Berger and Tsujimoto (1983) presented a classification program that is similar to the normal theory, null hypothesis significance testing models, except that it takes into account population base rates and allows the researcher to designate the positive utility of a correct classification in relation to the negative utility of an incorrect classification. If population base rates differ, then it is more likely that a case belongs to the more popular group. If the benefit of a correct decision is greater than the cost of an incorrect decision, then one should be liberal in group classification judgments, and vice versa, if incorrect classification is more costly, then one should be more conservative when making group classification judgments.
Classification in this model is designated by cutting scores, which represent the point at which the likelihood of a case coming from one group exceeds that of coming from the other group. These cutting scores, then, are the points where the base-rate/utility weighted normal probability density functions intersect, as can be seen in the following Examples 1, 2, and 3.
The classification applet is a Java implementation of Berger and Tsujimoto’s (1983) classification program. Java applets are computer applications that are designed to be distributed via the World-Wide Web. Applets are platform-independent meaning that one applet can run on multiple operating systems without having to be recompiled. Java applets also have security restrictions making them safe to download and execute on one’s computer.
The classification applet allows users to input parameter values based upon either observed or expected values. The parameters that can be manipulated are:
In Figure 1, Group 1 (shown in blue) has a higher mean, greater variability of scores in the population, and a higher base rate than Group 2 (shown in red). The utility applet shows that in this situation, one’s best choice is to classify all cases as Group 1, which yields 91% diagnostic accuracy.
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