Background

For any given sensitivity, d’, there is a range of possible outcomes according to signal detection theory. To simplify seeing all of the possible outcomes for a given signal strength, researchers have developed a way to summarize all of the possible outcomes for this situation across all possible criterions. This summary is called the receiver operating characteristic, or the ROC curve. The ROC curve is a graphical plot of how often false alarms (x-axis) occur versus how often hits (y-axis) occur for any level of sensitivity.

The advantage of ROC curves is that they capture all aspects of Signal Detection theory in one graph. Sensitivity of d’ is captured by the “bow” in the curve. The more the curve bends up to the right, the better the sensitivity. Moving along the bow captures the criterion. Adjusting your criterion so that you have few false alarms is a strict criterion. You position yourself near the origin (0,0) of the ROC curve, and you have few hits as well. Adjusting your criterion so that you have a lot of hits is a lax criterion, and you position yourself near the opposite corner of the ROC curve and you tend to have a lot of false alarms as well.

Instructions

Full Screen Mode

To see the illustration in full screen, which is recommended, press the Full Screen button, which appears at the top of the page.

Illustration Tab

Settings

Below is a list of the ways that you can alter the model. The settings include the following:

Hits: check to display the region of the graph that generates hits. This is the area above the criterion and under the Signal+Noise curve. The proportion of the Signal+Noise curve highlighted by the red color give the proportion of trials that have signal that are hits.
Misses: check to display the region of the graph that generates misses. This is the area below the criterion and under the Signal+Noise curve. The proportion of the Signal+Noise curve highlighted by the cyan color give the proportion of trials that have signal that are misses. Hits+misses = 1.0
False Alarms: check to display the region of the graph that generates false alarms. This is the area above the criterion and under the Noise curve. The proportion of the Noise curve highlighted by the yellowish color give the proportion of trials that do not have a signal that are false alarms.
Correct Rejections: check to display the region of the graph that generates correct rejections. This is the area below the criterion and under the Noise curve. The proportion of the Noise curve highlighted by the blue color gives the proportion of trials that do not have the signal that are correct rejections. False alarms+correct rejections = 1.0
Sensitivity-d': the difference in the position of the Noise and Signal+Noise curve relates to how easy it is to detect that the signal is present. The greater the difference, the easier the detection. We call this difference sensitivity and measure it with the measure called d' (pronounced d-prime). See how changing d' alters your hits and false alarm rates.
Criterion: the vertical yellow line on the pale blue line on the graph is the criterion. You can adjust it with this slider. Lower values are more lax criterions, and higher values are more strict criterions. Adjust to see how criterion alters hits and false alarm rates without changing d'.
Show Overlap: click to highlight the region where the Noise and Signal+Noise curves overlap. Where there is overlap, a given stimulus intensity could be by either the noise alone or by the signal. You cannot know for certain. As you increase d', the overlap gets smaller.
Show d': click to add a visual representation of d'. An orange line will connect the two peaks. The larger the d', the longer the line.

Reset

Pressing this button restores the settings to their default values.

		The Signal Is:
		Present	Not Present
Judgment:	Happened	0 0	0 1
	Did not happen	1 0	1 1

		The Signal Is:
		Present	Not Present
Judgment:	Happened	Hits	False Alarms
	Did not happen	Misses	Correct Rejections

Show Overlap | Show d'

This is a small d'. Notice how the ROC curve is close to the positive diagonal. Notice how changing the criterion does not change the shape of the ROC curve but just the position of the dot.

On the left is the signal detection theory Graph. In the middle is the receiver operating characteristic (ROC) curve. On the right is the table reporting the outcomes of the current signal detection situation (see Decisions in Signal Detection Theory). The false alarms are plotted on the x-axis and the hits are plotted on the y-axis of the ROC curve. The ROC curve is the green curve on the graph, and the green dot shows the current point on the ROC curve.Change both d' and the criterion to see how this alters both the performance in a particular situation and the ROC curve.