4.4.2—The basis of the sign test

For paired or one-sample data, the sign test counts positive and negative differences after removing zeros. Under a null median or no directional effect, the count follows a binomial model with p=0.5.

Choose the direction before counting, discard exact ties as specified, and use the smaller tail probability for a two-sided alternative only after defining the alternative.

With 9 non-zero paired differences, 8 positive results are assessed using X~Bin(9,0.5); the observed count is evidence about direction, not magnitude.

The sign test ignores how large differences are, and a tie is not automatically positive or negative.