Models for improvement of performance in psychophysical task

Tanner, W. P., Jr.

English

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c . 
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07814-2-P' 
T H E  U N I V E R S I T Y  O F  M I C H I G A N  
COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS 
Department of Psychology 
Semi-Annual S ta tus  Report 
OPTIMAL LEARNING I N  DETECTION SITUATIONS 
Wilson P. Tanner, Jr . 
ORA Pro jec t  07814 
supported by t 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
WASHINGTON, D C - 
GRANT NO. NGR-23-005-159 
administered through: 
OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR 
A p r i l  1967 
https://ntrs.nasa.gov/search.jsp?R=19670015744 2020-03-16T18:24:23+00:00Z
. 
STATUS REPORT: NASA RESEARCH GRANT NO. NGR-23-005-159 
OPTIMAL LEARNING I N  DETECTION SITUATIONS 
S e v e r a l  a u t h o r s  have proposed models f o r  t h e  improvement of performance 
observed  i n  psychoacous t i ca l  t a s k s  (Bush, Luce, and Rose, 1964; S c h o e f f l e r ,  
1965; Tanner and Wilcox, 1966). However, very l i t t l e  s y s t e m a t i c  experimen- 
t a t i o n  has  a c t u a l l y  been done i n  a n  a t t empt  t o  i s o l a t e  t h e  r e l e v a n t  parameters  
f o r  improved performance. Moreover, appa ren t ly  none of t h e s e  s t u d i e s  h a s  ac- 
t u a l l y  been guided by a n  a t t e m p t  t o  choose between the proposed models o r  
even t o  p o i n t  up t h e  c o n d i t i o n s  under which t h e s e  models may be adequate .  
Rudiments of Two Basic Learn ing  Models 
We s h a l l  p r e s e n t  he re ,  i n  a non-r igorous  way, t h e  main i d e a s  behind two 
q u i t e  d i s t i n c t  models which have been proposed t o  d e s c r i b e  pre-asymptot ic  
changes  i n  performance. 
I n  a s imple d e t e c t i o n  t a s k  t h e  i n p u t  c o n d i t i o n s  t o  t h e  o b s e r v e r  have 
been g e n e r a t e d  under  two exper imenta l  man ipu la t ions  ( f o r  example, tone  o r  no- 
t one  i n  a background of random no i se ) .  The t a s k  of t h e  o b s e r v e r  i s  t o  i d e n t i -  
f y  which of t h e s e  t w o  man ipu la t ions  was performed on each  t r ia l . .  
t h e  o b s e r v e r ' s  t a s k  i s  t o  d e t e c t  t h e  presence  o r  absence  of t h e  t o n e . )  It i s  
commonly assumed t h a t  t h e  o b s e r v e r  has a g r a d a t i o n  of sensory  e f f e c t s  which 
ar ise  from t h e  a p p l i e d  i n p u t  s t imu la t ion .  These sensory  e f f e c t s  have d i s t r i -  
b u t i o n s  c o n d i t i o n a l  upon t h e  manipula t ion  02 t h e  i n p u t  cond i t ions .  Thus, i t  
(For  example, 
i s  f u r t h e r  assumed t h a t  t h e  obse rve r  may c o n s t r u c t  a d e c i s i o n  a x i s  which i s  
t h e  l i k e l i h o o d  r a t i o  ( o r  a t  least some monotone f u n c t i o n  of l i k e l i h o o d  r a t i o )  
t h a t  a p a r t i c u l a r  sensory e f f e c t  w a s  ob ta ined  under  one of t h e  man ipu la t ions  
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. 
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of t h e  inpu t .  A cho ice  may then  be made by t h e  obse rve r  on each  t r ia l  by 
p l a c i n g  a c u t o f f  on h i s  d e c i s i o n  a x i s ,  so t h a t  i f  t h e  l i k e l i h o o d  r a t i o  of 
t h e  sensory  e f f e c t  i s  g r e a t e r  than  the  c u t o f f ,  he says  "Yes" ( t o n e  w a s  pre-  
s e n t )  and o the rwise  says  (These assumptions are exp la ined  i n  g r e a t e r  
d e t a i l  i n  Green and Swets,  1966). 
The f i r s t  model of psychophysical  l e a r n i n g ,  c a l l e d  t h e  v a r i a b l e - b i a s  
theory ,  i s  based on t h e  n o t i o n  t h a t  t h e  c u t o f f  on t h e  o b s e r v e r ' s  d e c i s i o n  
axis  v a r i e s  from t r i d l  t o  t r ia l .  It may be shown from t h i s  assumption t h a t  
t h e  r e s u l t i n g  mixture  of d e c i s i o n  cr i ter ia  i n v a r i a b l y  l e a d s  t o  a decrement 
i n  the Performance of t h e  observer .  Thus, converse ly ,  i f  ove r  a sequence of 
expe r imen ta l  t r i a l s  t h e  v a r i a b i l i t y  i n  t h e  c r i t e r i o n  ( o r  response  c u t o f f )  de- 
creases, an  i n c r e a s e  i n  t h e  o b s e r v e r ' s  l e v e l  of performance i n  t h e  t a s k  w i l l  
be  observed.  
t o  i t  a s p e c i f i c  assumption regard ing  t h e  changes i n  b i a s  as a resul t  of heedback 
from the exper imenter  ( S c h o e f f l e r ,  1965). 
A model h a s  been proposed which b u i l d s  on t h i s  theory  by adding 
A second theory  f o r  improvement i n  performance states t h e  " t rue" l i k e l i -  
hood r a t i o  of sensory e v e n t s  i s  n o t  p e r f e c t l y  known t o  t h e  observer .  The ob- 
s e r v e r  does have, however, an  e s t ima ted  l i k e l i h o o d  r a t i o  on each  tr ial  which 
depends upon a p r i o r  d i s t r i b u t i o n  f o r  t h e  parameter  set c h a r a c t e r i z i n g  t h e  d i s -  
t r i b u t i o n  of the l i k e l i h o o d  of a sensory event .  
of sensory  even t s ,  a r educ t ion  i n  u n c e r t a i n t y  about  t h e  parameter  set occurs .  
Because of an  i n t e r n a l  sampling 
The o b s e r v e r ' s  e s t ima ted  l i k e l i h o o d  r a t i o  thus  becomes an improved s ta t i s t ic  
f o r  d i s c r i m i n a t i o n  between t h e  events  g e n e r a t i n g  t h e  sensory e f f e c t s .  Hence, 
t h i s  t heo ry ,  t h e  v a r i a b l e  s e n s i t i v i t y  theo ry ,  also p r e d i c t s  t h a t  l e a r n i n g  w i l l  
occu r  i n  t h e  form of improved observer  performance over  t r ia ls  ( Tanner and W i l -  
cox,  1966). 
- 3- 
Both t h e  v a r i a b l e  b i a s  theory  and t h e  v a r i a b l e  s e n s i t i v i t y  theory  are 
based on assumptions t h a t  stem from t h e  theory  of s i g n a l  d e t e c t a b i l i t y  as 
a p p l i e d  t o  human d e t e c t i o n  performance. The t h e o r i e s  d i f f e r ,  however, i n  
t h e  manner i n  which t h e  obse rve r  processes  informat ion  a v a i l a b l e  from t h e  
environment t o  improve h i s  performance. The v a r i a b l e  b i a s  theory  i s  a re- 
sponse- l e a r n i n g  theory of improved performance. It ma in ta ins  t h a t  less- than- 
the-  b e s t - p o s s i b l e  performance i n  the  t a s k  i s  due s o l e l y  t o  m o t i v a t i o n a l  con- 
d i t i o n s  Mhich determine t h e  o b s e r v e r ' s  c r i t e r i o n .  I n  t h i s  theory ,  t h e  observ- 
e r ' s  response  b i a s  i s  cond i t ioned  by t h e  payoff s t r u c t u r e  and feedback con- 
d i t i o n s  i n  t h e  t a s k ,  b u t  n o t  by t h e  s t imu lus  c o n f i g u r a t i o n  i t s e l f .  On the 
o t h e r  hand, t h e  v a r i a b l e  s e n s i t i v i t y  theory  ma in ta ins  t h a t  t h e  obse rve r  i s  
unable  t o  a t t a i n  b e t t e r  performance i.n t h e  t a s k  u n t i l  he has  accumulated sta- 
t i s t ica l  ev idence  r ega rd ing  t h e  importance of d i f f e r e n t  sensory e f f e c t s  t o  t h e  
t a s k  of choosing between the manipula t ions  on t h e  i n p u t .  
D e s p i t e  t h e  c o n s i d e r a b l e  conceptual  d i f f e r e n c e  between t h e s e  two t h e o r i e s  
of psychophys ica l  l e a r n i n g ,  i t  i s  very d i f f i c u l t  t o  o b t a i n  exper imenta l  evi-  
dence t o  choose between them by us ing  c u r r e n t  p sychoacous t i ca l  procedures .  
(These procedures  are reviewed i n  Green and Swets, 1966, Appendix 111. One 
of t h e  b a s i c  r easons  f o r  t h e  d i f f i c u l t y  i n  o b t a i n i n g  adequate  exper imenta l  ev i -  
dence i s  t h a t  t h e  exper imenters  do not  know what t h e  l n p u t  c o n d i t i o n s  t o  t h e  
o b s e r v e r  are on a t r i a l - b y - t r i a l  bas i s .  
on ly  ave rage  s ta t i s t ics  of t h e  inpu t  p rocess ,  which, of course ,  are o f t e n  
adequa te  f o r  s tudying  t h e  asymptot ic  d e t e c t i o n  behavior  of obse rve r s .  
Experimenters  i n  t h e  p a s t  have had 
For 
t h e  exper imenter  t o  know t h e  i n p u t  cond i t ions  i s ,  e s s e n t i a l l y ,  an ins t rumenta-  
t i o n  problem. 
- 4- 
The i n s t r u m e n t a t i o n  problem of o b t a i n i n g  c e r t a i n  k i n d s  of t r i a l - b y - t r i a l  
s p e c i f i c a t i o n s  of t h e  i n p u t  p rocess  h a s  been so lved  a t  t h e  Sensory I n t e l l i g e n c e  
Labora tory .  Cur ren t ly ,  w e  are making p r o g r e s s  i n  t h e  c o n s t r u c t i o n  of a p p a r a t u s  
t o  p rov ide  t h e  necessary  measurements on t h e  i n p u t  waveform t o  conduct  a v a r i e t y  
of exper iments  on human l e a r n i n g  p rocesses  i n  d e t e c t i o n  t a sks .  
Cur ren t  Research 
S e v e r a l  p r o j e c t s  are c u r r e n t l y  underway as a d i r e c t  r e s u l t  of t h e  p r e s e n t  
r e s e a r c h  suppor t .  
A t h e s i s  e n t i t l e d  "Sensory P rocess ing  Models of Human Monaural Auditory 
This t h e s i s  c o n t a i n s  a n  ex- De tec t ion" ' i s  be ing  completed by Gordon Wilcox. 
p o s i t i o n  of t h e  v a r i a b l e  s e n s i t i v i t y  theo ry  i n  t h e  c o n t e x t  of improved d e t e c t i o n  
performance by human o b s e r v e r s  i n  a u d i t o r y  t a s k s .  I t  h a s  been necessa ry  t o  
e x p l o r e  t h e  i m p l i c a t i o n s  of t h e  theory of s i g n a l  d e t e c t a b i l i t y  i n  g r e a t e r  dep th  
i n  o r d e r  t o  o b t a i n  p r e d i c t i o n s  i n  l e a r n i n g  s i t u a t i o n s .  
f o r  l e a r n i n g  h a s  been ob ta ined  wi th in  t h e  framework of d e t e c t a b i l i t y  theory .  
Each member of t h e  class depends upon assumpt ions  r ega rd ing  t h e  mode of sensory  
p r o c e s s i n g  which t h e  o b s e r v e r  can assume. 
A g e n e r a l  class of models 
Data have been ob ta ined  on t h e  e a r l y  s t a g e s  of p r a c t i c e  i n  t h e  u s e  of 
conf idence  judgments as response  measures of performance i n  a s imple  monaural 
d e t e c t i o n  t a sk .  The o b j e c t i v e  of t h i s  s tudy  i s  a n  a t t empt  t o  a s c e r t a i n  t h e  
i m p r o v a b i l i t y  of  i n fo rma t ion  product ion  c a p a b i l i t y  f o r  human s u b j e c t s .  An 
e x t e n s i o n  of t h i s  s tudy  i s  aimed a t  de te rmining  whether  a n  o b s e r v e r ' s  i n f o r -  
mat ion p roduc t ion  c a p a b i l i t y  i s  d e t e r i o r a t e d  by i n c r e a s e d  n o i s e  l e v e l s .  The 
- 5- 
I 
c 
i s s u e ,  i t  may be noted,  is not whether t h e r e  is a dec rease  i n  obse rve r  
s e n s i t i v i t y  f o r  lower s i g n a l  t o  no i se  l e v e l s  (S/N),  bu t  r a t h e r  whether 
t h e r e  i s  a dec rease  i n  e f f i c i e n c y  at lower S/N l e v e l s .  I n  t h e  c u r r e n t  
program of s tudy an a t t empt  i s  being made t o  decompose t h e  decrement i n t o  
two sources :  t h a t  which occur s  on t r ia ls  when t h e  s i g n a l  i s  p r e s e n t  and t h a t  
which occur s  on t r ia ls  when s i g n a l  i s  absent .  It i s  expec ted  t h a t  t h i s  re-  
s e a r c h  w i l l  shed some l i g h t  on the problem of t h e  degree  of i n t e r o b s e r v e r  
agreement,  which appea r s  t o  depend upon t h e  presence  o r  absence of s i g n a l  
i n  n o i s e .  
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References 
Bush, R.  R . ,  Luce, R. D. ,  and Rose, R. N .  Learning models i n  spychophysics.  
I n  R. C. Atkinson (Ed. 1 S t u d i e s  in Mathematical  Psychology. Stan- 
f o r d :  S t a n f o r d  U n i v e r s i t y  P r e s s ,  1964, pp. 201-217. 
Green, D. M. and Swets, J. A. Signal Detec t ion  Theory and Psychophysics, 
New York: John Wiley and Sons, 1966. 
Schoeff ler ,  M. D. Theory f o r  psychophysical  l ea rn ing .  2. Acoust. SOC. h e r . ,  
1965, 37, 1124-1133. 
Tanner,  W .  P . ,  Jr. and Wilcox, G. W. Optimal l e a r n i n g  models f o r  d e t e c t i o n  
s i t u a t i o n s .  (Unpublished r e p o r t ,  1966 ). 


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