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

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The test statistic is:

t = \frac{\bar{x} - \bar{y}}{\sqrt{\frac{s_x}{m} + \frac{s_y}{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,
s^2_x and s^2_y are the variances in the two groups,
p = 2\Pr(t_v \ge |t|),
v = \frac{(\frac{s^2_x}{n} +\frac{s^2_y}{m} )^2}{\frac{(\frac{s^2_x}{n / d_{eff}})^2}{n-b}+\frac{(\frac{s^2_y}{m / d_{eff}})^2}{m-b} } ,
b is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise,
d_{eff} is Extra Deff.