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It is recommended that exact p-values be used for all of the distribution-free methods mentioned in this section whenever possible many commonly used statistical packages are able to produce only approximate p-values for distribution-free methods. (1998) were apparently unaware of this fact when they applied the K–W test to both the original and log-transformed data and obtained “virtually identical results” (p. One interesting feature of any distribution-free test based on ranks (of which the M–W–W and K–W tests are examples) is that applying a monotonic transformation (such as the logarithm) to the data does not affect the results of the analysis. It can also be shown that H has an approximate χ 2( k−1) distribution under the null hypothesis. The exact distribution of H can be obtained using a permutation argument and is available in StatXact and the NPAR1WAY procedure in SAS. If there are no ties, and (1/ c) H, where c is given by Eq. Name the sizes of the several samples n 1, n 2, …, n k n is the grand total 3.Ĭombine the data, keeping track of the sample from which each datum arose 4.Īdd the ranks from each sample separately, naming the sums T 1, T 2, …, T k 6.Ĭalculate the Kruskal–Wallis H statistic, which is distributed as chi-square, by Name the number of samples k (3 or 4 or …) 2.
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The chi-square approximation is valid only if there are five or more members in each sample. For practical purposes, the user may think of it informally as testing whether the several distributions have the same median. The hypothesis being tested is whether or not the value for a randomly chosen member of one sample is probably smaller than one of another sample. It is used when rank-order data arise naturally in three or more groups or if the assumptions underlying the one-way analysis of variance test are not satisfied. Methodologically, the Kruskal–Wallis test is just the rank-sum test extended to three or more samples. Changes in weight and blood pressure between Month 2 and Month 6 were measured. Patients were then followed for four additional months. Patients were followed initially for two months, and the baseline value was the blood pressure reading at the end of the two-month period. Patients already receiving medication were randomly assigned to Groups II or III. Group I consisted of patients who were not taking any antihypertensive medication and who were placed on a weight reduction program Group II patients were also placed on a weight reduction program in addition to continuing their antihypertensive medication and Group III patients simply continued with their antihypertensive medication. The patients either were not taking any medication or were on medication that had not reduced their blood pressure below 140 mmHg systolic or 90 mmHg diastolic. Patients in the study all weighed at least 10 percent above their ideal weight, and all were hypertensive. A study examined the effect of weight loss without salt restriction on blood pressure in overweight hypertensive patients ( Reisin et al. We first introduce a data situation appropriate for this test. The hypothesis being tested by the KW statistic is that all the medians are equal to one another, and the alternative hypothesis is that the medians are not all equal.
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The KW test also requires that the data come from continuous probability distributions. This method, the Kruskal-Wallis (KW) test, a generalization of the Wilcoxon test, is named after the two prominent American statisticians who developed it in 1952. In this section, a method for the comparison of the locations (medians) from two or more populations is presented. The Wilcoxon Rank Sum test is limited to the consideration of two populations. Mike Hernandez, in Biostatistics (Second Edition), 2007 9.5 The Kruskal-Wallis Test Moreover, it also assumed that the observations are independent and identically distributed.Ronald N. The Student's t-test and the z-test are parametric testsīoth the Student's t-test and the z-test are said to be parametric as their use requires the assumption that the samples are distributed normally. Use the z-test when the true variance σ² of the population is known. Use the Student's t-test when the true variance of the population from which the sample has been extracted is not known the variance of sample s² is used as variance estimator. Two parametric tests are possible but they should be used on certain conditions: The Student's t-test When to use the Student's t-test or the z-test This tool is used to compare the average of a sample represented by µ with a reference value.
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XLSTAT - One sample t and z tests Principle of the one-sample t- and z-tests