The Signed-Rank test
The Wilcoxon Signed-Rank test is a non-parametric alternative version of the paired t-test that is used when the assumption of normality is violated. This test is robust to outliers because of the use of ranks and medians instead of means in the null and alternative hypotheses. As indicated by the name of the test, it uses the magnitudes of differences between two stages and their signs.
In research, a null hypothesis considers that the median difference between stage 1 and stage 2 is zero. Similarly, as in a paired t-test, for the alternative hypothesis, for a two-tailed test, the median difference between Stage 1 and Stage 2 is considered not to be zero, or for a one-tailed test, the median difference between Stage 1 and Stage 2 is greater (or less) than zero.
Though the normality requirement is relaxed, the test requires independence between paired observations and these observations to be from the same population. In addition, the dependent variable is...
