QPRC 2016

A General Formula for the Pearson Chi-Squared Test Statistic

Duane K. Allen

Calculation of the Pearson chi-squared test statistic applies Pearson’s classical formula to the observed and expected frequencies of categorical data. This presentation provides a general formula for the Pearson chi-squared test statistic. For any real value of its parameter q, the general formula yields a test statistic value that is identical to that of Pearson’s classical formula. Depending on the selected parameter q, the general formula will have different values for summation terms in the calculation. Proper selection of q can improve the contrast of values of the summation terms, which leads to improved visual exploration of the categorical data.