Pearson's unrestricted chi-square procedure is reviewed, and an historical presentation of Neyman's restricted chi-square test is introduced with a discussion of its theory and applicability to education. An example of the Neyman procedure is discussed in detail to familiarize researchers with this useful technique for analyzing contingency tables. The analysis also displays the need for researchers to check model assumptions and power in order to produce constructive analysis. This presentation of a statistical procedure developed by mathematical statisticians allows researchers in the behavioral sciences a facility with the method for application in their particular research. (Author/PR)