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.

Ch 14 Experiment Target = ?

Fig. 1-13, p. 14 Genna Casady

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? Casady may tend to say “YES” more often than Genna. Genna may tend to say “NO” more often than Casady. Yes / NO Mentally represent the stimuli

Fig. 1-13, p. 14 Genna 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.

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) Rewarded when you don’t make mistakes (e.g., career advisor, drug test, judge)

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)

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. Very blueVery green Your feeling

Let’s record your internal representation of the stimuli after 1 million trials. Very blueVery green Your feeling

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. Very blueVery green Your feeling YESNO

Let’s create histograms for the responses made for the two stimuli. Very blueVery green Your feeling YES NO

Let’s create histograms for the responses made for the two stimuli. Very blueVery green Your feeling YES NO

Let’s create histograms for the responses made for the two stimuli. Very blueVery green Your feeling YES NO

What do these histograms tell you? Very blueVery green Your feeling YES NO You have 1 million responses. Each bin represents the number of trials you had a particular feeling. Out of 1 million trials, how many times you felt “very blue.” Out of 1 million trials, how many times you felt “very green.”

What do these histograms tell you? Very blueVery green Your feeling YES NO You have 1 million responses. Each bin represents the number of trials you had a particular feeling. Out of 1 million trials, how many times you said “No”? Out of 1 million trials, how many times you said “yes”?

Let’s generalize a bit Very blueVery green Your feeling YES NO 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”? Given the stimuli were blue, how many times you said “yes”? Given the stimuli were green, how many times you said “yes”?

Very certainVery uncertain Your feeling YESNO Stimuli were present (signal) Stimuli were absent (noise)

Very certainVery uncertain Your feeling YESNO Calculate hit = False alarm =

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 YESNO d’ Z2 Z1

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)

Calculate: Hit = False alarm= Miss = Correct rejection = d’ = Homework