Talk:Sign test

Point of this page

The introduction is rambling and favours two-sample tests but says it also covers one-sample tests (which, given the title, seems correct to me). The lack of clarity in the intro is probably why, for example, the median test page thinks only two-sample tests are covered here! Mebden (talk) 00:02, 11 August 2022 (UTC)

Incorrect passage about null hypothesis

It was stated previously that:

If X and Y are quantitative variables, the sign test can be used to test the hypothesis that the difference between the median of X and the median of Y is zero, assuming continuous distributions of the two random variables X and Y, in the situation when we can draw paired samples from X and Y.

Distributions with equal medians: X is top and Y is bottom

This is incorrect statement. Consider two random variables X and Y with probability distributions given in the figure. It is obvious that they have the same median (namely, zero) and the difference between medians is equal to zero. However, Y is stochastically greater than X: P(Y>X) > P(Y<X). Indeed, there are two cases possible: either XY>0 or XY<0. If XY<0, one value is above the median and the other is below the median and in this case P(Y>X) = P(Y<X) = 1/2. However, if XY>0, both values are either below of above the median. It is obvious from the distribution that in this case P(Y>X) is greater than P(X>Y). In this case W statistics is not distributed with Binomial distribution with p=0.5. Therefore, it is incorrect null. The correct one is the difference between X and Y has zero median.

I will fix this incorrect statement.

Ilya Voyager (talk) 02:56, 18 October 2016 (UTC)

Indeed, there is a problem. Another simple exemple :

A 1 2 3 4 5

B 1.1 2.2 3 4.1 5.1

They have the same median but P(Y>X)=4/5 > P(X>Y)=0