Independent Samples Z-Test - Comparing Two Means with Unequal Variances

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The test statistic is:

z = \frac{\bar{x} - \bar{y}}{\sqrt{\frac{\sigma_x}{m} + \frac{\sigma_y}{n}}}


\bar{x} and \bar{x} are the average values of variables x and y respectively, where each of these variables represents the data from two independent groups,
the groups have sample sizes of m and n respectively,
\sigma^2_x and \sigma^2_y are the variances in the two groups,
 p = 2(1-\Phi(|z|))