Wilcoxon Signed-Ranks Test for Median of Single Population

Consider an example of a novel rice variety genetically modified to produce longer rice grains.

To know if the grain length of the novel variety is significantly different from the natural population of rice or wildtype, 12 such grain lengths are compared with the median of grain lengths of the wildtype.

Here, the null hypothesis that no difference exists between the grain lengths of the novel and wildtype rice varieties can be tested using the Wilcoxon signed-ranks test.

First, calculate d by subtracting the median from each sample value.

Now, assign preliminary ranks to each value of d and calculate the actual ranks.

Assign appropriate signs to all.

Calculate the sum of positive and negative ranks separately.

Ignore the signs of these sums and take the smaller value as the test statistic T.

Get a two-tailed critical value at n = 12 at a significance level 0.05 from the standard table to compare it with T.

As the critical value is larger than the test statistic, the null hypothesis is rejected.