Independent Complex Samples t-Test - Comparing Two Means

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Where [math]\displaystyle{ \bar{x} }[/math] and [math]\displaystyle{ \bar{y} }[/math] are the two means and [math]\displaystyle{ s_\bar{x} }[/math] and [math]\displaystyle{ s_\bar{y} }[/math] are their Standard Errors, the test statistic is:

[math]\displaystyle{ t=\frac{\bar{x}-\bar{y}}{\sqrt{s^2_\bar{x} + s^2_\bar{y}}} }[/math],


[math]\displaystyle{ p = 2\Pr(t_v \ge |t|) }[/math],
[math]\displaystyle{ v = \frac{(s^2_\bar{x} +s^2_\bar{y})^2}{\frac{s^4_\bar{x}}{n-b}+\frac{s^4_\bar{y}}{m-b} } }[/math]
the groups have sample sizes of [math]\displaystyle{ m }[/math] and [math]\displaystyle{ n }[/math] respectively (or effective sample sizes if a design effect has been specified),
[math]\displaystyle{ b }[/math] is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise.