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Let p = P(X > Y), and then test the pair of measurements (xi, yi), then both xi and yi are equally likely to be larger than the other. Independent pairs of sample data are collected from the populations {(x1, y1), (x2, y2), . . ., (xn, yn)}. Pairs are omited for which there is no difference so that there is a possibly of a reduced sample of m pairs. Then let w be the number of pairs for which yi - xi > 0. Assuming that Ho is true, then W follows a Binomial Distribution B ~ b(m, 0.5). The left-tail value is computed by P(B <= w), which is the p-value for the alternative Ha: p < 0.50. This alternative means that the X measurements tend to be higher. The right-tail value is computed by P(B >= w), which is the p-value for the alternative Ha: p > 0.50. This alternative means that the Y measurements tend to be higher. For a two-sided alternative Ha: p does not equal 0.50, the p-value is twice the smallest tail-value. |
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