To analyze the data we calculate a hit rate which is the proportion of items that were in the list to which the subject said "yes" and a false alarm rate which is the proportion of items that weren't in the list to which the subject said "yes". Filling out the table we call a "no" response to a word that was in the list a miss and a no response to a word that wasn't in the list a correct rejection. The terminology actually comes from work that was done during the second world war where the problem was for human radar operators to determine if an enemy was approaching. This area is called signal detection theory.
| RESPONSE | |||
| Yes (subject says it was in the list) | No (subject says it was not in the list) | ||
| STIMULUS | Target (was in list) | Hit | Miss |
| Distractor (was not in the list) | False Alarm | Correct Rejection | |
During the 1980's there was a series of memory models that all used signal detection theory frameworks. These models all assume that when presented with a test word subjects calculate a continuous familiarty value. Words that did occur in the list have familiarities drawn from a normal distribution called S and words that did not occur in the list have familiarities drawn from another normal distribution called N. The mean of N is assumed to be lower than the mean of S. That is, it is assumed that a word that wasn't seen in the study list is on average less familiar than a word that was seen on the study list. A criterion value which lies between the two distributions is then choosen by the subject. Values of familairty above the criterion are labeled "yes" while values below the criterion are labeled "no". Since there will be some values of the N distribution above the criterion and some values of the S distribution below the criterion the paradigm allows for errors.
The overall performance of a subject is measured by d'. It is the distance between the means divided by the standard deviation of the N distribution. If you think about it this gives a single measure of how separate the distributions are. The larger the mean the more separate. The smaller the standard deviation the more separate.
If you place the criterion high on the scale it means you are unlikely to say yes to items. If you put it low on the scale you are more likely to say yes. The distributions may stay the same so that your overall performance is the same but the "bias" is changing. Using the hit and fasle alarm rates one can calculate both d' and the bias.
In fact if we have a way of manipulating bias (which we do in the memory paradigms) we can plot the z scores of the hits against the z scores of the false alarms at different levels of bias. This creates what is known as a zROC (ROC = Receiver Operator Curve). The X intercept of the zROC is d' and the slope of the zROC curve (which is usually fairly straight) is the ratio of the standard deviations of the N and S distributions.
There are also a number of competitors to signal detection theory including different ways of calculating the bias term which have been explored. The version above is by far the most widely used, however.