Signal Detection: Hits and False Alarms Examples

If we wish to compare memory ability for two people, why can’t we simply use the percent correct on identifying old items (i.e., hit rate) as the measure of ability?

Consider two participants in a recognition memory test. Participant A has a hit rate of .70 and participant B has a hit rate of .75

See the Decision Matrix

Old

New

Say “Old”

Hit

False Alarm

Say “New”

Miss

Correct Rejection

Can we be sure that B has a better memory than A? What if participant A had a false alarm rate of .05 and participant B had a false alarm rate of .24? This indicates that B is more willing to say “old.” ‘Would you still think that B is doing better than A? If we look at only the hit rate, we overlook the fact that participant B might have a higher hit rate just because he is willing to say “old” more often, and hence, he is getting more hits at the expense of more false alarms.

Participant

Hit Rate

False Alarm Rate

A

  .70

  .05

B

  .75

  .24

C

1.00

1.00

 

Participant C is an extreme case, with a hit rate of 1.00. He attains this rate by saying “old” to every item. Great Job! Or is it? This performance wouldn’t really say anything about his memory ability, however, because his false alarm rate would also be 1.00. This performance wouldn’t demonstrate any discrimination between Old and New items.

In the following sections, we will learn how the SDT model uses the relationship between hit and false alarm rates to compute separate measures of discrimination ability and criterion (willingness to say “old”)

An Application to Memory

Below is a decision matrix filled in with the frequencies of each response for a hypothetical memory experiment with 50 Old items and 50 New items.

Old

New

Say “Old”

40

5

Say “New”

10

45

TOTAL

50
50

 

The hit rate

The hit rate (say “Old” for Old items) is 40/50 or as a proportion .80.

The false alarm rate

The false alarm rate (say “Old” for New items) is 5/50 or .10.

Miss rate and rate of Correct Rejection

Note that Misses and Correct Rejections are redundant with Hits and False Alarms. The miss rate is 10/50 which is .20 or simply (1 – “hit rate”) and the Correct Rejection rate is 45/50 or .90 or (1 – “false alarm rate”). Therefore, you can perfectly describe all four measures of a person’s performance in a signal detection experiment through their Hit and False Alarm rates.

In the following sections, we will learn how the SDT model uses the relationship between hit and false alarm rates to compute separate measures of discrimination ability and criterion (willingness to say “old”).

P-values and Z-scores


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