Since the percentage of hits and false alarms depends not only on the subjects sensitivity to the signal, d', but also on the criterion, beta, 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 subjects 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 beta. This curve is called the receive 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 that part of the figure. Put a 0 in for curve two (red) and see what happens to that curve on both the left where it is the a signal plus noise curve and on the right where it is a ROC curve. As d' gets larger, the curve bows away from the diagonal until at extreme values it is along the outer walls of graph. Keep increasing the d' for curve 2 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.