Paired t-Test of Means

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Where \bar x_1 and \bar x_2 are the two means, and s_{{\bar x_1} - {\bar x_2}} is an estimate of the Standard Error of the difference between the means:

t=\frac{\bar x_1-\bar x_2}{s_{{\bar x_1} - {\bar x_2}}}


p \approx 2\Pr(t_{n-1} \ge |t|),
n is the sample size,
s_{{\bar x_1} - {\bar x_2}} is computed as the Standard Error of d,
the value for the ith observation is computed as d_i = x_{i1} - x_{i2} where x_1,x_2 are the observed values on the two variables.