The statistic on which this test is based is computed by assigning to each value in the dataset its ranking in the list of the absolute differences multiplied by the sign of (so values below get assigned a negative rank). These signed ranks are then summed to produce . If the null hypothesis is true, that is, if is the median of the distribution from which the sample comes, then the signs of the differences can be regarded as Bernoulli trials. Using this to assign probabilities to all the possible signed rank sums gives the distribution which is shown in blue in the upper image above. The mean of this distribution is zero and its variance is . The purple curve is the density of a normal distribution with this mean and variance, which gives a good approximation to this distribution for all but very small sample sizes.