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

The test statistic is:

[math]\displaystyle{ t = \frac{\bar{x} - \bar{y}}{\sqrt{\frac{s^2_x}{m} + \frac{s^2_y}{n}}} }[/math]

where:

[math]\displaystyle{ \bar{x} }[/math] and [math]\displaystyle{ \bar{x} }[/math] are the average values of variables [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] respectively, where each of these variables represents the data from two independent groups,

the groups have sample sizes of [math]\displaystyle{ m }[/math] and [math]\displaystyle{ n }[/math] respectively,

[math]\displaystyle{ s^2_x }[/math] and [math]\displaystyle{ s^2_y }[/math] are the variances in the two groups,

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

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

[math]\displaystyle{ b }[/math] is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise,

[math]\displaystyle{ d_{eff} }[/math] is Extra Deff.