Comparing 2 Groups in R using the Wilcoxon Test: Addressing Non-Normality Assumption

Comparing 2 Groups in R using the Wilcoxon Test: Addressing Non-Normality Assumption

Introduction:

In statistical analysis, the Wilcoxon test is used to compare two groups and determine if they are significantly different from each other based on a specific variable of interest. The Wilcoxon test can be easily performed in R using the same function, “wilcox.test()”.

This article discusses two scenarios: independent samples and paired samples. In the case of independent samples, the aim is to compare grades at a statistics exam between female and male students. The dataset used consists of grades for 24 students, 12 girls, and 12 boys. The distributions of grades are visually represented using boxplots, and it is determined that both groups do not follow a normal distribution. Consequently, the non-parametric Wilcoxon test is conducted, and the null hypothesis that grades are equal between girls and boys is rejected.

In the case of paired samples, the example considers a math test administered to the same class of 12 students at the beginning and end of a semester. The dataset consists of grades at the beginning and end, and the distributions of grades are once again displayed using boxplots. In this scenario, the paired Wilcoxon test is performed, considering the dependency between the two samples. The null hypothesis that grades before and after the semester are equal is not rejected.

Overall, the article provides a clear explanation of how to perform the Wilcoxon test in R for both independent and paired samples, illustrating the steps with relevant examples.

Full Article: Comparing 2 Groups in R using the Wilcoxon Test: Addressing Non-Normality Assumption

Comparing Two Groups with Wilcoxon Test in R

The Student’s t-test is commonly used to compare two groups and determine if they differ significantly in terms of a specific variable. However, when the distribution of the data does not follow a normal distribution, the Wilcoxon test can be used as an alternative. Luckily, both tests can be conducted in R using the same function – wilcox.test(). This article will discuss how to perform the Wilcoxon test for independent and paired samples using R.

Independent Samples

In the case of the Wilcoxon test with independent samples, let’s consider an example where we want to test if there is a difference in grades at a statistics exam between female and male students. We have collected grades for 24 students, with 12 girls and 12 boys. The grades are as follows:

Girl: 19, 18, 9, 17, 8, 7, 16, 19, 20, 9, 11, 18
Boy: 16, 5, 15, 2, 14, 15, 4, 7, 15, 6, 7, 14

To visualize the distribution of grades by sex, we can use ggplot2:

[INSERT IMAGE]

Before conducting the Wilcoxon test, we need to check if the two samples follow a normal distribution. We can do this by creating histograms and performing Shapiro-Wilk tests. The histograms show that both distributions do not seem to follow a normal distribution, which is confirmed by the Shapiro-Wilk tests.

Since the normality assumption is violated for both groups, we can proceed with the Wilcoxon test. The null and alternative hypotheses for the Wilcoxon test are as follows:

H0: The two groups are equal in terms of the variable of interest
H1: The two groups are different in terms of the variable of interest

In our case, the hypotheses are:
H0: Grades of girls and boys are equal
H1: Grades of girls and boys are different

With the wilcox.test() function in R, we can conduct the Wilcoxon test:

[INSERT R CODE]

The test provides the test statistic, p-value, and a reminder of the hypothesis tested. The p-value is 0.021, which means that at the 5% significance level, we reject the null hypothesis and conclude that grades are significantly different between girls and boys. This result is consistent with the observation from the boxplot that girls tend to perform better than boys.

To further investigate the performance difference, we can modify the alternative argument in the wilcox.test() function to “less” and conduct a one-sided test to determine if boys perform significantly worse than girls. The p-value obtained from this test is 0.01, which supports the conclusion that boys performed significantly worse than girls.

Paired Samples

In the case of paired samples, let’s consider an example where we administered a math test to a class of 12 students at the beginning and end of a semester. We have the following data:

Before: 16, 5, 15, 2, 14, 15, 4, 7, 15, 6, 7, 14
After: 19, 18, 9, 17, 8, 7, 16, 19, 20, 9, 11, 18

To work with this data, we first transform it into a tidy format:

[INSERT R CODE]

Visualizing the distribution of grades before and after the semester, we can observe the following:

[INSERT IMAGE]

In this case, the two samples are not independent since the same 12 students took the exam before and after the semester. Given that the normality assumption is violated and the small sample size, we can use the Wilcoxon test for paired samples. The null and alternative hypotheses for this test are:

H0: Grades before and after the semester are equal
H1: Grades before and after the semester are different

To conduct the Wilcoxon test for paired samples in R, we simply add the paired = TRUE argument to the wilcox.test() function:

[INSERT R CODE]

The test provides the test statistic, p-value, and a reminder of the hypothesis tested. The p-value obtained is 0.169, which suggests that at the 5% significance level, we do not reject the null hypothesis and conclude that the grades are similar before and after the semester.

In conclusion, the Wilcoxon test in R is a useful tool for comparing two groups in situations where the normality assumption is violated or when dealing with paired samples. By following the steps outlined in this article, you can confidently perform the Wilcoxon test and obtain reliable results for your data analysis.

Summary: Comparing 2 Groups in R using the Wilcoxon Test: Addressing Non-Normality Assumption

The Wilcoxon test is a statistical test used to compare two groups and determine if they are significantly different from each other in terms of a specific variable of interest. In R, both the Student’s t-test and Wilcoxon test can be performed using the same function, “wilcox.test()”. In the case of independent samples, the test can be used to compare grades at a statistics exam between female and male students. The test takes into account the non-normal distribution of the data and yields a p-value, which can be used to determine if the groups are significantly different. In the case of paired samples, such as before and after grades in a class, the test accounts for the dependency between the two samples and again provides a p-value to assess the difference. It’s important to note that while the t-test assumes normality, the Wilcoxon test does not, making it suitable for non-normal data as well.

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