Paired Samples Wilcoxon Test in R
The paired samples Wilcoxon test is a non-parametric alternative to paired t-test used to compare paired data. It’s used when data are not normally distributed.
Implementation in R
To perform Paired Samples Wilcoxon-test, the R provides a function wilcox.test() that can be used as follow:
Syntax: wilcox.test(x, y, paired = TRUE, alternative = “two.sided”)
Parameters:
- x, y: numeric vectors
- paired: a logical value specifying that we want to compute a paired Wilcoxon test
- alternative: the alternative hypothesis. Allowed value is one of “two.sided” (default), “greater” or “less”.
Example: Here, let’s use an example data set, which contains the weight of 10 rabbits before and after the treatment. We want to know, if there is any significant difference in the median weights before and after treatment?
R
# R program to illustrate# Paired Samples Wilcoxon Test# The data set# Weight of the rabbit before treatmentbefore <-c(190.1, 190.9, 172.7, 213, 231.4, 196.9, 172.2, 285.5, 225.2, 113.7)# Weight of the rabbit after treatmentafter <-c(392.9, 313.2, 345.1, 393, 434, 227.9, 422, 383.9, 392.3, 352.2)# Create a data framemyData <- data.frame(group = rep(c("before", "after"), each = 10),weight = c(before, after))# Print all dataprint(myData)# Paired Samples Wilcoxon Testresult = wilcox.test(before, after, paired = TRUE)# Printing the resultsprint(result) |
Output:
group weight
1 before 190.1
2 before 190.9
3 before 172.7
4 before 213.0
5 before 231.4
6 before 196.9
7 before 172.2
8 before 285.5
9 before 225.2
10 before 113.7
11 after 392.9
12 after 313.2
13 after 345.1
14 after 393.0
15 after 434.0
16 after 227.9
17 after 422.0
18 after 383.9
19 after 392.3
20 after 352.2
Wilcoxon signed rank test
data: before and after
V = 0, p-value = 0.001953
alternative hypothesis: true location shift is not equal to 0
In the above output, the p-value of the test is 0.001953, which is less than the significance level alpha = 0.05. We can conclude that the median weight of the mice before treatment is significantly different from the median weight after treatment with a p-value = 0.001953.
If one wants to test whether the median weight before treatment is less than the median weight after treatment, then the code will be:
R
# R program to illustrate# Paired Samples Wilcoxon Test# The data set# Weight of the rabbit before treatmentbefore <-c(190.1, 190.9, 172.7, 213, 231.4, 196.9, 172.2, 285.5, 225.2, 113.7)# Weight of the rabbit after treatmentafter <-c(392.9, 313.2, 345.1, 393, 434, 227.9, 422, 383.9, 392.3, 352.2)# Create a data framemyData <- data.frame(group = rep(c("before", "after"), each = 10),weight = c(before, after))# Paired Samples Wilcoxon Testresult = wilcox.test(weight ~ group, data = myData, paired = TRUE, alternative = "less")# Printing the resultsprint(result) |
Output:
Wilcoxon signed rank test data: weight by group V = 55, p-value = 1 alternative hypothesis: true location shift is less than 0
Or, If one wants to test whether the median weight before treatment is greater than the median weight after treatment, then the code will be:
R
# R program to illustrate# Paired Samples Wilcoxon Test# The data set# Weight of the rabbit before treatmentbefore <-c(190.1, 190.9, 172.7, 213, 231.4, 196.9, 172.2, 285.5, 225.2, 113.7)# Weight of the rabbit after treatmentafter <-c(392.9, 313.2, 345.1, 393, 434, 227.9, 422, 383.9, 392.3, 352.2)# Create a data framemyData <- data.frame(group = rep(c("before", "after"), each = 10),weight = c(before, after))# Paired Samples Wilcoxon Testresult = wilcox.test(weight ~ group, data = myData, paired = TRUE, alternative = "greater")# Printing the resultsprint(result) |
Output:
Wilcoxon signed rank test data: weight by group V = 55, p-value = 0.0009766 alternative hypothesis: true location shift is greater than 0
Wilcoxon Signed Rank Test in R Programming
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to estimate whether their population means ranks differ e.g. it is a paired difference test. It can be applied as an alternative to the paired Student’s t-test also known as “t-test for matched pairs” or “t-test for dependent samples” when the distribution of the difference between the two samples’ means cannot be assumed to be normally distributed. A Wilcoxon signed-rank test is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution.
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