Question

Suppose that you want to perform a hypothesis test to compare several population means, using independent samples. In each case, decide whether you wo

Normal distributions
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asked 2021-06-04
Suppose that you want to perform a hypothesis test to compare several population means, using independent samples. In each case, decide whether you would use the one-way ANOVA test, the Kruskal-Wallis test, or neither of these tests. Preliminary data analyses of the samples suggest that the distributions of the variable are not normal and have quite different shapes.

Expert Answers (1)

2021-06-05
When the distributions of the variable are approximately normal and have equal standard deviations, then it is most appropriate to use the one-way ANOVA test (although you could also use the Kruskal-Wallis test).
When the distributions of the variable are not approximately normal but do have approximately the same shape, then it is most appropriate to use the Kruskal-Wallis test.
When the distributions of the variable do not have approximately the same shape, then it is not appropriate to use either of the test.
In this case, the distributions of the variable do not have approximately the same shape and thus it is appropriate to use neither test.
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