How to perform a Wilcoxon signed-rank test?

To perform a Wilcoxon signed-rank test, follow these steps:

1. State the null and alternative hypotheses. The null hypothesis is that there is no difference between the two related samples, while the alternative hypothesis is that there is a difference.

2. Rank the absolute differences between the pairs of observations, ignoring the signs.

3. Calculate the sum of the positive ranks (W+) and the sum of the negative ranks (W-).

4. Calculate the test statistic, T, using the formula T = min(W+, W-).

5. Determine the critical value of T from the Wilcoxon signed-rank table, using the sample size and desired level of significance.

6. Compare the calculated T value to the critical value. If the calculated T value is less than or equal to the critical value, reject the null hypothesis and conclude that there is a significant difference between the two related samples. If the calculated T value is greater than the critical value, fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference.

7. Calculate the p-value associated with the calculated T value, using the Wilcoxon signed-rank table. If the p-value is less than the level of significance, reject the null hypothesis.

It is important to note that the Wilcoxon signed-rank test is a non-parametric test, meaning it does not assume a normal distribution of the data. It is also a paired test, meaning it is used when comparing two related samples.