Wilcoxon Rank Sum Test: Concepts, Examples

wilcoxon rank sum hypothesis explanation

The Wilcoxon rank sum test is a statistical test used to compare two sets of data. This test is also known as the Mann-Whitney U test. It is a non-parametric statistical hypothesis test used to compare two samples. It is similar to the Student’s t-test, but does not require the assumption of normality. The test is appropriate for use with small sample sizes. 

What is Wilcoxon Rank Sum Test?

The Wilcoxon rank sum test is a statistical test used to compare two independent samples. The test is used to compare the medians (location of medians) in the two samples. The null hypothesis is that the location of medians in two independent samples are same. The alternate hypothesis can be based on one or two-tailed tests. The Wilcoxon rank sum test is a nonparametric alternative to the individual samples t-test and can be used when the data are not normally distributed. In independent samples t-test, the data is normally distributed and the null hypothesis is that there is no difference between the mean of two samples. On the other hand, the data in Wilcoxon rank sum test is non-normal and the null hypothesis is that there is no difference between the medians of two samples. The picture below represents different scenarios of populations and their medians and the representation of when null hypothesis can be rejected.

wilcoxon rank sum hypothesis explanation

The Wilcoxon rank sum test can be used with quantitative or the ordinal data. Recall that the ordinal data is data that is arranged in order. This could be alphabetical order, numerical order, or any other type of order. This type of data is useful for organizing information and for determining rankings. The Wilcoxon rank sum test is also known as Mann-Whitney test, Mann-Whitney-Wilcoxon test, Wilcoxon Two-Sample Test, or Wilcoxon rank sum statistics test.

The Wilcoxon rank sum test works by calculating the sum of ranks for each sample. This test produces a result known as the Wilcoxon rank sum statistic, which is used to calculate the probability or p-value. This p-value is used to determine if there is a statistically significant difference between our groups. If this p-value is less than our predetermined significance level (typically 0.05), then we can reject the null hypothesis and accept that there is a statistically significant difference between our groups. The following are different steps which can be followed while performing Wilcoxon rank sum test:

  • Put the samples in two columns
  • In third column, stack the two samples
  • In fourth column, rank the samples. For tied rank, find the average
  • Sum the ranks for each sample
  • Use the test statistics to find the p-value
  • Compare the p-value to chosen alpha level (pre-determined significance level)

Conclusion

The Wilcoxon rank sum test is a non-parametric statistical hypothesis test used to compare two samples. It does not require the assumption of normality, and so it is appropriate for use with small sample sizes. The test works by calculating the sum of ranks for each sample, and if the p-value is less than 0.05, then the null hypothesis is rejected in favor of the alternative hypothesis. When interpreting results of Wilcoxon rank sum test, it is important to remember that the null hypothesis states that there is no difference between the two samples while the alternative hypothesis states that there is a difference between the two samples.

Ajitesh Kumar
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Ajitesh Kumar

I have been recently working in the area of Data analytics including Data Science and Machine Learning / Deep Learning. I am also passionate about different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia, etc, and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data, etc. For latest updates and blogs, follow us on Twitter. I would love to connect with you on Linkedin. Check out my latest book titled as First Principles Thinking: Building winning products using first principles thinking
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