{"id":3292,"date":"2023-01-02T14:40:00","date_gmt":"2023-01-02T13:40:00","guid":{"rendered":"https:\/\/www.gironi.it\/blog\/?p=3292"},"modified":"2024-10-17T14:43:40","modified_gmt":"2024-10-17T13:43:40","slug":"non-parametric-tests-the-wilcoxon-test-for-non-normal-data","status":"publish","type":"post","link":"https:\/\/www.gironi.it\/blog\/en\/non-parametric-tests-the-wilcoxon-test-for-non-normal-data\/","title":{"rendered":"Non-Parametric Tests: The Wilcoxon Test for Non-Normal Data"},"content":{"rendered":"\n

The Wilcoxon test<\/strong> is a non-parametric test<\/a><\/strong> used to compare two independent samples, or a sample with a known reference value.
The test is used when the data do not follow a normal distribution<\/a>, or when the distribution parameters are unknown.<\/strong><\/p>\n\n\n\n\n\n

The Wilcoxon test involves ranking the data from both samples<\/strong>, and then assigning a score to each value based on its position in the ranking<\/strong>. The scores are then summed for each sample, and the difference between the sum of scores of the two samples is compared to a known reference value, using the Wilcoxon distribution.
Based on the result of the comparison, one can decide whether to accept or reject the null hypothesis.<\/p>\n\n\n

The Wilcoxon test is often used to compare the values of a continuous variable between two groups. There is also a version of the test called the Wilcoxon-Mann-Whitney test, which is used when comparing two groups with an ordinal or categorical variable.<\/p>\n\n\n

A Practical Example of the Wilcoxon Test in R<\/h2>\n\n\n

In this example, I will generate sample data for two groups, group1<\/code> and group2<\/code>, using the rnorm()<\/code> function to generate random numbers that follow a normal distribution with a mean of 100 and standard deviation of 15 for the first group, and a mean of 110 and standard deviation of 15 for the second group.<\/p>\n\n\n

I use the wilcox.test() function to perform the Wilcoxon test, and specify the alternative hypothesis as “two.sided<\/em>” to test whether the two groups have significantly different means.<\/p>\n\n\n

The test results are printed on the screen and include the test statistic value, the p-value, and the test conclusion. Based on the p-value, one can decide whether to accept or reject the null hypothesis.<\/p>\n\n\n

# Create sample data\nset.seed(123)\ngroup1 <- rnorm(100, mean = 100, sd = 15)\ngroup2 <- rnorm(100, mean = 110, sd = 15)\n\n# Perform the Wilcoxon test\nwilcox_test <- wilcox.test(group1, group2, alternative = \"two.sided\")\n\n# Display the test results\nprint(wilcox_test)\n<\/pre>\n\n\n
The most commonly used significance level is 5% or 0.05. This means that a threshold of 5% is established, above which the observed effect is considered random, and below which the observed effect is considered statistically significant. In other words, if the p-value obtained from the test is less than 0.05, the null hypothesis is rejected, and it is concluded that there is a significant difference between the samples.<\/p>\n\n\n
It’s important to note that these threshold values are conventional and can be modified based on the specific needs of the study or the discipline in which one is working.<\/p>\n\n\n
Resources for Further Study<\/h2>\n\n\n