Non-parametric statistics are a set of statistical methods that do not make any assumptions about the underlying distribution of the data. One such non-parametric test is the Kruskal-Wallis test, which is used to compare three or more independent groups when the dependent variable is ordinal or continuous but not normally distributed.

Category : Non-parametric Statistics en | Sub Category : Kruskal-Wallis Test Posted on 2023-07-07 21:24:53

Non-parametric statistics are a set of statistical methods that do not make any assumptions about the underlying distribution of the data. One such non-parametric test is the Kruskal-Wallis test, which is used to compare three or more independent groups when the dependent variable is ordinal or continuous but not normally distributed.

The Kruskal-Wallis test is often referred to as the non-parametric equivalent of the one-way analysis of variance (ANOVA) test. It is used to determine whether there are statistically significant differences between the medians of the groups being compared.

The basic idea behind the Kruskal-Wallis test is to rank all the data points from lowest to highest across all groups, and then compare the average ranks of the groups. If the average ranks of the groups are significantly different, then we can conclude that there is a significant difference between the groups.

To conduct a Kruskal-Wallis test, the following steps are typically followed:

1. State the null and alternative hypotheses.
2. Rank all the data points from lowest to highest.
3. Calculate the sum of ranks for each group.
4. Calculate the test statistic using the formula:

H = (12 / (N(N+1))) * Σ(R_j^2 / n_j) - 3(N+1)

where:
- H is the test statistic
- N is the total number of observations
- R_j is the sum of ranks for group j
- n_j is the sample size for group j

5. Determine the degrees of freedom for the test statistic, which is calculated as k-1, where k is the number of groups.
6. Compare the calculated test statistic with a critical value from the chi-square distribution to determine statistical significance.

If the calculated test statistic is greater than the critical value, then we can reject the null hypothesis and conclude that there are significant differences between the groups. If the test statistic is not greater than the critical value, then we fail to reject the null hypothesis and conclude that there are no significant differences between the groups.

Overall, the Kruskal-Wallis test is a valuable tool for comparing three or more independent groups when the assumptions of parametric tests like ANOVA are not met. It is particularly useful in situations where the data is non-normally distributed or the sample size is small. By utilizing non-parametric statistics like the Kruskal-Wallis test, researchers can make valid inferences about group differences without relying on stringent assumptions about the data distribution.