Kruskal-Wallis test

Contents

Kruskal-Wallis test. The Kruskal-Wallis test is a non-parametric statistical test developed by William Kruskal and W. Allen Wallis, used to compare more than two groups, similar to the Analysis of Variance (ANOVA) test. This test is often used in Medical Research, Social Sciences, and Environmental Studies to compare the distribution of a variable across different groups, such as University of California, Berkeley students, Harvard University faculty, or National Institutes of Health researchers. The test has been widely applied in various fields, including Psychology, Biology, and Economics, by researchers like Daniel Kahneman, Amos Tversky, and Joseph Stiglitz.

Introduction

The Kruskal-Wallis test is a non-parametric alternative to the One-Way ANOVA test, which assumes that the data follows a Normal Distribution. However, in many cases, the data may not meet this assumption, and that's where the Kruskal-Wallis test comes in, as used by researchers at Stanford University, Massachusetts Institute of Technology, and University of Oxford. This test is also related to the Mann-Whitney U test, which is used to compare two groups, and has been applied in studies by World Health Organization, National Science Foundation, and European Union. The Kruskal-Wallis test has been widely used in various fields, including Sociology, Anthropology, and Geography, by researchers like Émile Durkheim, Karl Marx, and Charles Darwin. The test has also been used in Business and Finance to compare the performance of different companies, such as Apple Inc., Google, and Amazon (company).

The Kruskal-Wallis test involves ranking the data from all groups together, and then comparing the median ranks of each group, a method used by researchers at University of Cambridge, University of Chicago, and Columbia University. The test statistic is calculated using the formula, which is similar to the Wilcoxon Rank-Sum Test used by researchers at University of California, Los Angeles, New York University, and University of Michigan. The test is often performed using statistical software, such as R (programming language), Python (programming language), or SAS Institute, which are widely used by researchers at National Bureau of Economic Research, Brookings Institution, and RAND Corporation. The Kruskal-Wallis test has been applied in studies by United Nations, World Bank, and International Monetary Fund.

The Kruskal-Wallis test assumes that the data is independent and identically distributed, and that the groups are mutually exclusive, assumptions also made by Regression Analysis and Time Series Analysis used by researchers at London School of Economics, University of Tokyo, and Australian National University. The test also assumes that the data is at least ordinal, meaning that the data can be ranked, a requirement also made by Non-Parametric Statistics and Survival Analysis used by researchers at University of Pennsylvania, Duke University, and University of Southern California. However, the test does not assume that the data follows a specific distribution, such as the Normal Distribution assumed by Parametric Statistics used by researchers at California Institute of Technology, Princeton University, and Brown University. The Kruskal-Wallis test has been used in studies by American Statistical Association, Institute of Mathematical Statistics, and International Statistical Institute.

The Kruskal-Wallis test produces a test statistic, which is compared to a critical value or a p-value, similar to the T-Test and Analysis of Variance (ANOVA) used by researchers at University of Illinois at Urbana-Champaign, University of Wisconsin-Madison, and University of Minnesota. If the p-value is below a certain significance level, such as 0.05, the null hypothesis is rejected, and it is concluded that at least one of the groups is significantly different from the others, a conclusion also drawn by Hypothesis Testing and Confidence Intervals used by researchers at University of Washington, University of Texas at Austin, and University of North Carolina at Chapel Hill. The Kruskal-Wallis test has been applied in studies by National Academy of Sciences, American Academy of Arts and Sciences, and Royal Society.

The Kruskal-Wallis test has been used in various studies, such as comparing the Gross Domestic Product (GDP) of different countries, like United States, China, and Japan, or comparing the Life Expectancy of different populations, such as Japan, Singapore, and Iceland. The test has also been used in Medical Research to compare the effectiveness of different treatments, such as Chemotherapy and Radiation Therapy, used by researchers at Memorial Sloan Kettering Cancer Center, MD Anderson Cancer Center, and National Cancer Institute. The Kruskal-Wallis test has been applied in studies by Centers for Disease Control and Prevention, World Health Organization, and European Centre for Disease Prevention and Control.

The Kruskal-Wallis test is related to other non-parametric tests, such as the Mann-Whitney U test and the Wilcoxon Signed-Rank Test used by researchers at University of Edinburgh, University of Manchester, and University of Bristol. The test is also related to Parametric Tests, such as the One-Way ANOVA and the T-Test, used by researchers at University of California, San Diego, University of Florida, and University of Georgia. The Kruskal-Wallis test has been used in conjunction with other statistical methods, such as Regression Analysis and Time Series Analysis, used by researchers at Federal Reserve, International Monetary Fund, and World Bank. The test has been applied in studies by American Economic Association, Econometric Society, and Royal Economic Society. Category:Statistical tests