Independent Samples T-Test - Unequal Variance

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Where \bar{x} and \bar{y} are the two means and s_x and s_y are their Standard Deviations, the test statistic is:

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

where:

p = 2\Pr(t_v \ge |t|),
s^2_\bar{i} = \frac{s^2_i}{n_i},
i = x, y
v = \frac{(s^2_\bar{x} +s^2_\bar{y})^2}{\frac{(s^2_\bar{x})^2}{n_x-1}+\frac{s^2_\bar{y})^2}{n_y-1} }
n_i is the sample size.