It’s a great day in sports analytics! Today, we will discuss two similar sports analytics methods called the Wilcoxon Signed Rank Test and Kruskal Wallis H Test.
In the application of Wilcoxon Signed Rank Test and Kruskal Wallis H Test, coaches and sport analysts employ tests to compare two or more independent samples that are of different or the same sizes, and two dependent samples, respectively. This comparison allows analysts to determine whether or not the samples originate from the same distribution or are normally distributed. Wilcoxon Signed Rank Test and Kruskal Wallis H Test are typical tests that are used in Grand slam tennis matches to determine the percentage of points won based on serve.
Wilcoxon Signed Rank Test
Wicoxon Signed Rank Test is a non-parametric statistical test. In plain terms, the test is used to compare two samples that are related. And because it is non-parametric means that the population from which you draw your samples is not normally distributed.
Sport analysts employ this test when the differences between the sample data do not have a normal distribution. The analysts generate a null hypothesis for this test, and the null hypothesis is that the two samples to be used must have equal median.
Let’s see how tennis analysts use Wilcoxon Signed Rank test to analyze a grand slam tennis match. In a tennis study of 252 matches, it was discovered that players won a higher percentage of points in 15 matches on second serve, while a higher percentage of points was won by players in the other 237 matches on first serve. These results are then used with the median values to obtain the median percentage points. It is from this median percentage point that all other variables are obtained.
Kruskal Wallis H Test
Kruskal Wallis H Test is also a non-parametric statistical test. It is an alternative to the common one-way Analysis of Variance (ANOVA). This test is used when the assumptions that are normally used for ANOVA cannot be met and it is used to compare three or more independent samples. Sports analysts use this test to determine if the medians of two or more statistical groups are different.
Let’s see how Kruskal Wallis H Test is used for the same grand slam tennis matches mentioned above. Supposing a tennis analyst wants to carry out analysis of 252 matches in four different tennis tournaments, for instance, where the mean rally duration is compared , there are two important variables. They are (1) Test Variable List and (2) Grouping Variable. The length of the rally is used in the Test Variable List while the surface is used in the Grouping Variable. Now, in a tennis study of 252 matches, the expected mean rank should be about 126.5 provided there is no large difference between the surfaces.
This Kruskal Wallis H test results in a value that is used for a normal distribution. This value is called “H value” and the common normal distribution test used here is the “Chi-square distribution”. Now, from the result given by the H value and Chi-square distribution, the analyst can tell if there is a significant difference between the groups. However, it won’t be revealed yet the exact group that is different from the others. It is then the analyst will now carry out an “H test” or a “Post Hoc” test. It is this H test that reveals the group that is different from others causing the significant difference in the distribution.
Conclusively, Wilcoxon Signed Rank Test and Kruskal Wallis H Test help coaches and sports analysts to determine variation in performances of different tennis players.
Find out how Sports Analytics Expert Victor Holman can give your team the competitive advantage.
How mature is your team’s analytics program? Take the Sports Analytics Maturity Assessment.
Learn about the Groundbreaking Sports Analytics Model coaches and sports analysts are talking about!
Learn all about Sports Analytics here