Working out 2 group signal detection diagnostics
The area under Receiver Operating Characteristic (ROC) curves is a way of describing the magnitude of how well separated two groups are with respect to some diagnostic.
For two groups where the mean of A > mean of B it is a plot of sensitivity at each of T thresholds (Probability of being in group A given you have a value less than or equal to t) against 1 - specificity (probability of being in group B given you have a value less than or equal to t) as seen [attachment:rocplot.jpg here].
The sensitivity is the blue horizontal area and 1-specificty is the diagonal orange area evaluated at a score of 1. These can also be evaulated using frequencies.
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True |
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A |
B |
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Score |
<= t |
a |
b |
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> t |
c |
d |
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In the above table the sensitivity is the proportion of observations in group A which have values less than or equal to t and 1-specificty is the proportion of observations in group B which have a value less than or equal to a particular score t.
These probabilities are evaluated at each observed score, t and plotted with sensitivity on the y-axis and 1-specificity on the x-axis. The points may be joined together to form a curve and the area under the curve evaluated using, for example, the trapezium rule. The area under the ROC curve may be computed on the raw data [:FAQ/roc: using the LOGISTIC REGRESSION procedure in SPSS] or a [:FAQ/rocplot: SPSS macro.]