This graph, often referred to as the Taylor-Russell diagram, illustrates the consequences of making selection decisions with an imperfect predictor variable. The vertical line is the cutoff on the predictor--cases above the cutoff are selected; those below are rejected. Those above the criterion should have been selected; those below should not have been selected. Green points represent those cases that were selected and should have been ("hit"). Those with red points represent those cases that were not selected but should have been ("miss"). The hit rate is the number of green points divied by the sum of the green and red points. The orange points were selected, but should not have been ("false alarm or FA"). Finally, the blue points represent those who were rejected and should have been ("correct rejection or CR"). The false alaram rate is the number of orange points divided by the sum of the orange and blue points. Drag the cutoff line left or right to observe how the hit and false alarm rates change. Reload the page to generate a new sample.

Optional ROC Curve

It is useful to plot the respective values for the hit and false alarm rates on the separate graph to the right. In the signal detection literature, this graph is known as the "receiver operating characteristic" or "ROC" curve. The diagonal line represents the expected hit and false alaram rates if the predictor variable was no better than guessing. Slowly drag the cutoff line in the Taylor-Russell graph to trace out the ROC curve. The point corresponding to the current cutoff in the Taylor-Ruseell graph is indicated by a red point.