Description: The Wilcoxon test is a non-parametric statistical technique used to compare two paired samples. Unlike parametric tests, which assume that data follow a normal distribution, the Wilcoxon test does not require this assumption, making it particularly useful in situations where data do not meet normality requirements. This test is based on the differences between pairs of observations, ranking these differences, and assigning ranks to the absolute values of the differences. The goal is to determine if there is a significant difference in the medians of the two paired samples. The Wilcoxon test is particularly valuable in studies where the effect of a treatment or intervention on the same group of subjects is evaluated, such as in clinical studies or psychological experiments. Its ability to handle ordinal data and its robustness against assumption violations make it an essential tool in statistical analysis, especially in fields like medicine, psychology, and social sciences.
History: The Wilcoxon test was developed by Frank Wilcoxon in 1945. It was originally conceived as an alternative to Student’s t-test for small and non-normal samples. Since its introduction, it has evolved and become one of the most widely used non-parametric tests in statistics, especially in research where data do not meet the normality assumptions required by parametric tests.
Uses: The Wilcoxon test is used in various fields, including medicine, psychology, and social sciences. It is commonly applied in clinical studies to evaluate the effectiveness of treatments, as well as in psychological research to analyze changes in participants’ responses before and after an intervention. It is also used in market studies to compare consumer preferences between two products.
Examples: A practical example of the Wilcoxon test would be a study evaluating the blood pressure of a group of patients before and after antihypertensive treatment. By comparing the paired measurements, the test can determine if there is a significant difference in the medians of blood pressures before and after treatment. Another example could be a psychological experiment where participants’ performance on a task is measured before and after receiving specific training.
