more, w h i l e  constant  and e q u a l ,  (a) i n F i g .  3.  keeping  s h o u l d move  V/hile t h e  8  proportion the  of c o r r e c t a f f i r m a t i o n s  curve of Hypothesis A and  falls  ( i . e . the area under  to the r i g h t of the  a x i s decreases) so does the number of i n c o r r e c t (the areas under the curve of Hypothesis B and of the d e c i s i o n a x i s a l s o d e c r e a s e s ) . more cautious  and  i s l e s s w i l l i n g to say  I f the payoff c o r r e c t and f i n e d but one  affirmations to the r i g h t  subject  has  that  i n c o r r e c t d e c i s i o n s were e q u a l l y rewarded  the p r o b a b i l i t y of Hypothesis A o c c u r r i n g equal to . 9 , then the  a x i s would move to the f a r l e f t  extreme v i g i l a n c e and  there  and  in  any  decision  ( p o s i t i o n (b) i n F i g . 3 ) .  S i n c e nine out of ten observations rence of Hypothesis A,  become  "Yes."  m a t r i x were a g a i n constant so  d e c i s i o n s i t u a t i o n was  "Yes"  The  decision  are promoted by the  occur-  i s l i t t l e need f o r adopting  one would be  f i n a n c i a l l y prudent to  say  almost every time. Thus the b a s i c concepts of s t a t i s t i c a l  theory are a c t u a l l y q u i t e observations  of two  simple.  decision  Information a r i s i n g from  hypotheses can be  ordered along a  given  dimension and moving along t h i s dimension, i s a d e c i s i o n a x i s whose p o s i t i o n i s determined by t e d w i t h i n c o r r e c t and  the c o s t s and  rewards a s s o c i a -  c o r r e c t d e c i s i o n s as w e l l as by  p r o b a b i l i t y of the occurrence of each h y p o t h e s i s . difficulty  statistical  The  the major  d e c i s i o n t h e o r y meets when a p p l i e d  problems r e q u i r i n g , f o r example, the d e t e c t i o n  of an  to  auditory  s i g n a l from a n o i s y background, r e s i d e s i n adopting a s i n g l e  9  dimension signal is  on w h i c h t h e o b s e r v a t i o n s a r i s i n g  s o u r c e and  dealt with  (2)  The  a n o i s e s o u r c e c a n be  i n the next  Theory  was  individuals  based  upon a p r i o r i  the assumption "noisy"  or  arriving  theory to  problem  i n character.  than p e r i p h e r a l ,  i n f o r m a t i o n as w e l l  strong neurological  prim-  would  and w o u l d  as the  thus they  (Green,  that  this  i960)  the  same r e s u l t ,  system  of the o b s e r v e r  was  were  Although  "noise" assumption  support, of equal  ducing  be  " c o r r u p t e d " the i n f o r m a t i o n  decision-making areas.  felt  then  sensory data of  the sensory communication channels  at the c e n t r a l  (1956)  situation, i t  Decision-making  Somewhat more s p e c u l a t i v e  that  the  s e n s o r y mechanisms i n v o l v e d were  i m p e r f e c t and  Birdsall  decision  i n a signal-detection  process, rather  an o b s e r v a t i o n .  and  the  communicative  a central  This  of Signal Detection  assumed t h a t  arily be  of  ordered.  a  section,,  In a p p l y i n g s t a t i s t i c a l behaviour  from b o t h  importance,  i s the assumption  that  Swets  has  and,  pro-  the p e r c e p t u a l  i s o f a s c a n n i n g n a t u r e and  thus  the  i n f o r m a t i o n o b t a i n e d i n s u c c e s s i v e o b s e r v a t i o n s o f t h e same situation  is variable  In the  limiting  d e t e c t i o n paradigm, a delineated in  "white"  i n amount and  an  interval,  and c l a s s i c  individual  to s t a t i c  emphasis.  form of the  signal-  must d e c i d e w h e t h e r ,  a s i g n a l may  noise similar  particular  be or  a pure i t may  tone be  within  embedded  a faint  light  10  flashed might  against  a w e l l - i l l u m i n a t e d or  even c o n s i s t of the odour of  fume w h i c h must he To  detected  graphically illustrate  with  the  two  hypotheses  any  of these  i n F i g . 1,  such a t t r i b u t e s  phase, e t c . has, though both  must o c c u p y t h e noise an  and  equal  and  the  of  auditory signal,  many d i m e n s i o n s .  tenable are  there  on  ratio  to  either  a noise  i s a p o i n t , Y,  in  noise  occurrence  another  pSN,  and  ratio  gives  the  that  i t arose  from n o i s e  alone.  For  any  or s i g n a l - p l u s -  this point  Y,  from a s i g n a l - p l u s -  I f the  a likelihood  likelihood  from a s i g n a l - p l u s - n o i s e occurrence ity  For  pN.  jfche l a t t e r ,  of  continuum,  p r o b a b i l i t y value  from a n o i s e p r e s e n t a t i o n — i s d i v i d e d by  ordering  multidimensional  i t arose  —  the  introduced.  ) was  that  The  t o assume t h a t  (  i s a p r o b a b i l i t y value  results.  In a d d i t i o n ,  a x i s or  there  probability  for  a single  i t .  arose  the  c h a r a c t e r i z e d by  justify  space, which a c c u r a t e l y d e s c r i b e s  it  for  done  as p i t c h , v o l u m e , d u r a t i o n ,  i n order  likelihood  occurrence,  as was  attributes.  g i v e n o b s e r v a t i o n , b a s e d on noise  per-  signal-plus-noise, distributions  c l a s s e s of observations concept  of  It  o f h e a v y smoke.  situations,  signal-plus-noise occurrences number o f  type  is difficult,  same a x i s , i t i s n o t  Consequently, both  an  consequently,  the noise  a particular  i n a room f u l l  graph i s two-dimensional while example, w i t h  "noisy" background.  former ratio  that point Y  relative Since  that  arose  to the p r o b a b i l -  such a r a t i o  is a  11  r e a l , nonzero number, i t has Thus a l l o b s e r v a t i o n s may  a true dimension  of magnitude.  be ordered along t h i s one  r e g a r d l e s s of the number of a t t r i b u t e s r e q u i r e d to  dimension specify  them. Observations  a r i s i n g from a n o i s e source and  o r i g i n a t i n g from a s i g n a l - p l u s - n o i s e source are as X's The  and O's,  diagram may  those  represented  r e s p e c t i v e l y , on the Venn diagram of F i g . be c o n s i d e r e d 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 p o s s i b l e o b s e r v a t i o n s .  The d i s t r i b u t i o n s of the  o b s e r v a t i o n s are not separate but o v e r l a p s l i g h t l y , t h a t c e r t a i n o b s e r v a t i o n s have much i n common w i t h c l a s s e s of stimulus occurrence. c e n t r e of the diagram may  suggesting both  Those f a r removed from the  be c o n s i d e r e d as being v e r y d i s t i n c t  and c l e a r o b s e r v a t i o n s of t h e i r r e s p e c t i v e stimulus  events.  P l o t t i n g a l l o b s e r v a t i o n s on a l i k e l i h o o d r a t i o a x i s a g a i n s t the p r o b a b i l i t y they arose from t h e i r r e s p e c t i v e stimulus, c l a s s e s g i v e s a c l e a r e r i n d i c a t i o n of these  relationships.  In F i g . 5 the dashed l i n e r e p r e s e n t s the o b s e r v a t i o n s r e s u l t i n g from the occurrence 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  v a t i o n r e s u l t e d from n o i s e alone decreases. to  of n o i s e alone.  the Venn diagram of F i g . 5, n o i s e - a l o n e  l o c a t e d at the extreme l e f t  obser-  With r e f e r e n c e observations  are q u i t e separate from the  s i g n a l - p l u s - n o i s e o b s e r v a t i o n s and they would be expected have a low l i k e l i h o o d r a t i o .  Movement to the r i g h t  to  decreases  K  X  x X • k  •  •  •• .  •  * x ? ft* • X  * x* *lT** 5  FIG.  o o o x O x  4  t •  o  x  O  "  Venn, diagram of noise obser-vation(x) and signal plus noise observation (o) plotted in multi dimensional space.-  Probability, anI observation arose from noise r  from . signal+noise—  FIG. 5  * — L i k e l i h o o d Ratio  Probability an r| observation will promote a correct response  FIG. 6  noise  observation  ,  »•'  signal plus noise  observations  -10 0 +10 •10 0 *I0 Likelihood Transformed  13  the  " p u r i t y " o f these o b s e r v a t i o n s , thus  of the l i k e l i h o o d r a t i o .  i n c r e a s i n g the v a l u e  A s i m i l a r argument a p p l i e s to the  s i g n a l - p l u s - n o i s e o b s e r v a t i o n s , mutatis mutandis, , which are 1  r e p r e s e n t e d by a s o l i d l i n e i n F i g . 5 . the two l i n e s c r o s s i n F i g . 5  i  s  The p o i n t at which  the area o f g r e a t e s t  confu-  s i o n , f o r here the l i k e l i h o o d r a t i o s of the two c l a s s e s of o b s e r v a t i o n s are e q u a l .  T h i s p o i n t occupies a p o s i t i o n , on  the Venn diagram o f F i g . k,  halfway between the average  o b s e r v a t i o n s , as i n d i c a t e d by the two c r o s s e s , o f the two observation classes. T h i s average o b s e r v a t i o n represents t h a t p a r t i c u l a r o b s e r v a t i o n which occurs most f r e q u e n t l y f o r each stimulus class.  As one moves away from t h i s average, the d e n s i t y or  frequency  o f occurrence  t i o n s decreases. multidimensional  o f the a p p r o p r i a t e c l a s s of observa-  These mean o b s e r v a t i o n s occupy a p o i n t i n space and consequently  likelihood ratio axis.  can be l o c a t e d on the  About these two v a l u e s the other  o b s e r v a t i o n s must be d i 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 s i m p l i f y mathematical computations, a mathematical t r a n s f o r m a t i o n of the l i k e l i h o o d r a t i o a x i s must be undertaken. The p r o b a b i l i t y that a g i v e n o b s e r v a t i o n w i l l promote a c o r r e c t response i s a f u n c t i o n of the p r o b a b i l i t y that that o b s e r v a t i o n arose from t h a t stimulus c l a s s ( i . e . the c o r r e c t c l a s s ) and o f the frequency w i t h which that  Ik  observation left  of  noise  Fig. k  source  frequency of  these  by  that  two  to  the  towards  decrement  the  the  of  of  likelihood  Fig.  yardstick  equal  as  two  great  values  noise  for  two  the  ratio  a  distribution  observations  the  increased probability  HoAvever,  the  probability  as  noise  been  well  as  source,  the  the and  again  Plotting  classes  against  transformed normal  and  Moving  decreases  small.  both  two  the  larger  centre  of  which has  produces  is  is  increment  variables i s very  axis,  the  former  occurrence, a  the  product  c o r r e c t response.  i t o r i g i n a t e d from  these  class,  the  a  but  that  decreases.  gives  promote  The  a  c o r r e c t response,  noise  as  from  value)  small.  the  to  curves  a  of  6.  viewed  that  source  noise  i s not  occurring  observation  a  deviation scale,  The is  an  the  observation's  products  of  f a r to  probability a  mean o f  an  of  product  the  promote  the  the  normal  will  frequency  from  of  is very  gives  of  that  the  which  the  lying  low.1ikelihood ratio  i t occurs  these  probability  these  a  observation  probability  observation will  right  frequency  thus  values,  As  an  a high  observation  product  that  Thus  which  i t occurred  latter the  (and  small.  moving  has  with  particular very  occurs.  the to  as  subject  faced  utilizing  the  f o r making probability the  his of  probability  with  a  signal-detection situation  likelihood  decisions. the of  ratio I f he  as has  a  subjective  been  informed  signal-plus-noise occurring noise  alone  o c c u r r i n g , pSN  is =  pN,  15  and  i f the d e c i s i o n outcomes a r e a l l equal (a c o n s t a n t p a y o f f  m a t r i x ) , the, s u b j e c t  s h o u l d 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 t h a n t h i s v a l u e w i l l response and opposite  one  any v a l u e judged l e s s t h a n i t w i l l promote the  response.  W i t h the d e c i s i o n a x i s at t h i s p o i n t ,  w i l l be m a x i m i z i n g h i s expected e a r n i n g s . matrix  evoke  I f the  he  payoff  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 o c c u r r e n c e 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 The conveniently (ROC)  curves.  appropriately.  e f f e c t s of m a n i p u l a t i n g t h i s d e c i s i o n a x i s  are  summarized by R e c e i v e r O p e r a t i n g C h a r a c t e r i s t i c Consideration  l y i n g above the d i a g o n a l  of any  one  of the ROC  curves,  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 r e s p o n d i n g 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  ( p N l y ) under a  s e t of f i x e d s t i m u l u s 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-  e r a t e d 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 a l o n g a l i k e l i h o o d axis underlying  two  observation  i n F i g . 6) and measuring the p r o p o r t i o n s  d i s t r i b u t i o n s (as  of c o r r e c t  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 t o the r i g h t of the axis.  and  decision  For example, the curve c l o s e s t t o the d i a g o n a l  was  g e n e r a t e d by moving such an a x i s a l o n g the l i k e l i h o o d r a t i o  16  axis  o f t h e two d i s t r i b u t i o n s  i n the inset  of F i g . 7.  The  d i s t a n c e d b e t w e e n t h e means o f t h e two d i s t r i b u t i o n s i s measured  i n terms o f t h e d e v i a t i o n u n i t  M d  S N  - M  and t h u s :  N  = CT  Here d i s equal curve  exists,  As increases, events (Fig. two  t o 1 and f o r s u c h  a distance, a definite  HOC  as p l o t t e d .  the d i s t a n c e b e t w e e n t h e two d i s t r i b u t i o n s  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 c l a s s e s o f s t i m u l u s  is facilitated 7).  a n d t h e ROC c u r v e s move up t o t h e l e f t  The d e v i a t i o n d i s t a n c e s b e t w e e n t h e means o f t h e  d i s t r i b u t i o n s u n d e r l y i n g each o f these  ROC c u r v e s a r e  noted.  The  importance  o f t h e s e ROC  curves  show t h e i n f l u e n c e o f a v a r i a b l e c r i t e r i o n response  one  needs o n l y p l o t  fit  them w i t h  on t h e p o s i t i v e  classes.  I n any e x p e r i m e n t  t h e o b t a i n e d v a l u e s o f p S N l y a n d p N l y and  t h e a p p r o p r i a t e ROC  has a p a r t i c u l a r  sensitivity  curves.  Since  e a c h ROC  d v a l u e , we have a p u r e m e a s u r e o f t h e  o f the s u b j e c t or o f the p s y c h o l o g i c a l d i s t a n c e  b e t w e e n t h e two s t i m u l u s  Besides the  they  r a t e a n d a l s o g i v e a p u r e measure o f t h e p s y c h o l o g i c a l  d i s t a n c e b e t w e e n t h e two s t i m u l u s  curve  i s that  events.  indicating  criterion variability  the s e n s i t i v i t y  and c o n t r o l l i n g  of a subject, the theory of s i g n a l  -L7--  F I G , 7 R O C c u r v e s , o b t a i n e d by. m o v i n g a variable criterion t h r o u g h two , normal distributions. T h e ; greater the disTonce between their m e a n s , the greater the value of. d , a n d - t h e f u r t h e r -displaced t o . J . h e _l.ef.t__are,' the". ROC curves.  18  d e t e c t i o n 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 l o c a t e the d e c i s i o n a x i s f o r a g i v e n set of experimental r a t i o , denoted  conditions.  This v a l u e of the l i k e l i h o o d  by B, w i l l maximize the expected v a l u e of a  d e c i s i o n s i t u a t i o n and f o r any d e c i s i o n s i t u a t i o n w i t h f i x e d d e c i s i o n outcomes and s i g n a l  P(N)  =  P(SN)  (v <V  characteristics.  + K . )  y > B  S N J L  M  +  K  A  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 o f 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 o c c u r r i n g . where V  N  i s the reward v a l u e of a c o r r e c t  B  identification  of n o i s e . where  i s the f i n e v a l u e of an i n c o r r e c t  A  identification  of n o i s e . where Vg-^ of  A  i s the reward value of a c o r r e c t  identification  S N .  and where K g  N  fi  i f the f i n e value of an i n c o r r e c t  identifica-  t i o n of S N . B so weights  the v a l u e s , c o s t s and p r o b a b i l i t i e s  a s s o c i a t e d w i t h d e c i s i o n outcomes that the best s t r a t e g y , one m i n i m i z i n g r i s k while maximizing defined.  p o t e n t i a l outcome, i s  The optimum s t r a t e g y a s u b j e c t should have  19  adopted  i n o r d e r t o maximize h i s expected  decision situation  i s determined  outcome i n a g i v e n  by p l o t t i n g  t h e 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 b e t w e e n t h e means o f the d i s t r i b u t i o n s curve.  equal  to the d value  of the obtained  B i s l o c a t e d on  the l i k e l i h o o d  ratio  p o i n t where t h e v e r t i c a l ratio  d i s t a n c e between t h e l i k e l i h o o d distribution,  c u l a t e d B.  axis at that  d i s t a n c e between t h e l i k e l i h o o d  a x i s and t h e n o i s e d i s t r i b u t i o n ,  plus-noise  ratio  d i v i d e d by the v e r t i c a l a x i s and t h e s i g n a l -  gives a quotient equal  affirmations slope equal  t o B, t a n g e n t  alarm"  to the determined  touches  or i n c o r r e c t  Thus,  the curve  affirmation  i t h a s b e e n shown how  can both  faced with  a decision-making  sensitivity,  behaviour, what  was a r r i v e d  various  called  ROC  o f an  While  comparison of the observed  This aspect  observers  individual what h i s  d , t h e measure  o f d s h o u l d be, independent  the t h e o r y o f i d e a l  The  of s i g n a l  and p r e d i c t  a t on the b a s i s o f  of the observer.  curve.  the theory  situation  with  rate.  i n v e s t i g a t o r s have a t t e m p t e d  the i d e a l value  sensitivity  incorrect  defines the optimal  d e s c r i b e the behaviour  optimum d e c i s i o n s t r a t e g y s h o u l d b e . of  of  a l l o w a b l e , i s found by drawing a l i n e ,  p o i n t where t h e l i n e  detection  to the c a l -  A s i m p l e r d e t e r m i n a t i o n o f t h e 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 t e r m s o f t h e maximum number  "false  ROC  observed to p r e d i c t of the  of the theory i s  (Green,  d w i t h the i d e a l  i960)  and a  d, p r o v i d e s an  20  e f f i c i e n c y measure o f the sensory processes i n v o l v e d .  The  i d e a l v a l u e of d i s d e f i n e d i n terms of the phase, time power spectrum  o f the s i g n a l .  To comply w i t h t h i s  and  definition  a simple s i g n a l , such as a pure tone, which can he measured on the above a t t r i b u t e s , must be chosen  and s i n c e 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 s i g n a l , a measure of the i d e a l d was  not  attempted.  Experimental R e s u l t s w i t h the Theory of S i g n a l D e t e c t i o n (1)  The T h r e s h o l d Concept One  and the V a r i a b l e C r i t e r i o n  of the e a r l i e r r e p o r t s 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 t h r e s h o l d concept was by Smith and Wilson they c o n s t r u c t e d a s t a t i s t i c a l  (1953).  While  theory of d e c i s i o n , i t d i f f e r s  i n c e r t a i n important aspects from that presented here. strong s i m i l a r i t y however e x i s t s i n t h e i r i m p l i c i t that 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 determines which w i l l be d e t e c t e d and those which w i l l be Two  different  A  assumption  those  signals  missed.  confidence a t t i t u d e s were induced  w i t h i n s u b j e c t s r e q u i r e d to d e t e c t an a u d i t o r y s i g n a l i n noise.  One  group was  whenever they f e l t the other was  t o l d to a f f i r m the s i g n a l ' s  presence  i t had o c c u r r e d (a l i b e r a l a t t i t u d e ) while  to a s s e r t the s i g n a l ' s occurrence o n l y when  they were c e r t a i n i t had o c c u r r e d (a c o n s e r v a t i v e a t t i t u d e ) .  21  In c o n v e n t i o n a l psychophysics a measure of " t r u e " s e n s i t i v i t y i s supposedly  obtained by a c o r r e c t i o n 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-  t i o n s of s i g n a l present) to weight the c o r r e c t i o n  procedure.  I f the t h r e s h o l d concept were v a l i d , then the performance of the " l i b e r a l "  group, when c o r r e c t e d f o r " f a l s e p o s i t i v e s , "  should c o i n c i d e w i t h that of the " c o n s e r v a t i v e s . " found to s t i l l  be s i g n i f i c a n t l y b e t t e r , Smith and Wilson  c l u d e d that the t h r e s h o l d concept was, substantial  As i t was con-  at b e s t , i n need of  revision.  Since the t h e o r y of s i g n a l d e t e c t i o n p r e c l u d e d the e x i s t e n c e of a t h r e s h o l d , much of the e a r l y was  experimentation  p r i m a r i l y designed t o t e s t t h i s assumption.  The t h r e s h o l d ,  i n i t s c l a s s i c a l f o r m u l a t i o n , i s that value of s t i m u l u s i n t e n s i t y which promotes a c o r r e c t d e t e c t i o n or r e c o g n i t i o n response  f i f t y percent o f the time the s t i m u l u s i s presented.  Thus, s t i m u l i of i n t e n s i t i e s below t h i s v a l u e should be impossible to order and they should generate whichcrosses pNly =1.  an ROC  curve  the r i g h t hand corner of the graph where .pSNly =  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 which suggest  (195^)  r e p o r t two  experiments  that s u b j e c t s are not o n l y capable of o r d e r i n g  o b s e r v a t i o n s on "below-threshold"  s i g n a l s but a l s o of o r d e r i n g  the l i k e l i h o o d r a t i o v a l u e s of n o i s e alone as the theory of  22  signal  detection predicts.  s u b j e c t s were r e q u i r e d light  to detect  s i g n a l s , c o n s i s t i n g of  intensity, Various  flashed against  payoff  matrices  were i n t r o d u c e d axes.  relative  obtained upper  ROC  right  adopts  to  hand c o r n e r with  the  the  in disregarding  sensitivity  extremely  the  three  o f the  axis  illuminated  subjects  screen.  subjects' of  graph.  d i d not  the  occurrence decision the the  cross  Similar reports  the have  signals in  thus adding s u b s t a n t i a l  theory  a threshold  of  of  of s i g n a l  intensities  G r e e n , 195&)  of s e n s o r y  of s i g n a l d e t e c t i o n  c o n c e p t when  considering  modalities.  a subject's the  observed  performance  in a  complex  rank c o r r e l a t i o n between  of B f o r each set  corresponding  A high  low  degrees  d e t e c t i o n of auditory  decision-making s i t u a t i o n , computed v a l u e s  different  probabilities  p o s i t i o n that  In e v a l u a t i n g  the  four  the  presence or absence  to manipulate the  ( T a n n e r , Swets and  support  the  experiment,  to the w e l l - i l l u m i n a t e d background,  curves of  been obtained noise,  the  first  a uniformly  and  i n order  In s p i t e o f  signals  the  In the  of s t i m u l u s  "false  alarm"  c o r r e l a t i o n indicates a subject  rates  has  the  conditions  and  i s determined.  varied his decision  appropriately.  In the m e n t i o n e d above values  first  the  ( T a n n e r and  ranged from  m i g h t be  of  considered  .25  to  two  visual  Swets,  3.00.  to d e f i n e  experiments  195*0 t h e c a l c u l a t e d B  S u b j e c t i v e l y , these a degree of  caution  values  concerning  23  the occurrence of an i n c o r r e c t "fairly  liberal"  "Yes" which ranges from  to "moderately c o n s e r v a t i v e . "  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 c a l c u l a t e d v a l u e s of B and the observed f a l s e alarm r a t e s were . 7 0 , »k6 and f o r the three s u b j e c t s .  Except f o r the second  .71  coefficient,  i t would seem that the s u b j e c t s were capable of a p p r o p r i a t e l y altering their decision  axis.  In the second v i s u a l experiment 195M  (Tanner and Swets,  the four s u b j e c t s had t h e i r r e s p e c t i v e B.0C curves  drawn and the a p p r o p r i a t e d v a l u e s determined f o r the d e t e c t i o n of l i g h t  f l a s h e s h e l d at one i n t e n s i t y v a l u e .  By the  methods r e f e r r e d to above, the a p p r o p r i a t e f a l s e alarm r a t e f o r each s u b j e c t was determined and communicated to that subject.  He then resumed the d e t e c t i o n procedure.  At i t s  t e r m i n a t i o n , the rank 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 and the a s s o c i a t e d f a l s e alarm r a t e was  determined.  The i n f o r m a t i o n concerning the optimum f a l s e alarm r a t e s p r o moted c o e f f i c i e n t s of .9^, subjects.  .97,  . 8 6 and . 9 8 f o r the four  A c o e f f i c i e n t of . 6 8 , here and i n 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 dence.  l e v e l of c o n f i -  The higher c o e f f i c i e n t s were not only the r e s u l t of  the communicated optimum f a l s e alarm r a t e but a l s o due to the f a c t that the B v a l u e s extended over a wider range, from to 9 . 0 0 .  N e v e r t h e l e s s , f u r t h e r support i s g i v e n by  study to the concept of a v a r i a b l e d e c i s i o n a x i s .  this In  .16  (196l) r e f e r to a 1956  a d d i t i o n , Swets, Tanner and B i r d s a l l  experiment where the c o r r e l a t i o n between t h e . c a l c u l a t e d B values  and observed f a l s e alarm r a t e s f o r the d e t e c t i o n of  an a u d i t o r y s i g n a l i n n o i s e , was equal two  observers.  to 1 , 0 . f o r each of  T h i s p e r f e c t c o r r e l a t i o n was achieved  even,  though n e i t h e r subject had been informed o f h i s optimum f a l s e alarm r a t e , (2)  The D e t e c t i o n of Complex S i g n a l s There has been a s u r p r i s i n g r e l u c t a n c e t o apply  the conventional  framework of the theory of s i g n a l d e t e c t i o n  to the r e c o g n i t i o n of complex sounds and words i n n o i s e . P a r t of t h e c a u t i o n i s due to an understandable d e s i r e t o f i r s t d e s c r i b e the d e t e c t i o n of simple t i o n s b e f o r e proceeding patterns.  tones and other  sensa-  w i t h more complex combinations and  In a d d i t i o n , many r e s u l t s , such as the d e t e c t i o n  of d, obtained  from the a p p l i c a t i o n o f the theory  d e t e c t i o n , compare w e l l w i t h psychophysical  those obtained  from  methods such as the f o r c e d choice  (Swets, Tanner and B i r d s a l l , 1961).  of s i g n a l other technique  Consequently, s e v e r a l  i n v e s t i g a t o r s have u t i l i z e d the l a t t e r technique t o d e s c r i b e more a c c u r a t e l y the s t a t i s t i c a l nature of the a u d i t o r y recognition process.  A complex tone may be presented  of s e v e r a l experimental  i n t e r v a l s and the s u b j e c t  i s required  to i n d i c a t e i n which i n t e r v a l the complex o c c u r r e d . as no attempt  i n one  However,  i s made to c o n t r o l the i n d i v i d u a l ' s c r i t e r i o n  25  f o r s e l e c t i n g any p a r t i c u l a r  interval,,much o f the p r e c i s i o n  of the t h e o r y o f s i g n a l d e t e c t i o n i s l o s t . Thus i n t h i s study an attempt  was made to determine  the e f f i c a c y o f the c o n v e n t i o n a l theory of s i g n a l d e t e c t i o n i n d e s c r i b i n g the behaviour o f s u b j e c t s r e q u i r e d to d i f f e r e n t i a t e between two complex words embedded i n n o i s e .  It i s  true that Egan (1955) and o t h e r s have u t i l i z e d the conventiona l approach i n the r e c o g n i t i o n of d i f f e r e n t words, but t h e i r emphasis has been on the c o n f i r m a t i o n or r e j e c t i o n o f a response a l r e a d y made.  From these f i r s t  responses, response-response  and second order  BOC curves are d r a m and the  c h a r a c t e r i s t i c s of conununication networks are i n v e s t i g a t e d . The c o n v e n t i o n a l BOC curve, however, i s a s t i m u l u s response one and thus no attempt  i s made i n t h i s study to  i n v e s t i g a t e any r e l a t i o n s h i p s w i t h f u r t h e r c o n f i r m a t i o n s or r e j e c t i o n s of these responses.  I t i s hoped that the curves  c o n s t r u c t e d from the performances o f the s u b j e c t s i n t h i s experiment,  will  i l l u s t r a t e the e f f e c t o f a v a r i a b l e  criterion  on the r e c o g n i t i o n o f two complex words as w e l l as d e t e c t the e f f e c t s of v a r y i n g the amount of i n f o r m a t i o n a s s o c i a t e d w i t h these words.  Should t h i s be the case, the g e n e r a l i t y and  p r e d i c t a b i l i t y of the theory of s i g n a l d e t e c t i o n w i l l have been s i g n i f i c a n t l y i n c r e a s e d .  26  The  Time Compression of Speech The  stimulus m a t e r i a l i n t h i s study c o n s i s t e d of  the a u d i t o r y p r e s e n t a t i o n of two shortened  words which had heen markedly  i n d u r a t i o n , or time, compressed, by the random  removal of i n t e r n a l 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  (1950).  first  s t u d i e d by M i l l e r and L i c k l i d e r  The  segments were removed by a h i g h speed on-off s w i t c h i n g of the p r e s e n t a t i o n apparatus. (when the s w i t c h was  on-"off')) there was  t o t a l d u r a t i o n of the word. percent  Though segments were removed  It was  removal of a word, had  bility.  In 1953  tape and  s p l i c e d the remaining  was  no speed-up i n the  found that even  little  e f f e c t on  fifty  intelligi-  Garvey manually removed segments of lengths together.  The  recorded tape  a p p r o p r i a t e l y speeded-up i n order to r e t u r n the speech  p i t c h to i t s proper sion.  l e v e l , thus a c h i e v i n g true time compres-  Garvey's r e s u l t s confirmed  those  of M i l l e r  and  L i c k l i d e r , v i z , removal o f up to f i f t y percent  of the  of a word ( f i f t y  not markedly  d e t r i m e n t a l to In 195^  percent  time compression) was  intelligibility. Fairbanks,  E v e r i t t and Jaeger r e p o r t e d  i n v e n t i o n of a machine capable thereby and  duration  of time compressing  the  speech,  e l i m i n a t i n g the t a s k . o f t e d i o u s l y measuring, removing  s p l i c i n g tape segments.  The machine permits v e r y p r e c i s e  compression, o p e r a t i o n s , so that both the d u r a t i o n of segments  27  r e t a i n e d and d i s c a r d e d can be independently manipulated. The net e f f e c t of t h i s c o n t r o l  i s that a g i v e n compression  v a l u e can be o b t a i n e d by s e v e r a l combinations o f the sampling and d i s c a r d  intervals.  F a i r b a n k s and Kodman (1957) found that w i t h t h i s machine, compression of up to f i f t y percent had l i t t l e on the i n t e l l i g i b i l i t y  effect  of a l a r g e number of common words.  However, compression of f i f t y percent o b t a i n e d by the d i s c a r d of  a few l a r g e segments was more d e t r i m e n t a l to  bility  than the f i f t y percent compression o b t a i n e d by the  removal of many short segments. p e r c e n t compression was intelligibility the  intelligi-  In a d d i t i o n ,  seventy-five  found t o be more d e t r i m e n t a l to  than s i x t y percent compression, the s i z e of  discard interval  i n each case b e i n g r e l a t i v e l y c o n s t a n t .  Hypotheses The r e s u l t s o f the three speech compression s t u d i e s reviewed above s t r o n g l y suggest that the amount of i n f o r m a t i o n w i t h i n a word f a r exceeds the amount r e q u i r e d for of  recognition.  I t might be contended that the redundancy  i n f o r m a t i o n serves to more a c c u r a t e l y d e f i n e that p o i n t  i n m u l t i d i m e n s i o n a l space which the word c o u l d be c o n s i d e r e d 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 o r d e r i n g o f d i f f e r e n t  s t i m u l i on the same  continuum, no mathematical e r r o r i s made i f one c o n s i d e r s the  28  l i k e l i h o o d r a t i o to he e q u i v a l e n t Thus, the g r e a t e r  the d i s t a n c e ,  between the means of two amount of i n f o r m a t i o n  to an i n f o r m a t i o n measure.  on the l i k e l i h o o d r a t i o a x i s ,  d i s t r i b u t i o n s , the g r e a t e r  i s the  a v a i l a b l e to d i s t i n g u i s h between them.  I f the d i s t i n c t i o n between s e n s a t i o n and p e r c e p t i o n the former r e q u i r e s l e s s i n f o r m a t i o n the d i s t r i b u t i o n s of the two may  ment.  In any  i s quite  latter,  curves i n a s e n s a t i o n  be assumed to l i e f u r t h e r to the l e f t  r a t i o a x i s than the two  one  than the  i s that  experiment  on a l i k e l i h o o d  d i s t r i b u t i o n s of a p e r c e p t i o n  experi-  event, the d i s t i n c t i o n i s q u i t e a r b i t r a r y arid  (1961)  j u s t i f i e d , as Swets, Tanner and B l r d s a l l  have suggested i n assuming that the s i g n a l d e t e c t i o n p r e v i o u s l y r e p o r t e d were i n f a c t p e r c e p t u a l the theory  then  studies  s t u d i e s and  of s i g n a l d e t e c t i o n a p p l i e s q u i t e  that  appropriately  to decision-making i n a p e r c e p t u a l s i t u a t i o n . Whatever the r o l e that amount of i n f o r m a t i o n i n the theory two  of s i g n a l d e t e c t i o n ,  stimulus words u t i l i z e d  i n multidimensional axis.  The  i t was  assumed that  plays the  i n t h i s study c o u l d be p l o t t e d  space and o r d e r e d on a l i k e l i h o o d r a t i o  p s y c h o l o g i c a l d i s t a n c e between the two  t i o n s of t h e i r observations the amount of i n f o r m a t i o n  was  distribu-  assumed to be a f u n c t i o n of  inherent  i n them.  hypotheses f o l l o w from these assumptions and  Certain their  verifica-  t i o n forms the b a s i s of the experimental study undertaken. Since Fairbanks and Rodman  (1957)  found that  fifty  29  percent  c o m p r e s s i o n 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 was  detrimental to i n t e l l i g i b i l i t y  than f i f t y percent  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 , an ROC  more  compression  curve o b t a i n e d  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 large d i s c a r d i n t e r v a l should  t o the graph's d i a g o n a l  t h a n an ROC  curve obtained  l i e closer from an  i d e n t i c a l t a s k but w i t h compression o b t a i n e d t h r o u g h s m a l l 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  s i z e d , would remove l t i r g e r segments of those v i t a l portions necessary for i n t e l l i g i b i l i t y . r e m o v a l , i t was the v i t a l gibility.  Small  hypotheword  segment  f e l t , would remove o n l y s m a l l p o r t i o n s of  segments, t h e r e b y b e i n g  l e s s detrimental to  intelli-  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 o b s e r v a t i o n 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 c o n s e q u e n t l y p r o d u c i n g c l o s e t o the d i a g o n a l .  an ROC  curve s i t u a t e d  and Kodman a l s o r e p o r t e d t h a t  c o m p r e s s i o n was  than s i x t y percent held constant,  lying  left.  Fairbanks percent  curve  I n the l a t t e r , the p s y c h o l o g i c a l  d i s t a n c e s h o u l d be g r e a t e r , g e n e r a t i n g f u r t h e r t o the  an ROC  ROC  more d e t r i m e n t a l t o  seventy-five  intelligibility  c o m p r e s s i o n , w i t h the d i s c a r d i n t e r v a l c u r v e s g e n e r a t e d 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  s t i m u l u s words s h o u l d l i e f u r t h e r  t o the l e f t when they are compressed by s i x t y p e r c e n t c l o s e r to the d i a g o n a l when they are compressed by  and  seventy-  30  f o u r p e r c e n t , the s i z e s o f the d i s c a r d i n t e r v a l b e i n g e q u a l i n each c a s e  0  S e v e n t y - f o u r p e r c e n t compression s h o u l d r e s u l t  i n a g r e a t e r removal of i n f o r m a t i o n t h a n s i x t y p e r c e n t comp r e s s i o n , and c o n s e q u e n t l y the 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 the two s e v e n t y - f o u r p e r c e n t compressed words s h o u l d l i e closer  t h a n the o b s e r v a t i o n d i s t r i b u t i o n s of the two  p e r c e n t compressed words.  sixty  Chapter  III  METHOD  The experiments, to  as A  of  the  of  which,  i n v e s t i g a t i o n c o n s i s t e d o f two  f o r purposes  c o m p l e x and B c o m p l e x .  In the former,  o f s t i m u l u s words t i m e  the d i s c a r d  signal  w o r d s w h i c h were t i m e percent while  referred  the  framework  a p p l i e d to the  compressed by  interval varied.  d e t e c t i o n was  separate  of e x p o s i t i o n , are  t h e o r y o f s i g n a l d e t e c t i o n was  entiation with  present  In the  differ-  fifty  latter,  percent  the  a p p l i e d to the r e c o g n i t i o n of  c o m p r e s s e d by  the d i s c a r d  sixty  i n t e r v a l was  and  held  theory stimulus  seventy-four  relatively  constant.  Stimulus M a t e r i a l  Three, "commiiiation" In  one  In  the other  times,  list,  were t h e n per Avith  10  and  tAvo,  =  lists  o f the  s t i m u l u s words  " c o m m i n u t i o n " Ave r e r a n d o m l y c o n s t r u c t e d .  the .1  Avord  and  appeared 11  pCA  100  times,  commination" =  .9  r e a d out b y  speed  and  stant voice level  Avas  pCA  respectively.  on a R o b e r t s  and  3-3/^" p e r s e c o n d . maintained  by  A  tape  The  lists Avord  recorder  relatively  o b s e r v i n g the  180  (Refer to  Avords)  990  .5.  =  t h e e x a m i n e r , a t t h e r a t e o f one  recorded  set at  thus  o c c u r r e d 20  A f o r the o r d e r s of the s t i m u l u s  seconds,  tape  item,  "commination"  t h u s pCA  Appendix  200  con-  fluctuations  32  o f t h e r e c o r d e r ' s V.U. probabilities utilized  of  meter.  "commination  These t h r e e t a p e s , w i t h equal to  11  .5,  .1,  and  .9 were  t o f o r m t h e s t i m u l u s t a p e s o f Complex A and  Complex  B.  A V a r i Voc  19979,  speech  compression  r e c e i v e d the a p p r o p r i a t e l y  above m e n t i o n e d  t a p e s and  specifications  o f T a b l e 1.  consisted  of the  a Wollensack  speeded  compressed The  machine, S e r i a l of  the  them a c c o r d i n g t o  the  output  playbacks  o f the V a r i  c o m p r e s s e d s t i m u l u s w o r d s , was  r e c o r d e r w i t h tape  speed  No.  s e t at  Voc,  which  t a k e n up  3-3/^"  by  per  second.  This tape, which c o n s i s t e d s t i m u l u s w o r d s , was output Eicor  of t h i s  transferred  r e c o r d e r was  recorder playing  Wollensack  Mixer,  the Wollensack  and  noise.  The  of "white" n o i s e by  speed  each of t h e . s t i m u l u s elements  99°.  of  from  an  a  o u t p u t s were t a k e n up  3-3/^".  were embedded  n o i s e , g e n e r a t e d by  The  "mixed" w i t h t h a t  the.combined  w i t h a tape  compressed  to the Roberts  then  a tape  o f the  t u r n i n g up  In t h i s  by  manner  i n "white" the g a i n of  a  F e r r i o g r a p h Recorder  and h a v i n g , t h e m a c h i n e r e c o r d t h e n o i s e  g e n e r a t e d by  t u b e s , was  25OO c p s ,  i t s own  indicating  the speech  spectrum  the e s s e n t i a l noise ratio  that  "flat"  f r o m 50  to  a l l o f t h e f r e q u e n c i e s common t o  were e q u a l l y r e p r e s e n t e d and  criterion  (giving  relatively  f o r "white" n o i s e .  The  the a u d i t o r y s t r e n g t h of the  thus  meeting  signal-tocompressed  TABLE 1 TABLE  OF EXPERIMENTAL TAPES CONSTRUCTED  COMPLEX A Treatment  A  -50% C o m p r e s s i o n w i t h a large discard interval  COMPLEX B Treatment  B  -50$> C o m p r e s s i o n w i t h a small discard interval  Treatment  A  -6of C o m p r e s s i o n w i t h a constant discard interval 0  Treatment  B  7WJ0Compress i o n w i t h a constant d i s c a r d interval  pCA  = . 5 , Tape B  pCA  = . 5 , Tape A  pCA = . 5 , Tape I  pCA  = „ 5 , Tape K  pCA  = . 5 , Tape D  pCA  = o 5 , Tape C  pCA  = . 5 , Tape H  pCA  = . 5 , Tape L  pCA  = . 5 , Tape F  pCA  = . 5 , Tape E  pCA  = . 5 , Tape J  pCA  = . 5 , Tape M  pCA  = .1, Tape P  pCA  = .1, Tape N  pCA = .1, Tape R  pCA  = .1, Tape T  pCA  = . 9 , Tape Q  pCA  = . 9 , Tape 0  pCA  = _9> Tape S  pCA  = . 9 , Tape U  34  words  relative  to  approximately of  the  ratio  -12  mixer was  the  auditory  <;d'b  and  dials.  The  selected  between the  two  to  Each tape giving  the  200  was low  that  of  consisted  of  not  the  of  14  the  end  of  seconds  of  mentioned  above.  A  lapsed was  three  20  of  20  before  about  to  signals,  pause  signal  seconds of  noise  warned  10  followed  i n the  signal presentations, a voice  of  presentation.  c o m p r e s s e d s i g n a l embedded  a block  next block  occur.  blocks  consisted  At  manipulation  differentiation  The  the  was  perfect  e x i s t e d between each  i m m e d i a t e l y by  the  10  of  noise)  signal-to-noise  seconds d u r a t i o n presentation  the  the  words c o u l d  s i g n a l s as  of  c o n t r o l l e d by value  insure  stimulus  strength  the  a  noise. pause  subject  that  commence.  Subjects  The had  at  10  male  subjects  l e a s t one  year  o f U n i v e r s i t y , and  factory hearing university  ability.  pay,  employment o f f i c e  this  i n the  amount w o u l d be  participate t i m e was  at  and  were  l e a s t 10  t h e y w e r e w a r n e d w o u l d be  performance, but  i n the  arranged  i n age  from  event  experiment f o r the  informed hours  of  that  under  first  the  session.  on  29,  satisthe  the  their  contingent  I f the  to  through  t h e y made a n y t h i n g  forfeited.  18  were a l l of  They were c o n t a c t e d  experiment would require Their  ranged  time. their  over  $10.00,  individual  agreed  to  conditions  cited,  a  35 Instructions  When t h e s u b j e c t a r r i v e d he was r a n d o m l y t o Complex A o r Complex B, w i t h  the r e s t r i c t i o n  s u b j e c t s were r e q u i r e d f o r e a c h e x p e r i m e n t .  that 5  A s each  consisted  o f two d i f f e r e n t  the  i n w h i c h a s u b j e c t r e c e i v e d them was a l s o  order  determined. pCA  = .5  matrices  treatments  assigned  Random a s s i g n m e n t  (refer  t o Table  a s s o c i a t e d with  of the stimulus  of the three  s u b j e c t was t h e n  He was t o l d  phones, w i t h  having payoff  condition.  individuals  11  o r absence o f "commination"  subject)  c o u l d make  t h a t he w o u l d be p r e s e n t e d  r e c o r d i n g s o f comminat i o n "  (Refer  that the focus of  v i a ear-  and "comminution"  embedded i n n o i s e , and t h a t h i s t a s k w o u l d the presence  randomly  sequence f o r e a c h  informed  e x p e r i m e n t was t o s e e how w e l l  decisions.  words,  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  to Appendices B and C f o r t h e tape  the  tapes  1) t o t h e t h r e e d i f f e r e n t  made f o r e a c h s u b j e c t u n d e r e a c h t r e a t m e n t  The  complex  be t o d e t e r m i n e  a n d t o communicate  h i s d e c i s i o n b y a v e r b a l " Y e s " o r "No" r e s p e c t i v e l y .  The with his f i r s t detail  meaning o f the p a y o f f m a t r i x experimental  t o each s u b j e c t .  t a p e was e x p l a i n e d  statements.  Thus,  o f t h e 200 s t i m u l u s words t o be p r e s e n t e d  "commination"  i n extensive  E a c h was a l s o i n f o r m e d  meanings o f t h e p r o b a b i l i t y 100  t o be a s s o c i a t e d  a n d 100 w o u l d be "comminution.".  of the i f pCA =  ,5,  w o u l d be The p o s s i b i l i t y  36  that to  any one s t i m u l u s  the p r o b a b i l i t y  word w o u l d he " c o m m i n a t i o n " was  that  i t would be  "comminution,"  I t was h o p e d t h a t t h e s u b j e c t s w o u l d be of u t i l i z i n g to guide  their  their  associated.with  operated served  light  the adjacent  the  actual stimulus  order  stimulus  sort  values  s e t o f b u t t o n s v/as  lightbulb  push on a  button  to f l a s h ,  thereby  Not o n l y was t h e m o n e t a r y  also served  given to each  subject,  t o i n f o r m h i m o f what  p r e s e n t a t i o n h a d been.  A 10 m i n u t e p r a c t i c e s e s s i o n was g i v e n to f a m i l i a r i z e presentations  him w i t h  both  the nature  each s u b j e c t o f the  a n d t h e method w h e r e b y he w o u l d be  immediate knowledge o f h i s p e r f o r m a n c e .  The informed  experiment  then  commenced.  Each subject  t h a t he h a d a $1.00 b a n k r o l l t o h i s c r e d i t ,  to  t h e commencement  it  or s u b t r a c t  told  disc.  ,  mounted on s i x o p a l e s c e n t  o f the d e c i s i o n thereby  knowledge o f t h i s  .  the monetary  A corresponding  t o cause the a p p r o p r i a t e  or v a l u e  given  matrices  Consequently, a  by t h e e x p e r i m e n t e r and a s l i g h t  but  in  display, with  the payoff  capable  i n the.decision situation  i n the present.  constructed.  illuminating cost  performance  behaviour  battery operated  discs,.was  past  equal  of,each  tape  from i t depending  prior  a n d t h a t he c o u l d a d d t o on h i s p e r f o r m a n c e .  t o so make h i s d e c i s i o n s t h a t he c o u l d l e a v e  m e n t a l room w i t h  was  a s much money as p o s s i b l e .  He was  the e x p e r i -  In addition, a  37  copy o f t h e p a y o f f m a t r i x and t h e p r o b a b i l i t y occurrence subject  a s s o c i a t e d w i t h e a c h t a p e was p l a c e d b e f o r e  f o r constant  In treatments constant  tape  f o r e a c h o f t h e two  one with, a l l v a l u e s and f i n e s o f "commination  the p r o b a b i l i t y  equal  11  "Yes" was  o t h e r m a t r i x v a l u e s were t h i r d tape,  fourth stant of  the p r o b a b i l i t y  tapes  The  first  and was  the  devoted  la-ter e x p e r i m e n t a l  now  intervals.  sessions complex.  i n order  again.  f i v e cents while the  fined nine  the f i r s t  tape.  cents.  allowed halfway  f o r an  con-  respectively.  approximately  tape.  through  i n succession, with  A short  t h i s tape.  s e s s i o n s , t h e s u b j e c t was  t o complete  again  In the  session lasted  Each s u b j e c t thus  In  tape, but the p r o b a b i l i t y  s o l e l y to the f i r s t  c o m p l e t e up t o t h r e e t a p e s rest  t o .5  equal  t o one c e n t , e x c e p t  experimental  f i v e m i n u t e b r e a k was  second  o f " c o m m i n a t i o n " was  s e t a t .1 and . 9  " c o m m i n a t i o n " was  In the  t h e p a y o f f m a t r i c e s were a g a i n  and i d e n t i c a l w i t h  an h o u r  equal  "Yes" w h i c h was  and f i f t h  (refer to  i d e n t i c a l w i t h the f i r s t  and t h e m a t r i x v a l u e s  incorrect  t o .5  sequences).  fined  a  e q u a l t o one c e n t a n d  o f " c o m m i n a t i o n " was  However, an i n c o r r e c t  .5  stimulus  o f Complex A and Complex. B , t h e m a t r i x was  A p p e n d i c e s B and C f o r , t h e m a t r i x  the  each  reference.  the f i r s t  the p r o b a b i l i t y  tape  of stimulus  allowed to  appropriate  r e q u i r e d at l e a s t  the t e n tapes  In  four  of the assigned  38  Analysis  o f The  Data  From t h e response probability pCAly,  of responding  all  ten tapes.  tion  plotted fitted  To v e r i f y  value  subject the  on d o u b l e  f o r each  the assumption  with  subject  that the  a straight (Swets,  line  running  paper, parallel  Tanner & B i r c l s a l l ,  c o n s t r u c t e d and t h e obtained  lines  on  observa-  o f t h e s t i m u l u s words were normal,  normal p r o b a b i l i t y  —  w i t h a "Yes" t o  t o show t h a t when t h e above o b t a i n e d  the graph.  were  of responding  p C U l y , was c a l c u l a t e d  distributions  necessary  of  —  of each  w i t h a "Yes" t o "commination"  and t h e p r o b a b i l i t y  "comminution"  records  i t was  values are  they  are best  to the diagonal  1961).  Such .plots  a l s o gave a  ready  of d.  To information  test  a n d t h e p o s i t i o n o f t h e SOC  were p l o t t e d interval  the hypotheses concerning  f r o m t h e same d a t a  amount o f  curve,  the curves  but on a graph o f equal-  units. Finally,  individuals  t o determine  manipulate  c o r r e l a t i o n was  their  the efficiency  decision axis,  computed f o r t h e B v a l u e s  with  a rank  which order  associated with  each stimulus  c o n d i t i o n and f o r t h e observed  corresponding  to that condition.  false  alarm  rate  Chapter  IV  RESULTS Complex  A  The d a t a p o i n t s behaviour to  of the f i v e  Appendix  subjects  B) w e r e p l o t t e d  probability  graphs  appropriate  averages  to  o b t a i n e d from  a s s i g n e d t o Complex A  on t h e f i v e  i n F i g . 8.  the data points  the d e c i s i o n  The  double  sixth  of these points.  of the individual  normal-  graph  gives  Fitting  averaged  ROC  lines  g r a p h s was  the  assumption  distributions  comparatively parallel  was  not  of  with  to the diagonal.  of the data points  C o m p l e x A, v i z . t h a t  two Thus  observation  on a l l s i x g r a p h s  of  counter to the primary hypothesis  large-discard-interval  be more d e t r i m e n t a l  discard- interval  attempted  negated.  8 suggested a result  would  lines  However, i n  o f e q u a l v a r i a n c e s f o r t h e two  Inspection Fig.  not  graph t h e d a t a p o i n t s were b e s t f i t t e d  each  the  straight  because of the wide v a r i a n c e s i n data points. the  (refer  to i n t e l l i g i b i l i t y  compression.  compression  than  small-  T h e d v a l u e o f t h e ROC  (or  curve) produced  by  large-discard-interval  .50  i n the averaged  graph while  that  discard-interval  compression  i s . ii-6.  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  produced  compression i s by  small-  Thus t h e l a t t e r rather  line  than  was  facilitative.  I n F i g . 9 t h e same d a t a p o i n t s a r e p l o t t e d equal-interval that but  t h e BOC  probability  curves  suggested  The a v e r a g e d  are not only very  not too f a r d i s t a n t  distance  graph.  from  g r a p h shows  c l o s e to each  the c h a n c e d i a g o n a l .  t h a t t h e S/N r a t i o  on a n  other, The  latter  was somewhat t o o low.  I t was e l e v a t e d t o an e x t e n t b y r e m o v a l o f a l l s t i m u l u s  pre-  s e n t a t i o n s w h i c h were c o r r e c t l y p e r c e i v e d o n l y once o r n e v e r at  all.  Figs. the  10 a n d 11.  two ROC  ting has  The r e v i s e d d a t a p o i n t s a r e p l o t t e d  curves  Note, t h a t are s t i l l  t h a t t h e removal not a l t e r e d  i n the averaged parallel  significantly.  l i e f u r t h e r up a n d t o t h e l e f t .  graphs o f F i g s .  The d v a l u e  obtained v i a large-discard-interval that  1.0 5.  These v a l u e s  with  The  and  f o r t h e ROC  compression  are approximately  averaged curves  i s now  rank-order  unrevised data  i s now  what t h e y were  c o r r e l a t i o n between t h e c a l c u l a t e d each payoff matrix  and t h e c o r r e s p o n d i n g  are given  double  1.2  data.  associated with  probability pCUly —  The r e l a t i v e p o s i t i o n s  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  the u n r e v i s e d  B values  10 and 11 t h e d a t a  r e m a i n t h e same, as shown i n t h e  10 a n d 11.  while  indica-  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  t h e two d i s t r i b u t i o n s  o f t h e two c u r v e s  g r a p h o f F i g . 10  to the d i a g o n a l ,  In. a l l o f t h e g r a p h s o f F i g s . points  on t h e g r a p h s o f  i n Table are equal  2.  "false  and  alarm"  A l lcoefficients  t o .9  at the l e a s t .  stimulus rates  —  for revised A  -41-r  pcqly  .  FIG.6.  C o m p a r i s o n of  Small  discard  Large  .»  the R O C c u r v e s  interval »  .  pcaly  obtained from.: 5 0 % c o m p r e s s i o n .  = « B  •  , Unrevised  Data.  -42-  0  0  I  -2 -3 -4 -5 -6 7 -8 -9 i-0 pculy  \ -2  -3-4 -5 -6 7 -8 9 pculy  0  10  1 2  -3-4 5 6 7 pculy  Q S  •I -2 -3 -4 -5 -6 7 -8 -9 pculy  10  10  d=-50  •46  •I  2 -3 4 -5 6 7 -8 pculy  F I G . 9 . Comparison Small Large  discard, <•  9 of  •I -2 -3 4 -5 6 7 -8 -9 pculy the  ROC  interval  = o «  •  curves  obtained  from  1  5 0 % compr'n.  Unrevised  Data  -43-  pcjuly FIG.10 Small Large  pculy  C o m p a r i s o n of discard  the R O C c u r v e s  interval  - • "  •  .  obtained f r o m : 5 0 %  compr'n.  - „ ' ' ' • ' ' Revised  Data.  -44-  0  0  i — > — i — .  i  V  I  I  1  <  i  i  2 -3 -4 -5 -6 7 -8 -9 1-0 pculy  2  3 4 -5 6 7 -8 -9 pculy  FIG.If. Comparison Small Large  discard »  of  I  10 the  interval  0  0 ROC  curves  I  2 -3-4 -5 6 pculy  7 -8 9  10  I -2 3 -4 -5 6 pculy'  7 -8-9  10  obtained  from•• 5 0 % c o m p r ' n .  = o = •  ,  Revised  Data..  TABLE 2  CORRELATION BETWEEN OBTAINED FALSE ALARM RATES AND OPTIMAL B VALUES  A COMPLEX  Unrevised S.D.I. L.D.I.  Subject  Revised S.D.I. L.D.I.  B.I.  1.00+++  B.L.  1,00+++  T.O.  .95++  .90+  .95++  .90+  M.P.  1.00+++  .90+  1.00+++  .90+  R.W.  1.00+++  .90+  1.00+++  .90+  +P  .05  ++p  .05  +++P  .1  (a)  .90+ 1.00+++  .90+ 1.00+++  C o r r e l a t i o n b y Spearman's Rank C o r r e l a t i o n Method.  .90+ 1.00+++  k6  coefficient of  of  is significant  at the  percent bility  hypothesis  compression than  o f Complex B,  s i x t y percent  contains  could best straight  the  f i t the  and  and  two  The  percent  compressed  that  level  averaged  small  and  f o r t h e ROC  from the  the  curve  served  15.  situated The  two  as  that  equal  sixty  o f .35;  while  interval  curves  As i s quite  negligible.  and  ROC  two  produces  t o the  curves  a g a i n show t h a t t h i s  the v a r i a n c e s of the  from  o f F i g . 13. two  up  straight  and  ,25*  i n Complex A,  further  the  seventy-four  of  same d a t a p o i n t s on  i n F i g . Ik  to a l t e r  relatively  a value  curves  which  are normal  a d value  Fig.  plotted  curves  originating  s e p a r a t i o n between t h e  d a t a p o i n t s which are  graph  ROC  d i f f e r e n t i a t i o n of  R e v i s i o n of the data,  averaged  The  the d i s t a n c e from the d i a g o n a l  i n F i g . I** and  supported.  to' t h e d i a g o n a l , s u g g e s t i n g  p r o b a b i l i t y p a p e r p r o d u c e s t h e ROC the  intelligi-  data points  s t i m u l u s m a t e r i a l has  Plotting  seventy-four  d a t a p o i n t s are  c o m p r e s s e d m a t e r i a l has  Complex A,  was  stimulus populations  d value  originating  percent  averaged  parallel  equal.  that  compression,  individual  v a r i a n c e s of the  not  .05  w o u l d he more d e t r i m e n t a l t o  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.  as  than  B  The  in  less  confidence.  Complex  12  .9  of  left, the  revision  has  distributions  appreciably. The d v a l u e s of the two HOC  curves on the  averaged  graph of F i g . 1 5 are equal to . 7 3 and  . 6 8 f o r s i x t y percent  and seventy-four percent compression  respectively.  These are  approximately double the v a l u e s of the u n r e v i s e d data. The rank c o r r e l a t i o n  of the B v a l u e s a s s o c i a t e d  w i t h each set of experimental c o n d i t i o n s and the observed Table 3 .  corresponding  " f a l s e alarm" r a t e s are g i v e n f o r each s u b j e c t i n 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 t h i s v a l u e i s s i g n i f i c a n t at the l e s s than . 0 5 l e v e l of confidence.  4 8 -  •99,  -2  -1  l  0  I  1  2  1  1  1/ 2  I  °o /  -  */*  -  0  -f  6.D.  -2 •01 r •01  pculy  pcaly  II -MM -I  I I  i i_.  -2 -4 -6 -8 pculy  99  pcaly  •I  2  4 -6 -8 pculy  •I -2 4 -6 -8 pculy  01  pcaly  vm I I  •01  I  -2  i i III i i — i — i — j 2 -4-6 -8 '99 pculy  FIG.J 2. C o m p a r i s o n of 6 0 % 7 4 %  01  compression  =  '  • <iI I I I I 1 L I 2 4 6-8 pculy  the R O C c u r v e s obtained f r o m : . .  6 0 and  •99  7 4 % compr'n  ' Unrevised  Data.  -49-  pculy  pculy  F|G.13. Comparison 6 0 % 7 4 %  of  the  ROC  curves  obtained  from  1  60and74%compr'n  compression = * "  B  •  Unrevised-  Data.  -50-  •2-1  0  1  H-2 •I -2 -4 -6  •01  pcdy  pculy  pcaly  -2  J L III I I I I •I -2 4-6 -8  99  01  99  •01  •I -2 -4 -6 -8  -2 §9  pculy  pculy  Pcaly.  8  t  4  •01  i  i  i • lilt  i  •I 2 -4-6 -8  i L  pculy  FIG. 14 C o m p a r i s o n of  the ROC  60 %  compression  °  7 4 %  ii  =  = ••  curves  '  I  I  I  i  I  I  I  I L L  -I 2 4-6 -8 pculy  99  obtained from : 6 0 8» 7 4 % c o m p r ' n . Revised  Data.  -51 -  2 -3  4 -5  -6  7 -8  9  •I -2 -3  -4 -5  -6  7 -8  -9  I  0  -I  -2-3  0  I  2 -3  4 -5  pculy  4 -5  pculy  6  7 -8  9  10  6  7 -8  -9  IO  FIG. 15.Comparison 6 0 %  74 %  compression  „  of 3  the  pculy  pculy  10  pculy R O C curves  obtained  from 60 1  8t  74%comprh  • Revised  Data.  TABLE 3  CORRELATION BETWEEN OBTAINED FALSE ALARM RATES AND OPTIMAL B VALUES  B COMPLEX Unrevised 60f Comp. 7^0 Comp.  Subject  0  cc.  1.00+++  S.D.  1.00+++  B.L.  1.00+++  R,P«  1,00+++ .90+  G.W.  +p  .05  ++p  .05  +++p  .01  (a)  1,00+++ .90+ 1.00+++ .90+ 1.00+++  C o r r e l a t i o n b y Spearman's Rank Method,  Revised 6of Comp. 7h°j Comp. 0  0  1.00+++  1.00+++  1.00+++  1.00+++  .90+  .90+  .90+  1.00+++  .90+  1.00+++  Correlation  Chapter V  DISCUSSION  The  negation of the hypothesis  with the compression r a t i o h e l d interval  i s more d e t r i m e n t a l  discard  interval,  account  for.  the  short  large discard  failed  their  accurate  o f t h e words were  were r e q u i r e d  severly  to l i s t e n  words v a r i e d w i d e l y  altered  A small  discard  a l l s e c t i o n s w o u l d be r e p r e s e n t e d  with the large d i s c a r d  i n t e r v a l meant  p o r t i o n s w o u l d be l e f t  out.  s o u n d s were a l w a y s p r e s e n t  With  (1957),  i n s o u n d so t h a t f o r  i t was n e c e s s a r y t o h e a r  o f t h e word.  only  that the  t h e r e c o g n i t i o n o f t h e s e two s o u n d s .  recognition  sections  sounds,  i n the compression  t o t h e r e s u l t s o f F a i r b a n k s and Kodman  stimulus  to  of the  o f t h e c o r r e s p o n d i n g w o r d s were s e v e r e l y  t o hamper  reference  that  shortened  portions  the subjects  small  sounds were  t h e c o m p l e x sounds o f " a " and "u," t h e f a c t  remainder  all  Since  than a  and " c o m m i n u t i o n , " a r e  Consequently, these  procedure, while the other  discard  speech  i n comparison w i t h the d u r a t i o n  interval.  that  too d i f f i c u l t  of the s i g n i f i c a n t  often missed or only p a r t i a l l y  excoriated.  a large  to i n t e l l i g i b i l i t y  " a " a n d "u" o f " c o m m i n a t i o n "  relatively  for  constant,  i s not, i n retrospect,  The d u r a t i o n  o f Complex A,  In t h i s  interval  while that  something  from  insured  compression  certain  important  s t u d y , t h e " a " and "u"  after small-discard-interval  5k  compression but t h e y were always compressed and a l t e r e d somewhat, w h i l e w i t h 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 such was  not t h e ca,se, t h e r e b y  i n s u r i n g , over a l a r g e number of  presentations, better i n t e l l i g i b i l i t y  for large-discard-  i n t e r v a l compression. One  of the more s e r i o u s drawbacks of the t h e o r y  s i g n a l d e t e c t i o n , i s t h a t no s t a t i s t i c a l determining,the  tool exists for  s i g n i f i c a n c e of d v a l u e or the d i f f e r e n c e  between two d v a l u e s . o b t a i n e d ROC  of  C o n s e q u e n t l y , the v a l i d i t y of  the  c u r v e s must be judged by i n s p e c t i o n r a t h e r t h a n  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  v a r i a n c e s of t h e r e v i s e d and u n r e v i s e d d a t a 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 t h a t many v a r i a b l e s were not a d e q u a t e l y c o n t r o l l e d . variance  i s due  P a r t of  the  t o 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 v a r i a n c e and g i v e s a more o b v i o u s i n d i c a t i o n of the e f f e c t s o f v a r y i n g amounts o f i n f o r m a t i o n on S e r i o u s e r r o r v a r i a n c e may  intelligibility.  have a l s o been i n t r o d u c e d because  o f the manual c o n t r o l of the S/N mental changes i n the e x p e r i m e n t a l  r a t i o , disruptive environroom and g r o s s f l u c t u a -  t i o n s i n t h e 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 . S i n c e these e r r o r s tend t o . c a n c e l each o t h e r out when combined, the averaged graphs are p r o b a b l y  the  purest  55  i n d i c a t i o n of the e f f e c t s of the manipulated experimental variables. . In s p i t e of these c r i t i c i s m s , the data p o i n t s of the i n d i v i d u a l and averaged graphs of both complexes cons i s t e n t l y indicate relative 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.  compression, d decreases i n magnitude.  With increased  With the unrevised  data, f i f t y percent compression gave d values of . 5 0 and ,k6  f o r the large and small d i s c a r d i n t e r v a l s r e s p e c t i v e l y .  S i x t y percent compression gave a d value of . 3 5 while seventyfour percent compression promoted a d value of . 2 5 . In the r e v i s e d 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 f a c t that  two d i f f e r e n t groups were u t i l i z e d and adds f u r t h e r support to the argument presented e a r l i e r that the d i f f e r e n c e between . observation means on a l i k e l i h o o d r a t i o a x i s may be considered a f u n c t i o n of amount of information. F i f t y percent compress i o n , v i a e i t h e r 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 m a t e r i a l i s l e s s 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 m a t e r i a l . The ROC curves of both complexes, as p l o t t e d 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 "hits" — pCUly.  pCAly, i s a f u n c t i o n of the " f a l s e alarm" rate  —  Or, from a d i f f e r e n t p e r s p e c t i v e , the d e t e c t i o n and  56  recognition criterion  of the stimulus  the subject  words were f u n c t i o n s  adopted and n o t o n l y  Manipulation o f the c r i t e r i o n , of  of h i s s e n s i t i v i t y .  by changing the p r o b a b i l i t i e s  s i g n a l o c c u r r e n c e and t h e v a l u e s and c o s t s  outcomes, s e r v e s t o p e r m i t from the s e n s i t i v i t y  the separation  of the subjects.  t o those psychophysicists  Thus, f u r t h e r  given  of  t h e d e c i s i o n c r i t e r i o n must be m a i n t a i n e d . differences  experimental is  tivity  of signals  insist  i n the understanding  to manipulate the c r i t e r i o n  detection  who  i n s t r u c t i o n s , the best  c a n be s e p a r a t e d  ranged from  and r e c e p t i o n o f this  i t s influence  control  on t h e  from t h e " t r u e "  the subjects  decision axis.  .11 t o .90, d e s c r i b i n g  continuum e x t e n d i n g from v e r y  sensi-  alarm"  coefficient  a subjective  .9.  "liberal"  Such a v a l u e  of confidence.  o c c u r when t h e p a y o f f  to v e r y  "conservative.  and the o b s e r v e d  Thus c r i t e r i o n  manipulation  and p r o b a b i l i t y c o n d i t i o n s I t would appear t h a t  capable of a p p r o p r i a t e l y  weighing  The h i g h  the lowest  i s s i g n i f i c a n t at the l e s s  e x p e r i m e n t were v a r i e d .  decisions.  study  caution-  r a t e s was computed f o r e a c h s u b j e c t ,  was  .05 l e v e l  i n this  The c a l c u l a t e d B v a l u e s  When a r a n k c o r r e l a t i o n b e t w e e n t h e s e v a l u e s  did  control  Because o f  way t o i n s u r e  so t h a t  i s no d o u b t t h a t  possessed a v a r i a b l e  than  that  support  of the subject.  There  "false  of decision  of this variable  is  individual  o f the  of the  i n d i v i d u a l s are  t h e s e f a c t o r s when making  c o r r e l a t i o n obtained also  adds  further  57  support a  t o t h e concept  of the likelihood  form of s u b j e c t i v e y a r d s t i c k .  the  one c l a s s  this  a x i s evoke  The those case not  a second  obtained  t h e above  inform  their  should  those  of decision, while  four  experiment  authors  (1961).  i n a visual  subjects  f o r three  i n a slightly  informed  obtained  approximate  of their  of this  i n this  study.  different  the values  study  o f 1.0  the instructions  this  high  below when  detection  alarm  obtained  alarm  i n accord  coefficient  that the subject  t h a t he w o u l d  leave  rates,  here.  t h e above  rates. with  who  Thus,  :  other  may b e d u e i n p a r t  should  so choose h i s  the experimental  s u b j e c t w o u l d have done so e v e n  instructed,  alarm  f o r some t w o s u b j e c t s  optimum f a l s e are quite  did.  Only  visual  false  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 the  In the  findings.  Although  decisions  with  subjects f e l l  of the appropriate  coefficients  were n o t informed  experimental  above  detection study  i n an auditory d e t e c t i o n experiment,  results  ordered  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  the coefficients  However,  yardstick pro-  compare f a v o u r a b l y  and B i r d s a l l  f o r the ten subjects  were  this  below  responses.  coefficients  authors  used as  falling  observations  of  be, the c o e f f i c i e n t s  obtained  another  to  class  o b t a i n e d by Swets, Tanner where  rate  the  Observations  p o i n t where the d e c i s i o n a x i s c r o s s e s  mote  did  ratio heing  a s most  room w i t h t o contend  as that  i f he h a d n o t b e e n so  o f them were n o t i n good f i n a n c i a l  standing  58  at  the time.  I t should  subject  i n particular  one  attempt rates nine to  he p o i n t e d —  out at t h i s  G. D.  cents.  alarm"  Whether he f o u n d  be more s a t i s f y i n g  than  was  the cost  to say.  situation  a s t h i s may b e o f v a l u e  I n any event,  resistance to pressure.  investigate  these  subject  the application  special  variant,  decision-making The  t h e o r y was  their  of s t a t i s t i c a l  the theory situations,  sensitivity. decision likely  Thus,  theory  to  i s both  strongly  Certainly  of caution  indicate  decision theory,  or i t s  detection, to perceptual  justified  and p r o d u c t i v e .  information differences i nthe of the subjects.'  could be s e p a r a t e d  t o be more w i d e l y u s e d  be shown.  and measuring  as degree  study  of signal  or the theory  the a c t u a l sensory  alarm i s  h o w e v e r , was made t o  as a p s y c h o p h y s i c a l  Whether these with  such  the s u b j e c t s ' d e c i s i o n axes,  decision criterion  of a decision  decision-making  i n probing  of this  able to detect  manipulating  value  and  variables.  stimulus m a t e r i a l by examination By  a  and d e t e c t i o n  a s much a s f i v e  of a false  No a t t e m p t  Thus, the r e s u l t s that  fined  such  certain personality characteristics or  alarm"  the gambling  difficult  that  ( s e e A p p e n d i x C ) , made n o  to significantly vary h i s "false  even when a " f a l s e  point,  of signal  responses.  the effects from t h e i r  technique,  of  actual  statistical  d e t e c t i o n would  appear  i n the future.  t h e o r i e s have any t r u e and perceptual processes  correspondence still  the findings of neurophysiology  remains that  59  the s e n s i t i v i t y of r e c e p t o r organs i s not c o n s t a n t 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 o b s e r v a t i o n s o f t h e "same" s t i m u l u s s i t u a t i o n .  The  v a l u e and f a m i l i a r i t y of s t i m u l i might be c o n s i d e r e d corresponding  survival as  t o the p a y o f f m a t r i x and t h e p r o b a b i l i t y of  s t i m u l i occurrence.  To p e r m i t p r e d i c t i o n on the b a s i s of  t h e s e 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, g r e a t i n c o n s i s t e n c i e s and problems  then  arise.  utility  S t u d i e s of gambling b e h a v i o u r  o f money i s not l i n e a r .  suggest t h a t the  Moreover, i f A i s judged more d e s i r -  a b l e than B, a,nd B more d e s i r a b l e t h a n C, t h i s does not mean t h a t the o b s e r v e r 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 t h a n C.  In a d d i t i o n , s u b j e c t i v e or p e r s o n a l  probabilities  have not been found t o e q u a l 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 i n f 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 t o make 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 , or the 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 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 s u b s t a n t i v e t h e o r i e s of p e r c e p t i o n or human b e h a v i o u r .  A P P E N D I X  S T I M U L U S  A  M A T E R I A L  6l  ORDER OF  S T I M U L U S WORDS  TAPES HAVING  THE  OF COMMINATION  SET  SET  1  2  A U U U A U  U U A A A U U U A A A A  A  U U A U A A A A A U U u u  u  U U U A A A U  SET  SET  3  k  u A A A A A U u A U U u u A u A U A A A  U A U A A U U A A U  U A A A U A A U A U  PROBABILITY EQUAL  TO  .5  SET  SET  SET  SET  5  6  7  8  9  10  u u A u A A U A U A U U A A A U A U u u  A A u u A A A A  A U U A A U u A A TJ U A A U A U A U A U  A U  u u u u u A A A A U A A U U A U A U U U  A U A U U U A u u u A A  SET  SET  FOR  U  U U u TJ A A  U A U A  A  u  A U u A A U A A A U U A U u A U A  k  A u U A A A A  62  ORDER OF  STIMULUS  WORDS FOR  TAPES HAVING THE PROBABILITY  EQUAL  OF COMMINATION  SET 1  A  U U U u U u u u u u u A  u u u u u u  A  SET 2  U U  A  U U  A  U u u u u u u u u u u u u u  SET  SET  3  k  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  SET  SET  5  6  u u u u u  u u u u  A  U U u u u u u u u u u u u u  A  u u  A  u U U u u u u u u u u u  SET  TO  .1  SET  7  8  u  A  A  U U U u U U U u u  A  u u  A A  u u U U  U U u  A  u u u u u u u u u u u u u u u  SET  SET  9  10  A  u u u  U U u u u  A  U U U U u u u u u u u u u  A  U  A  U u u u u A  U U U u u u u u  OSDER OF STIMULUS WORDS FOR TAPES HAVING THE PROBABILITY OF COMMINATION EQUAL TO , 9  SET 1  A A A U A A A U A A A A . A A A A A A U A  SET 2  A U A A A A U A U A A A A A A A A A A A  SET  SET  3  k  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  SET  SET  5  6  A A A A U A A A U A A A A A A A A A A A  A U A A U A A A A U A A A A A A A A A A  SET  SET 8  SET  SET  7  A U A A A A A A A A .'A A A A A A A A U A  A A U A A U A A A A U A A A A A A A A A  A A A A U A A A A A A U A A 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  9  10  A P P E N D I X  B  Data of Complex A 50$  Compression  SUBJECT B . I .  Discard Interval  Tape  pCA -  Matrix  Unrevised pCAly,pCUly  Revised pCAly,pCU:  +1,-1  .56,^31  .65,.28  E  .5 .5  +1,-5  .27,.10  .^5,.09  Smal 1  C  .5  +1,-9  .25,.08  .^3,.01  Small  N  .1  +1 ,-1  .25,.0/+  .50,.05  Small  0  .9  +1,-1  .90,.70  .90,.38  Large  D  .5  +1,-1  .^,.27  .57,.19  Large  B  .5  +1,-5  .36,.Ok  .71,.0^  Large  F  .5  +1,-9  .15,.07  .25,.03  Large  P  .1  +1,-1  .15,.03  .38,.0ir  Large  Q  .9  +1,-1  .93,-75  .98,.68  Small  A  Small  SUBJECT B..L Biscard Interval  Tape  pCA  Matrix  Unrevised pCAly,pCUly  +1, -1  .58,.,; 60  .73,. .58  +1 ,.-5  ..52,  M  .80,.46  Revised pCAly,.pCU:  Small  A  Small,  E  Smal 1  C  ..5  +1,-9  .,30 ,,.22  .55 ,..,20  Small  N  a  +1 ,-1  ao,. .05  .20,; 05  Small  0  ..9  +1,-1  ..95 ,..90  ..95 ,,..75  Large  B  .5  +1 , - l  ..69,. 63  .,88 , . 5 7  Large  F  *5  +1,-5  a 7, ,;15  .27, a 5  Large  B  .5  +1,-9  .08,.06  „21, ,06  Large  P  a  +1 , - l  a5, o4  .9  +1 , - l  .95,.90  Large  Q  .5  8  o  a  0  .98,.78  67  SUBJECT Discard Interval  Tape  pCA  Matrix  Unrevised pCAly,.pCUly  Revised pCAly,pCU]  Smal 1  C  .5  +1,-1  .65,.53  .86,.53  Small  A  .5  +1,-5  o39,.27  .A8..23  Small  E  .-5  +1,-9  .13,-05  . 2 3 , , 0*4-  Smal 1  N  .1  +1,-1  .15,.03  .30,.03  Small  0  ,9  +1,-1  .92,.85  .90,.88  Large  D  .5  +1,-1  .57, M  .76,.2k  Large  F  .5  +1,-5  .29,.10  .50,.10  Large  B  .5  +1,-9  .09,.01  .22,.01  Large  P  a  +1,-1  .15,.0*+  . . 3 8 , . 0*4-  Large  Q  .9  +1,-1  .90,.85  .90,.78  :  SUBJECT T . O .  Discard Interval  Tape  pCA  Matrix  Unrevised pCAly,pCUly  Revised pCAly,pCUl;  Large  F  ".5  +1,-1  .60,V33  .82,.33  Large  D  .5  +1,-5  .33,.16  .42,,08  Large  B  .5  +1,-9  .17,.02  .39,.02  Large  P  a  +1,-1  .10,,0^  ,25,.oip  Large  Q  .9  +1,-1  .98,.95  .98,.89  Small  A  .5  +1,-1  V69,.58  .81,.57  Smal 1  C  .5  +1,-5  .07,.03  a3,.oi  Small  E  .5  +1,-9  .10,.00  .18,.00  Small  N  a  +1,-1  .00,.00  .00,.00  Small  0  .9  +1,-1  1.00,1.00  1.00,1.00  SUBJECT R  Discard Interval  Tape  pCA  Matrix  w. Unrevised pCAly,pCUly  Revised pCAly,pCUly  Large  B  .5  +1,-1  .73,.68  Large  D  .5  +1,-5  .66,.69  .85,'; 60  Large  F  .5  +1,-9  .51,.38  .82,.38  Large  P  .1  +1,-1  .to), .13  1.00,.0^  Large  Q  .9  +1,-1  .95,.85  .93,.67  *  •  -  .  Smal 1  E  .5  +1,-1  .67,.60  .82,.60  Small  C  .5  +1,-5  M , M  .80,'.42  Small  A  .5  +1,-9  .37,.13  .48,. 12  Smal 1  N  .1  +1,-1  .30,.08  .60,.08  Small  0  .9  +1,-1  .93,.90  .93,.75  70  AVERAGES Discard Interval  e  Unrevised p C A l y . pCUly  Revised p C A l y pCUly  pCA  Matrix  Small  .5  * +1, -1  .63  .52  •77  .51  Small  .5  . +1, -5  .35  .26  .53.  :zk  Smal 1  .5  +1, -9  .23  .38  .08  Smal 1  .1  +1, - l  .16  Smal 1  .9  .. +1, -1  .9^  Large  .5  +1, -1  .61  Large  .5  • +1, -.5  .36  .23  Large  .5  +1, -9  .20  . .11  Large  .1  - +1,  """ JL.  .-19  .06  Large  .9  ., +1,  -1  1  .95  . .10 ..  '.ok  .89 .  :  .k?  . .86  ...32. . 0i}a  .9^ .'69. .,  .75 .kk  '.55. . .19 :  .38 .  .10  .^8 .  »ok  .96  .76  A P P E N D I X  . C  D a t a o f Complex B 60<f a n d o  7kf  0  Compress  72  SUBJECT C.C.  Compression  Tape  pCA  Matrix  Unrevised pCAly,pCUly  Revised pCAly,pCUly  .59  .58  .68  .60  .^9  .49  .70  >7  +1, -9  .to*  .36  .56  .33  .1  +1, -1  .25  .09  .63  .09  U  .9  +l,  -1  .91  .85  .91  .73  0  J  .5  +1, -1  M  .30  .60  .29  0  H  .5  +1, -5  .26  .28  .3^  .25  60$  I  .5  +1, -9  .20  .5^  .17  6of  R  .1  +1, -1  .25  .09  .56  .09  S  »9  +1, -1  .92  .80  .92  .50  7*4  K  .5  +1,  -1  7W/0  M  .5  +1,  —J  7^jo  L  .5  7kfo  T  7^/o  6of 6of  0  6of  0  _  73  SUBJECT  Compression  Tape  pCA  C.D.  Matrix  6cf  0  I  .5  +1, : - l  60$  H  .5  +it  6of  J  6o<?o  Unrevised pCAly,pCUly  Revised pCAly.pCUly  .5.6  .60  .65  .57  -5  .64  .5^  .7^-  .5^  .5  +1, -9.  .60  .43  .7^  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  .28  7ty  T  .1.  +1, -1  .15  .05  .38  .05  7kio  U  •9.  +l,  -1  .9^  .85  .9^  .73  0  SUBJECT B.L.  Compression  Tape  pCA  Matrix  Unrevised pCAly,pCUly  Revised pCAly,pCUly  6ofo  I  .5  +1, -1  .52  .40  .65  .37  6of  0  H  .5  +1, -5  .37  .17  .47  .13  6of  0  J  .5  +1, -9  .14  .47  .14  6of  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  0  75  SUBJECT  Compression  Tape  pCA  R.P.  Matrix  Unrevised pCAly.pCUly  Revised pCAly,pCUly  6o  .^5  M  .18  .20  .25  .16  .05  .10  .13  .10  -1  .91  .95  .95  .91  +1,  - l  .61  .55  •'.7 * .53  .5  +1,  -5  .25  .12  .35  I  .5  +1,  -9  .18  .13  60$  R  .1  +1,  -l  .10  .05  .22  .05  6o$  S  .9  +1,  - l  .95  .80  .95  .50  K  .5  + 1, - l  7^o  M  .5  +1,  -5  .28  '.28  :  7ty  L  .5  +1,  -9  .19  7^jo  T  .1  +1,  -1  7^o  U  .9  +1,  6o<?  H  .5  6o$  J  6o$  0  M  0  1  .11  .10  76  SUBJECT G.W.  Compression  Tape  pCA  Matrix  Unrevised pCAly pCUly ?  Revised pCAly,pCUly  0  I  .5  -1  .56  .51  .72  .75  0  J  .5  +1, -5  .20  .10  .32  .10  6Q<?o  H  ,5  +l,  -9  .21  .05  .25  .05  6of  R  .1  +1, -1  .05  .07  .11  .07  S  .9  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  U  .9  -1  . .98  1..00  6of 6of  0  6of  7kf  0  0  +  +  1  1  >  >  -I  .,98 1.00  77  AVERAGES .  Compression  Unrevised p C A l y pCUly  Revised p C A l y . pCUly  pCA  Matrix  .5  +1, -1  .56  .51  .67  .50  6o<?  .5  +1,  .38  .25  \hh  .23  6o$  .5  +1, -9  .35  .19  .45  .18  6o$  .l  +1, -1  .25  .08  .33  .08  6ofo  .9  +1, -1  .93  .85  .93  .65  7^  .5  +1, -1  .5^  .53  .71  .54  .5  +1, -5  .3^  .3^  ,i*<8  .28  7^  .5  +1, -9  .28  .2^  .36  .20  7&/o  .1  +1, -1  .12  ,06  .28  .06  7^  .9  +1, -1  .92  .85  .93  .75  60f  o  0  REFERENCES  B o r i n g , E . G. (2nd e d . ) .  1950.  E d w a r d s , W. Bull.,  A histo ry of experimental psychology. New Y o r k : Appleton Century-Crofts,  The t h e o r y  1954,  ,51,  o f d e c i s i o n making;  380-417.  Psychol.  E g a n , J . P. Message r e p e t i t i o n , o p e r a t i n g c h a r a c t e r i s t i c s and confusion matrices i n speech communication. T e c h n i c a l Report,(AF19(6o4)-1962, Indiana University, 1957. F a i r b a n k s , G., E v e r i t t , W. S., a n d J a e g e r , R. P. Method f o r time o r frequency compression, expansion o f speech, Inst. Radio Engrs. Trans. P r o f e s s i o n a l Group on I n f o r m a t i o n Theory, 1954,  AV-2, 7-12.  F a i r b a n k s , G., a n d K o d m a n , F. W o r d i n t e l l i g i b i l i t y , as a f u n c t i o n o f t i m e c o m p r e s s i o n . J . acoust. S o c . A m e r . . 1957, 29, 636-641. ( ; ; G a r v e y , W. D. 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 . speech. J . a'cous. Socj A m e r . . 1953, ^ 5 , 102-108. G r e e n , D. M. Psychoacoustics and d e t e c t i o n theory. J . a c o u s t . S o c . A m e r . , 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 speech. J . acoust. S o c . A m e r . , 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 hypotheses 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 . Proc. 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., a n d 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 . Inst. Radio Engrs. Trans. P r o f e s s i o n a l Group on 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 . M e a s u r e m e n t a n d S t a t i s t i c s . York: MacMillan., 1958.  New  S m i t h , M., a n d W i l s o n , E d n a A . A model 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 multiple observer. P s y c h o l . Monogr., 1953, 67, N o . 9 ( W o l e N o . 359).  79  Swets, J . A., Tanner, W. P., J r . , and B i r d s a l l , T. G. D e c i s i o n processes i n p e r c e p t i o n . P s y c h o l . Rev., 1961, 68, 301-3*10. Tanner, W. P., J r . , and Norman, R. T. The human use of i n f o r m a t i o n I I . S i g n a l d e t e c t i o n f o r the case of an unknown s i g n a l parameter. I n s t . Radio Engrs. Trans. Information Theory. 195^, PGIT-*l,  222-226.  Tanner, W. P., J r . , and Swets, J . A. A decisionmaking theory of v i s u a l d e t e c t i o n . P s y c h o l . Rev..  195**, 61, *M)1-*K)9.  Tanner, W. P., J r . , Swets, J . A., and Green, D. M. Some g e n e r a l p r o p e r t i e s of the h e a r i n g mechanism. Techn. Rep. No. 30, E l e c t r o n i c Defense Group, U n i v e r s i t y of Michigan, 1956. Thurstone, L, L, A law of comparative P s y c h o l . Rev., 1927, 3^, 273-286. Thurstone, L..L. J. Psychol.,  Psychophysical  judgement. (a)  analysis. (h)  1927, 38, 368-389.  Wald, A. S t a t i s t i c a l decision functions. Wiley, 1950.""  Amer. New  York:  

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