The Wilcoxon Signed Rank test is a non-parametric analysis that statistically compared of the average of two dependent samples and assess for significant differences.


The Wilcoxon sign test is the non-parametric alternative of the  dependent samples t-test.

Questions Answered:

Are test scores different from 4th grade to 5th grade on the same students?

Does a particular diet drug have an effect on BMI when tested one the same individuals?


Data comes from two matched, or dependent, populations.

The data is continuous.

Because it is a non-parametric test it does not require a special distribution of the dependent variable in the analysis.

The Wilcoxon Sign test is a repeated measures test of dependency. This test is mathematically similar to conducting a Mann-Whitney U-test (which is sometimes also called Wilcoxon 2-sample t-test). It is also similar to the basic principle of the dependent samples t-test, because just like the dependent samples t-test the Wilcoxon sign test, tests the difference of observations when the observations are matched.

However this test pools all differences, ranks them and applies a negative sign to all the ranks where the difference between the two observations is negative. This is called the signed rank..  Whereas the dependent samples t-test tests whether the average difference between two observations is 0 the Wilcoxon test tests whether the difference between two observations has a mean signed rank of 0.  Thus it is much more robust against outliers and heavy tail distributions. .  Thus it is the best test to compare mean scores when the dependent variable is not normally distributed.

Statistics Solutions can assist with your quantitative analysis by assisting you to develop your methodology and results chapters. The services that we offer include:

Data Analysis Plan

  • Edit your research questions and null/alternative hypotheses
  • Write your data analysis plan; specify specific statistics to address the research questions, the assumptions of the statistics, and justify why they are the appropriate statistics; provide references
  • Justify your sample size/power analysis, provide references
  • Explain your data analysis plan to you so you are comfortable and confident
  • Two hours of additional support with your statistician

Quantitative Results Section (Descriptive Statistics, Bivariate and Multivariate Analyses, Structural Equation Modeling, Path analysis, HLM, Cluster Analysis)

  • Clean and code dataset
  • Conduct descriptive statistics (i.e., mean, standard deviation, frequency and percent, as appropriate)
  • Conduct analyses to examine each of your research questions
  • Write-up results
  • Provide APA 6th edition tables and figures
  • Explain chapter 4 findings
  • Ongoing support for entire results chapter statistics

*Please call 877-437-8622 to request a quote based on the specifics of your research, or email [email protected].

Related Pages:

Conduct and Interpret a Wilcoxon Sign Test

Assumptions of the Wilcoxon Sign Test

How to Conduct the Wilcoxon Sign Test