Wilcoxon sign test: It is a type of test of significance done in paired data if the data is non-parametrically distributed or ordinal data. Compared to paired t-tests which analyzes if the average difference of two repeated measures is zero and require metric (interval or ratio) and normally distributed data.
The Wilcoxon signed rank test relies on the W-statistics. For large samples with n>10 paired observations the W-statistics approximates a Normal Distribution. The W statistics is a non-parametric test, thus it does not need multivariate normality in the data.
The first step of the Wilcoxon sign test is to calculate the differences of the repeated measurements and to calculate the absolute differences.
The next step of the Wilcoxon sign test is to order the cases by increasing absolute differences.
For the Wilcoxon signed rank test we can ignore cases where the difference is zero. For all other cases we assign their relative rank. In case of tied ranks the average rank is calculated. That is if rank 10 and 11 have the same observed differences both are assigned rank 10.5.
The next step of the Wilcoxon sign test is to sign each rank. If the original difference < 0 then the rank is multiplied by -1; if the difference is positive the rank stays positive.
The W-statistic is simply the sum of the signed ranks.
PSM / COMMUNITY MEDICINE by Dr Abhishek Jaiswal is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at learnpsm@blogspot.com.
Permissions beyond the scope of this license may be available at jaiswal.fph@gmail.com.
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