Receiver Operating Characteristics (ROCs)

The receiver-operating characteristic (ROC) is a fundamental plot in signal detection theory. A ROC is essentially a scatterplot that shows the relationship between false alarm rates on the x-axis, and hit rates on the y-axis. ROCs describe the relationship between the underlying Signal Absent and Signal Present distributions.

Exercise 6: ROC

To see how ROCs are formed, you need to look at both the Normal Distributions and the ROC panels (the leftmost and center panels in the applet). On the ROC panel, there is a yellow dot on the ROC curve which is connected to the Criterion box on the Normal Distributions panel. This point marks an observer's hit rate and false alarm rate based upon this individual's current criterion.

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a. Move d' from 0 to 3, and note how the ROC changes. Describe how the ROC reflects sensitivity.

b. Compare the ROCs generated by Anita and Bob. Anita had a false alarm rate = .3 and hit rate = .9 while these rates for Bob were .09 and .68, respectively.

c. Chris has the same hit rate as Anita (.90) and the same false alarm rate as Bob (.09). Find d' and criterion for Chris. Compare the performance of Chris to that of Anita and Bob (recall that Anita and Bob both had a d' = 1.81 and criterion of .52 and 1.34, respectively).

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