Wilcoxon Test

The Wilcoxon signed-rank test, also known as the Wilcoxon rank-sum test, is a non-parametric statistical hypothesis test used to compare two related samples, matched or paired samples, where the distribution of the differences between the two samples may not be normal. It is used to assess whether the distributions of two paired samples are the same, or whether the difference between the paired samples is statistically significant.

The Wilcoxon signed-rank test is a non-parametric test, which means that it does not make any assumptions about the distribution of the data. This makes it a more robust test than parametric tests, such as the t-test, which require the data to be normally distributed.

The Wilcoxon signed-rank test is also a more powerful test than the t-test, meaning that it is more likely to detect a statistically significant difference between the two samples. This is because the Wilcoxon signed-rank test does not require the data to be normally distributed, which can lead to a loss of power in the t-test.

The Wilcoxon signed-rank test is a relatively simple test to perform. The first step is to calculate the difference between each pair of observations in the two samples. The second step is to rank the absolute values of these differences from smallest to largest. The third step is to assign a signed rank to each difference, where a positive rank is assigned to the differences in the first sample and a negative rank is assigned to the differences in the second sample. The fourth step is to sum the ranks for each sample. The fifth step is to compare the two sums of ranks. If the sum of ranks for the first sample is greater than the sum of ranks for the second sample, then the null hypothesis is rejected.

The Wilcoxon signed-rank test is a useful tool for comparing two related samples when the distribution of the differences between the two samples is not normal. It is a more robust and powerful test than the t-test, and it is relatively simple to perform.