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If We Want to Perform a Two-Tail Test for Differences p1p2p _ { 1 } - p _ { 2 }

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If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of p1p2p _ { 1 } - p _ { 2 } , or the chi-squared test of a contingency table. (Squaring the value of the z-statistic yields the value of the x2x ^ { 2 } -statistic.)

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