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

The test statistic is:

[math]\displaystyle{ z = \frac{\bar{x} - \bar{y}}{\sigma \sqrt{\frac{1}{m} + \frac{1}{m}}} }[/math]

where:

[math]\displaystyle{ \bar{x} }[/math] and [math]\displaystyle{ \bar{x} }[/math] are the average values of variables [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] respectively, where each of these variables represents the data from two independent groups,

the groups have sample sizes of [math]\displaystyle{ m }[/math] and [math]\displaystyle{ n }[/math] respectively,

[math]\displaystyle{ \sigma = \sqrt{\frac{(m-1)\sigma^2_x + (m-1)\sigma^2_y }{m + n - 2b}} }[/math],

[math]\displaystyle{ b }[/math] is 1 if Bessel's correction for Means is selected in Statistical Assumptions and 0 otherwise,

[math]\displaystyle{ \sigma^2_x }[/math] and [math]\displaystyle{ \sigma^2_y }[/math] are the variances in the two groups, and

[math]\displaystyle{ p = 2(1-\Phi(|z|)) }[/math]