Signal detection theory
Appendix
Takashi Yamauchi
Texas A&M University
• How do you measure the sensitivity of
stimulus (color, sound, light) perception?
• Measure threshold
• How do you compare Genna’s threshold and
Casady’s threshold?
– Do an experiment. OK, but how?
Present many stimuli that require “yes” responses and “no”
responses.
Change the stimulus intensity, and calculate the average
detection.
Experiment
Target = ?
Ch 1
4
Casady
Genna
Fig. 1-13, p. 14
What’s the problem with this?
Genna and Casady are different.
1. Genna likes basketball; Casady likes
football.
2. Genna loves surfing; Casady likes
hunting.
3. Genna like sushi; Casady like pasta.
Compare Genna’s threshold and Casady’s
threshold?
Mentally represent the stimuli
Yes / NO
Casady may tend to say “YES” more often than Genna.
Genna may tend to say “NO” more often than Casady.
So, the thresholds measured
in this way may simply reflect
how Genna and Casady are
different in their attitudes,
but not in their “perceptual”
sensitivity per se.
Casady
Genna
Fig. 1-13, p. 14
• The same situation arises simply by changing the
pay-off scale of the experiment
Rewarded when you find stimuli (e.g., car
mechanics, psychiatrist, surgeon)
100 trials
Your response
100 trials
trials
Stimuli
Yes
Yes
No
Stimuli
Yes
40
10
50
(present / absent)
No
40
10
50
50
100
(present / absent)
No
50
100
Rewarded when you don’t make mistakes
(e.g., career advisor, drug test, judge)
100 trials
Your response
Yes
No
Stimuli
Yes
10
40
50
(present / absent)
No
10
40
50
100
How can we measure Genna’s and
Casady’s perceptual thresholds
free from these variables?
Signal Detection theory
• SDT is extremely powerful.
• It can be applied to any test situation that involves
“yes” “no” responses.
– memory test (did you see it or not?)
– clinical test (does the drug (therapy) work or not?)
– Mechanical test (does this new engine work or not?)
– Software implementation (does this software give
what the user wants or not).
Signal Detection theory
• important technical terms (very important)
Your response
Yes
No
Stimuli
Yes
hit
miss
(present / absent)
No
false alarm
correct rejection
Your response
Stimuli
Yes
(present / absent)
No
Yes
P(resp = yes |
stim = yes)
P(resp = yes |
stim = no)
No
P(resp = no |
stim = yes)
P(resp = no |
stim = no)
SDT (conceptual background)
• Assume that your task is to judge whether a stimulus
is blue or green.
• If you feel the stimulus is blue, you say “yes”. If you
feel the stimulus is green, you say “no”.
• Further assume that you are shown two stimuli one
at a time in 1 million trials.
Your feeling
Very green
Very blue
• Let’s record your internal representation of
the stimuli after 1 million trials.
Your feeling
Very green
Very blue
• Let’s simulate your decision criterion.
– When you are more conservative, the bar shifts to the right.
– When you are more liberal, the bar shifts to the left.
NO
YES
Your feeling
Very green
Very blue
• Let’s create histograms for the responses made for
the two stimuli.
NO
YES
Your feeling
Very green
Very blue
• Let’s create histograms for the responses made for
the two stimuli.
NO
YES
Your feeling
Very green
Very blue
• Let’s create histograms for the responses made for
the two stimuli.
NO
YES
Your feeling
Very green
Very blue
• What do these histograms tell you?
You have 1 million
responses. Each bin
represents
the number of trials
you had a particular
feeling.
NO
YES
Out of 1 million
trials, how many
times you felt
“very blue.”
Out of 1 million
trials, how many
times you felt
“very green.”
Very green
Your feeling
Very blue
• What do these histograms tell you?
You have 1 million
responses. Each bin
represents
the number of trials
you had a particular
feeling.
NO
YES
Out of 1 million
trials, how many
times you said
“yes”?
Out of 1 million
trials, how many
times you said
“No”?
Very green
Your feeling
Very blue
• Let’s generalize a bit
You have infinitely
many trials and your
histograms are
divided into very
small bins.
how many times
you said “No”?
how many times
you said “yes”?
NO
YES
Given the stimuli
were blue, how
many times you
said “yes”?
Given the stimuli
were green, how
many times you
said “yes”?
Your feeling
Very green
Very blue
Your response
Yes
No
Stimuli
Yes
hit
miss
(present / absent)
No
false alarm
correct rejection
Your response
Stimuli
Yes
(present / absent)
No
Yes
P(resp = yes |
stim = yes)
P(resp = yes |
stim = no)
NO
Stimuli were present
(signal)
Stimuli were absent
(noise)
No
P(resp = no |
stim = yes)
P(resp = no |
stim = no)
YES
Your feeling
Very uncertain
Very certain
Your response
Stimuli
Yes
(present / absent)
No
100 trials
Yes
P(resp = yes |
stim = yes)
P(resp = yes |
stim = no)
No
P(resp = no |
stim = yes)
P(resp = no |
stim = no)
Your response
Yes
No
Stimuli
Yes
40
10
50
(present / absent)
No
20
30
50
Calculate
hit =
False alarm =
100
NO
YES
Your feeling
Very uncertain
Very certain
• Your hit, FA, miss, and correct rejection are still influenced
by the decision criterion you have.
• How do you measure the sensitivity?
• How do you measure d’?
• d’=Z2-Z1
Z2
Z1
d’
NO
YES
Assume that both signal and
noise are normally distributed
(bell curves)
Standardize the normal
distributions  N(0, 1)
The area below the standard
normal distribution corresponds
to the probability.
d’ = Z2 – Z1
Calculate Z1 and Z2 from hit
and false alarm scores
Signal Detection theory
• important technical terms (very important)
Your response
Yes
No
Stimuli
Yes
hit
miss
(present / absent)
No
false alarm
correct rejection
Your response
Stimuli
Yes
(present / absent)
No
Yes
P(resp = yes |
stim = yes)
P(resp = yes |
stim = no)
No
P(resp = no |
stim = yes)
P(resp = no |
stim = no)
Homework
100 trials
Your response
Yes
No
Stimuli
Yes
40
10
50
(present / absent)
No
40
10
50
100
Calculate:
Hit =
False alarm=
Miss =
Correct rejection =
d’ =