Sign test

Sign test

In statistics, the sign test can be used to test the hypothesis that there is "no difference" between the continuous distributions of two random variables "X" and "Y". Formally:

Let "p" = Pr("X" > "Y"), and then test the null hypothesis H0: "p" = 0.50. This hypothesis implies that given a random pair of measurements ("x""i", "y""i"), then "x""i" and "y""i" are equally likely to be larger than the other.

Independent pairs of sample data are collected from the populations {("x"1, "y"1), ("x"2, "y"2), . . ., ("x""n", "y""n")}. Pairs are omitted for which there is no difference so that there is a possibility of a reduced sample of "m" pairs.

Then let "w" be the number of pairs for which "y""i" − "x""i" > 0. Assuming that H0 is true, then "W" follows a binomial distribution "W" ~ b("m", 0.5).

The left-tail value is computed by Pr("W" &le; "w"), which is the p-value for the alternative H1: "p" < 0.50. This alternative means that the "X" measurements tend to be higher.

The right-tail value is computed by Pr("W" &ge; "w"), which is the p-value for the alternative H1: "p" > 0.50. This alternative means that the "Y" measurements tend to be higher.

For a two-sided alternative H1 the p-value is twice the smaller tail-value.


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