Simplified Independent Complex Samples T-Test - Comparing Two Means

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

t=\frac{\bar{x}-\bar{y}}{\sqrt{s^2_\bar{x} + s^2_\bar{x}}},

where:

p = 2\Pr(t_v \ge |t|),
v = \frac{(s^2_\bar{x} +s^2_\bar{x})^2}{\frac{(s^2_\bar{x})^2}{n-1}+\frac{s^2_\bar{y})^2}{m-1} }
the groups have sample sizes of m and n respectively.
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