Signal Detection Theory 
TopicsQuiz

Receiver Operating CharacteristicSince the percentage of hits and false alarms depends not only on the subjects sensitivity to the signal, d', but also on the criterion researchers sometimes what to get a more complete description of the subjects responses than a single experiment with a single criterion. Since criterion can be altered by the subject, it is possible to manipulate the costs and benefits of a situation to see what happens to the subject's responses under a variety of criterions. If the subject is rewarded for hits and not punished for false alarms, then the subject should set the beta very low and maximize hits, not worrying about false alarms. This would a lax criterion. If the subject is not rewarded much for hits but punished for false alarms, then the subject should set beta very high so that false alarms will be low (of course, so will hits). In these different situations, d' stays the same because the signal has not be changed. Researchers then plot the results of these situations on a graph with false alarms on the x axis and hits on the y axis as below on the right half of the figure. The curve represent the pattern of responding expected for a given d' at all values of criterion. This curve is called the receiver operating characteristic (ROC). When d' is 0, the noise and the signal + noise curve are the same and false alarms and hits will be the same. That is represented by the diagonal in ROC graph below. Use the Sensitivity  d' slider and adjust it to 0 and then increase the value of d' gradually. As d' gets larger, the ROC curve bows away from the diagonal until at extreme values it is along the outer walls of graph. Keep increasing the d' below and watch what happens to both the signal + noise curve and the ROC curve. As you change d', change it in small values to best see how changing d' is reflected in changes in the ROC curve. You can also adjust the Criterion on its slider. The yellow circle on the ROC curve indicates the current predicted percentage of hits and false alarms for the current settings of d' and criterion. As you make the criterion lower, more lax, the dot moves to the upper right corner of the graph where both hits and false alarms move toward 100%. As you make the criterion more strict, a higher value, the hits and false alarms move towards 0%.
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