Independent Samples T-Test - Pooled Variance

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Where \bar{x}_i is the mean of variable x for the ith of g groups, s_{x_i} is its Standard Deviation and n_i its sample size, the test statistic is for the difference between groups i and i' is given by:

t=\frac{\bar{x}_i-\bar{x}_{i'}}{\sqrt{s^2_x(n^{-1}_i + n^{-1}_{i'})}},


p = 2\Pr(t_v \ge |t|),
v = \sum^g_{i=1} n_i - g, and
s^2_{x} =  \sum^g_{i=1}{ ( n_i - 1 ) s^2_{x_i}} / v .