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 $p _ { 1 } - p _ { 2 }$ , or the chi-squared test of a contingency table. (Squaring the value of the z-statistic yields the value of the $\chi ^ { 2 }$ -statistic.)

Question

Quizplus · Accepted Answer

The z-test for two proportions and the chi-squared test for a 2x2 contingency table are equivalent; squaring the z-statistic gives the chi-squared statistic.

If We Want to Perform a Two-Tail Test for Differences p1−p2p _ { 1 } - p _ { 2 }p1​−p2​

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