The Wilcoxon Signed-Rank Test is a non-parametric statistical test used to compare two related samples or repeated measurements to determine if their population distributions differ. Unlike the paired t-test, which assumes normal distribution, the Wilcoxon Signed-Rank Test is suitable for non-normally distributed data or data with outliers. Advantages: ✔️ Suitable for non-normally distributed, ordinal data, or data with outliers. ✔️ Ideal for small sample sizes, providing robust results where the paired t-test may not be reliable. ✔️ Uses rank differences instead of actual values, reducing the impact of outliers and making fewer assumptions about the data. Limitations: ❌ Compares ranks of differences, not specific measures like means or medians, potentially losing information about the magnitude of differences. ❌ Results can be misleading if data isn’t truly paired or if the assumptions, such as symmetry of differences around the median, are not met. ❌ Less powerful than the paired t-test when data is normally distributed. Important Considerations: While often used to assess differences between medians, the Wilcoxon Signed-Rank Test actually tests for differences in ranks of paired observations. This means it is sensitive to various aspects of the data, including the distribution's shape. If the data isn’t symmetric or doesn’t meet the test's assumptions, the test may not compare medians accurately and could lead to increased Type I error. For direct median comparisons, especially with non-symmetric data, consider alternatives like quantile regression or Mood's median test. Permutation tests also offer a flexible, non-parametric option for testing hypotheses about various statistics without relying on rank transformations. Visualization Explanation: The visualization compares the distributions of two skewed samples, "Time 1" and "Time 2," using density plots with dashed lines indicating their medians. Although the medians are displayed, the Wilcoxon Signed-Rank Test actually assesses the ranks of paired differences, rather than directly comparing medians. The test can only be used to compare medians if the samples are independent and identically distributed (IID), have the same dispersion and shape, and are symmetric about their medians. If these conditions are not met, the test may not accurately compare medians. In such cases, consider alternatives like quantile regression or permutation tests, which do not depend on rank transformations. Explore more on this topic and other statistical methods in my online course on Statistical Methods in R! More info: statisticsglobe.com/online-c… #VisualAnalytics #DataViz #Statistical #programmer #DataAnalytics #datastructure