# Wilcoxon Signed Rank Test

Statistics Solutions provides a data analysis plan template for the Wilcoxon Signed Rank Test analysis. You can use this template to develop the data analysis section of your dissertation or research proposal.

The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis. Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.

**Data Analysis Plan: Wilcoxon Signed Rank Test**

Copy and paste the following into a word document to use as your data analysis plan template.

*Research Question:*

RQ: Will there be statistically significant differences on dependent variable by administration?

H_{o}: There will be no statistically significant differences on dependent variable by administration.

H_{a}: There will be statistically significant differences on dependent variable by administration.

*Data Analysis*

To examine the research question, a Wilcoxon Signed Rank test will be conducted on dependent variable by administration. The Wilcoxon test is the nonparametric equivalent to the paired or dependent sample *t*-test and the appropriate analysis to compare differences derived from the same population when the dependent variable is ordinal or continuous. It is used to assess differences from matched pair designs or repeated measures. The Wilcoxon Signed Rank test compares the number of times a score from one sample is ranked higher than a score from another sample. The scores from both samples will be ranked together; rank 1 is used for the lowest score, rank 2 for the next lowest score, and so on. When scores have the same value, a tie is determined. The scores are ranked and those ranks are added together and then divided by the number of scores. Each of the tied scores is then assigned the same ranking. Once the data is ranked, calculations will be carried out on the ranks. Given the nonparametric nature of this statistical analysis, there are fewer assumptions to assess. The assumptions include random samples from population, the two samples have independent observations, and the measure of the two samples have at least an ordinal scale of measurement. The Wilcoxon Signed Rank Test can be conducted when the assumptions of the dependent sample *t* test (such as normality) are violated.

**Reference**

Statistics Solutions. (2013). Data analysis plan: Wilcoxen Signed Rank Test [WWW Document]. Retrieved from http://www.statisticssolutions.com/academic-solutions/member-resources/member-profile/data-analysis-plan-templates/data-analysis-plan-wilcoxen-signed-rank-test/