# How to Perform Wilcoxon Signed-rank Test in R

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## What is a Wilcoxon Signed-Rank Test?

The Wilcoxon signed-rank test is a non-parametric statistical technique and an alternative to the paired sample t-test. We use the Wilcoxon signed rank test when there is one continuous variable measured two times or under two conditions. To clarify, we use the Wilcoxon test to compare two sets of scores that come from the same participants but we should measure in two different periods or before and after some event for example, before and after the training.

When Should a Wilcoxon Signed Rank Rest be Used?

The Wilcoxon Signed-Rank Test is a statistical test used to determine if two measurements from a single group are significantly different from each other on your variable of interest.  The Wilcoxon Signed Rank test is a nonparametric alternative to a Paired Samples t-test. Non-parametric means that the test doesn’t assume your data comes from a particular distribution. The test doesn’t require the data to be normal but instead uses the rank of the data values instead of the actual data values for the analysis.

### An Example Of Wilcoxon Signed Rank Test

For example, the researcher wants to examine the effect of psychotherapy on anxiety levels; therefore, the researcher measures the level of anxiety before psychotherapy and after psychotherapy.

Therefore, we test the following hypotheses:

Null hypothesis: There is no significant effect of psychotherapy on anxiety levels.

Alternative hypothesis: There is a significant effect of psychotherapy on anxiety levels.

## R function to Compute Wilcoxon Signed Rank Test

The code to run a Wilcoxon Signed Rank test using R is as follows:

wilcox.test(x, y, Paired=TRUE, data = dataframe)

x: numeric vector (pre-scores)

y: numeric vector (post or follow-up scores)

paired: a logical value specifying that we want to compute a paired t-test

## Running Wilcoxon Signed Rank Test in Rstudio

In this section, we will show you how to run the wilcoxon signed rank test using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the wilcoxon signed rank test. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the wilcoxon signed-rank test in APA format.

# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
preanxiety <- data\$preanxiety
postanxiety <- data\$postanxiety

# SHOW MEDIAN FOR VARIABLES
median(preanxiety)
median(postanxiety)

# PERFORM WILCOXON SIGNED-RANK TEST
wilcox.test(preanxiety, postanxiety, paired=TRUE)

``> median(preanxiety)``
``## [1] 9``
``> median(postanxiety)``
``````## [1] 6
``````
> wilcox.test(preanxiety, postanxiety, paired=TRUE)``````
``````##
##  Wilcoxon signed rank test with continuity correction
##
## data:  preanxiety and postanxiety
## V = 4001, p-value = 3.385e-15
## alternative hypothesis: true location shift is not equal to 0``````

## Reporting Wilcoxon Signed Rank Test in R

Wilcoxon signed-rank test was conducted to determine whether there is an effect of psychotherapy on anxiety levels. The results indicate a significant difference between anxiety level before psychotherapy (median = 9) and anxiety level after psychotherapy (median = 6), V = 4001, p < 0.001. We therefore must reject the null hypothesis and conclude that there is a significant effect of psychotherapy on anxiety levels. The median anxiety level was higher before psychotherapy.

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