Paired Z-Test of Means

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Where \bar x_1 and \bar x_2 are the two means, the test statistic is:

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

where:

p \approx 2(1-\Phi(|z|)),
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}, and
x_1,x_2 are the observed values on the two variables.
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