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The Pearson statistic, a well-known goodness-of fit test in the analysis of contingency tables, gives little guidance as to why a null hypothesis is rejected. One approach to determine the source(s) of deviation from the null is the decomposition of a chi-squared statistic. This allows writing the statistic as the sum of independent chi-squared statistics. First, three major types of contingency tables and the usual chi-squared tests are reviewed. Three types of decompositions are presented anddoi:10.20381/ruor-3377 fatcat:2xoiyzmi6ndf3axksf7hrmwmti