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

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The test statistic is:

z = \frac{\bar{x} - \bar{y}}{\sigma \sqrt{\frac{1}{m} + \frac{1}{m}}}


\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 = \sqrt{\frac{(m-1)\sigma^2_x + (m-1)\sigma^2_y }{m + n - 2b}},
b is 1 if Bessel's correction for Means is selected in Statistical Assumptions and 0 otherwise,
\sigma^2_x and \sigma^2_y are the variances in the two groups, and
 p = 2(1-\Phi(|z|))