Wilcoxon Test
The Wilcoxon test, which can refer to either the Rank Sum test or the Signed Rank test version, is a nonparametric statistical test that compares two paired groups. The Wilcoxon test is a nonparametric statistical test that compares two paired groups, and comes in two versions the Rank Sum test or the Signed Rank test. The Wilcoxon test, which can refer to either the Rank Sum test or the Signed Rank test version, is a nonparametric statistical test that compares two paired groups. As the nonparametric equivalent of the paired student's t-test, the Signed Rank can be used as an alternative to the t-test when the population data does not follow a normal distribution. The Wilcoxon Rank Sum test can be used to test the null hypothesis that two populations have the same continuous distribution.
What Is the Wilcoxon Test?
The Wilcoxon test, which can refer to either the Rank Sum test or the Signed Rank test version, is a nonparametric statistical test that compares two paired groups. The tests essentially calculate the difference between sets of pairs and analyzes these differences to establish if they are statistically significantly different from one another.
The Basics of the Wilcoxon Test
The Rank Sum and Signed Rank tests were both proposed by American statistician Frank Wilcoxon in a groundbreaking research paper published in 1945. The tests laid the foundation for hypothesis testing of nonparametric statistics, which are used for population data that can be ranked but do not have numerical values, such as customer satisfaction or music reviews. Nonparametric distributions do not have parameters and cannot be defined by an equation as parametric distributions can.
The types of questions that the Wilcoxon Test can help us answer include things like:
These models assume that the data comes from two matched, or dependent, populations, following the same person or stock through time or place. The data is also assumed to be continuous as opposed to discrete. Because it is a non-parametric test it does not require a particular probability distribution of the dependent variable in the analysis.
Versions of the Wilcoxon Test
Calculating a Wilcoxon Test Statistic
The steps for arriving at a Wilcoxon Signed-Ranks Test Statistic, W, are as follows:
- For each item in a sample of n items, obtain a difference score Di between two measurements (i.e., subtract one from the other).
- Neglect then positive or negative signs and obtain a set of n absolute differences |Di|.
- Omit difference scores of zero, giving you a set of n non-zero absolute difference scores, where n' ≤ n. Thus, n' becomes the actual sample size.
- Then, assign ranks Ri from 1 to n to each of the |Di| such that the smallest absolute difference score gets rank 1 and the largest gets rank n. If two or more |Di| are equal, they are each assigned the average rank of the ranks they would have been assigned individually had ties in the data not occurred.
- Now reassign the symbol “+” or “–” to each of the n ranks Ri, depending on whether Di was originally positive or negative.
- The Wilcoxon test statistic W is subsequently obtained as the sum of the positive ranks.
In practice, this test is easily performed using statistical analysis software or a spreadsheet.
Related terms:
Alpha Risk
Alpha risk is the risk in a statistical test of rejecting a null hypothesis when it is actually true. read more
Goodness-of-Fit
A goodness-of-fit test helps you see if your sample data is accurate or somehow skewed. Discover how the popular chi-square goodness-of-fit test works. read more
Hypothesis Testing
Hypothesis testing is the process that an analyst uses to test a statistical hypothesis. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. read more
Nonparametric Method
Nonparametric method refers to a type of statistic that does not require that the data being analyzed meet certain assumptions or parameters. read more
Nonparametric Statistics: Overview
Nonparametric statistics refer to a statistical method in which the data is not required to fit a normal distribution. Rankings should not change. read more
Normal Distribution
Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean. read more
Null Hypothesis : Testing & Examples
A null hypothesis is a type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations. read more
Statistical Significance
Statistical significance refers to a result that is not likely to occur randomly but rather is likely to be attributable to a specific cause. read more