One-Sample Wilcoxon Test in R: Understanding and Implementing this Statistical Analysis

One-Sample Wilcoxon Test in R: Understanding and Implementing this Statistical Analysis

Introduction:

In a previous article, we discussed how to perform a two-sample Wilcoxon test in R. This test is used to compare two independent samples and is the non-parametric version of the Student’s t-test. However, there is another version of the test called the Wilcoxon signed-rank test, which is used to compare two paired samples. This test does not rely on the assumption of normality and is useful when dealing with outliers and Likert scales. In this article, we will explore when and how to perform the one-sample Wilcoxon test in R, and how to interpret its results. We will also provide some appropriate visualizations and examples to illustrate the concept.

Full Article: One-Sample Wilcoxon Test in R: Understanding and Implementing this Statistical Analysis

Performing the One-Sample Wilcoxon Test in R

Introduction

In a previous article, we discussed the two-sample Wilcoxon test in R. Now, we will delve into the one-sample Wilcoxon test, which is a non-parametric test used to compare observations to a specified value. This test is particularly useful when the data does not follow a normal distribution.

Understanding the One-Sample Wilcoxon Test

The one-sample Wilcoxon test helps determine if a group is significantly different from a known or hypothesized population value. Instead of relying on the assumption of normality, this test computes a test statistic based on the ranks of the difference between the observed values and the default value.

Hypotheses in a Two-Tailed Test

In a two-tailed test, we have the following null and alternative hypotheses:

– Null Hypothesis (H0): The location of the data is equal to the chosen value.
– Alternative Hypothesis (H1): The location of the data is different from the chosen value.

It’s important to note that some authors suggest that this test is a test of the median, but only if the data is symmetric. Without further assumptions about the data distribution, the one-sample Wilcoxon test is a test about the location of the data, not the median.

Verifying Assumptions

While the one-sample Wilcoxon test does not require the normality assumption, it still assumes independence among observations. Thus, random sampling is necessary to achieve independence. It’s also worth mentioning that this test is suitable for various types of data, including interval data and Likert scales.

Performing the One-Sample Wilcoxon Test in R

To perform the one-sample Wilcoxon test in R, we can use the `wilcox.test()` function. Before conducting the test, it’s helpful to visualize the data using a boxplot and calculate some descriptive statistics:

Boxplot:

“`R
boxplot(dat$Score, ylab = “Score”)
“`

Descriptive statistics:

“`R
round(summary(dat$Score), digits = 2)
“`

From the boxplot and descriptive statistics, we observe that the mean and median scores in our sample are 11.33 and 14, respectively. Now, let’s run the one-sample Wilcoxon test to determine if the scores are significantly different from 10:

“`R
wilcox.test(dat$Score, mu = 10) # default value
“`

Interpreting the Results

Based on the results of the one-sample Wilcoxon test (at a significance level of 0.05), we do not reject the null hypothesis. Therefore, we cannot conclude that the scores at this exam are significantly different from 10 ((p)-value = 0.378).

One-Sided Test

If we want to perform a one-sided test, such as testing if the scores are higher than 10, we can specify the alternative hypothesis in the `wilcox.test()` function:

“`R
wilcox.test(dat$Score, mu = 10, alternative = “greater”) # H1: scores > 10
“`

In this case, we still do not reject the null hypothesis that the scores are equal to 10. Thus, we cannot conclude that the scores are significantly higher than 10 ((p)-value = 0.189).

Conclusion

The one-sample Wilcoxon test is a useful non-parametric test for comparing observations to a specified value. It does not rely on the assumption of normality and can handle various types of data. By using the `wilcox.test()` function in R, we can easily perform this test and interpret the results. However, it’s essential to verify the independence assumption and consider the appropriate significance level when drawing conclusions from the test.

Summary: One-Sample Wilcoxon Test in R: Understanding and Implementing this Statistical Analysis

In this article, we will discuss the one-sample Wilcoxon test, which is a non-parametric test used to compare observations to a specified value. We will explain when to use this test, how to perform it in R, and how to interpret the results. Unlike parametric tests, the one-sample Wilcoxon test does not require the assumption of normality and can handle outliers and Likert scales. We will also provide some appropriate visualizations to aid in understanding the results. Using a sample of 15 students’ scores at an exam, we will illustrate the steps involved in conducting the test. Finally, we will interpret the results and discuss the meaning of the p-value.

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