If we want to 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 related; squaring the z-statistic from the z-test gives the chi-squared statistic for the same data. Both tests assess the difference between two proportions.

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

If We Want to Test for Differences Between Two Populations $p _ { 1 } - p _ { 2 }$