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Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. You know that the two

Significance tests
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asked 2021-06-30
Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. You know that the two distributions of the variable under consideration have the same shape and may be normal. You take the two samples and find that the data for one of the samples contain outliers. Which procedure would you use? Explain your answer.

Answers (1)

2021-07-01
Pooled t-test: both normal and equal population standard deviation (thus same shape)
Nonpooled t-test: both normal and unequal population standard deviations (thus not the same shape)
Mann-Whitney: same shape but not normal.
Thus it is best to use the Mann-Whitney test (and it is also resistant to outliers).
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