Two group discriminant diagnostics
For 2 x 2 tables there are four terms used to summarise the classification table of observed and predicted group membership outputted by discriminant procedures such as binary logistic regression.
Let’s call the two groups positive (+) and negative (-) with classification table given below.
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True |
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|
+ |
- |
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Pred |
+ |
a |
b |
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|
- |
c |
d |
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The following four quantities are often quoted and asked for by journals as a means of evaluating the sharpness of the model fit in the two group case.
- Sensitivity = a/(a+c)= proportion of those who are really + who are predicted to be +
- Specificity = d/(b+d) = proportion of those who are really - who are predicted to be -
- Positive Predictive Value (PPV) = a/(a+b) = proportion of those predicted as + who really are +
- Negative Predictive Value (NPV) = d/(c+d) = proportion of those predicted as - who really are -
An example is available using wavelength.
An example of high sensitivity and low positive predictive value
References
Fleiss, JL (2003) Statistical Methods for Rates and Proportions, 3rd Edition. Wiley:New York. (in South Wing 5 of University library).
Warrens MJ (2011) Chance-corrected measures for 2 x 2 tables that coincide with weighted kappa. British Journal of Mathematical and Statistical Psychology 64 355-365. This quotes the above indices and others showing they are special cases of the weighted Cohen's kappa measure of agreement.