A Study on Cell Influences to Chi-square Statistic in Contingency Tables

Once a contingency table is constructed, the first interest will be the hypotheses of either homogeneity or independence depending on the sampling scheme. The most widely used test statistic in practice is the classical Pearson's statistic. When the null hypothesis is rejected, another natural interest becomes which cell contributed to the rejection of the null hypothesis more than others. For this purpose, so called cell components are investigated. In this paper, the influence function of a cell to the statistic is derived, which can be used for the same purpose. This function measures the effect of each cell to the statistic. A numerical example is given to demonstrate the role of the new function.