Independent Samples T-Test - Unequal Variance

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

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

where:

[math]\displaystyle{ p = 2\Pr(t_v \ge |t|) }[/math],

[math]\displaystyle{ s^2_\bar{i} = \frac{s^2_i}{n_i} }[/math],

[math]\displaystyle{ i = x, y }[/math]

[math]\displaystyle{ 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} } }[/math]

[math]\displaystyle{ n_i }[/math] is the sample size.