Modern educational and psychological testing uses a body of techniques somewhat pompously called "item response theory" (IRT) to examine the performance of individual questions and to assemble complete tests. The technology of IRT is now used, for example, to assemble and score on-the-fly such tests as the Graduate Record Examination (GRE). The GRE is an example of a "computerized adaptive test" (CAT), in which the selection of questions "adapts" to the responses already given, administering increasingly difficult questions to high-scoring examinees and easier ones to the less proficient, while providing comparable scores for all.

The technology of IRT is also used, for another example, to compute the kinds of "scoring tables" that one sees in test-prep and other books for the purpose of converting number-correct scores to "scale scores" for large-scale tests such as the SAT. Such tables are used to "adjust" the scores on each form for the fact that one form may be slightly easier or more difficult than another.

Analyses and computations using IRT are based on relatively simple nonlinear equations, or equivalently graphical displays. The equations or (usually, more clearly) the graphs summarize properties of the test questions such as their difficulty and the chance that they can be guessed correctly. These properties are considered by professionals analyzing data from item tryouts, and those involved in the assembly of new forms for large-scale tests.

Many of these professionals would like wonderful working versions of the programs described here as possible projects, complete with easy-to-use GUI interfaces for the platform they happen to have. (Believe it or not, as esoteric as these applications sound, there is an audience for them! But it's too small an audience for M$ to deal with.) We would love to give them to those folks. But somebody would need to make the applications first; this is where you can come in!