Statistics 1-1
- Introduction to Statistics
- Descriptive Statistics
- Probability Distribution
- Sampling and Sampling Methods
- Estimation and Hypothesis Testing
- Comparison of Two Populations
- Analysis of Variance (ANOVA)
- Regression Analysis
- Nonparametric Statistics
- Statistical Applications in Quality and Productivity
- Software Application in Statistics
Nonparametric Statistics
Understanding the Kruskal-Wallis Test
Continuous probability distribution.
The Kruskal-Wallis test is a nonparametric method for testing whether samples originate from the same distribution. It is used for comparing two or more independent samples of equal or different sample sizes. It extends the Mann-Whitney U test, which is used for comparing only two groups.
Introduction to Kruskal-Wallis Test
The Kruskal-Wallis test is named after William Kruskal and W. Allen Wallis. This test is a rank-based nonparametric test that can be used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable.
Assumptions of the Kruskal-Wallis Test
The Kruskal-Wallis test has some assumptions that must be met for the results of the test to be valid. These assumptions include:
- The dependent variable should be measured at the ordinal or continuous level.
- The independent variable should consist of two or more categorical, independent groups.
- The distribution of the ranks for each group should be similar.
Applications of Kruskal-Wallis Test
The Kruskal-Wallis test is used when the assumptions of one-way ANOVA are not met. It is also used when dealing with ordinal variables. For example, it can be used to test if there is a difference in satisfaction levels of customers across different stores, where satisfaction is measured on an ordinal scale.
Steps to Perform Kruskal-Wallis Test
- Rank all data from all groups together; i.e., rank the data from 1 to N ignoring group membership.
- Compute sum of ranks for each group.
- Calculate the Kruskal-Wallis H statistic based on the ranks of the data.
- The H statistic is compared to a Chi-square distribution to derive a p-value.
Interpretation of Kruskal-Wallis Test Results
The result of the Kruskal-Wallis H test is a Chi-square statistic and a p-value. If the p-value is less than the chosen significance level (typically 0.05), the null hypothesis that the medians are equal is rejected.
In conclusion, the Kruskal-Wallis test is a useful nonparametric method for comparing two or more groups of data. It is particularly useful when the assumptions of parametric methods cannot be met.