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Glen_b
Glen_b
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The derivation of the Mann Whitney assumes continuous data. When you have heavier-tailed than normal data, it's also typically more powerful than the t-test; if you assume only location shift alternatives, it's a test of difference in means;means (along with any other reasonable location measure); if that doesn't hold, it's testing something else.

That said, the t-test can tolerate moderate skewness and heavy-tailedness (though in the latter case your actual significance levels will tend to be lower than the nominal $\alpha$).

There's also the possibility of a permutation test rather than either of the choices you mention - it would allow you to test a difference in means and have it be valid when the assumptions of the t-test are not satisfied.

Another possibility if you think that some exponential family distribution might suit better (such as a gamma distribution) would be to fit a GLM with a group factor representing the groups whose means you are comparing. An identity link will even give you a direct estimate of the difference in means.

The derivation of the Mann Whitney assumes continuous data. When you have heavier-tailed than normal data, it's also typically more powerful than the t-test; if you assume only location shift alternatives, it's a test of difference in means; if that doesn't hold, it's testing something else.

That said, the t-test can tolerate moderate skewness and heavy-tailedness (though in the latter case your actual significance levels will tend to be lower than the nominal $\alpha$.

There's also the possibility of a permutation test rather than either of the choices you mention - it would allow you to test a difference in means and have it be valid when the assumptions of the t-test are not satisfied.

Another possibility if you think that some exponential family distribution might suit better (such as a gamma distribution) would be to fit a GLM with a group factor representing the groups whose means you are comparing. An identity link will even give you a direct estimate of the difference in means.

The derivation of the Mann Whitney assumes continuous data. When you have heavier-tailed than normal data, it's also typically more powerful than the t-test; if you assume only location shift alternatives, it's a test of difference in means (along with any other reasonable location measure); if that doesn't hold, it's testing something else.

That said, the t-test can tolerate moderate skewness and heavy-tailedness (though in the latter case your actual significance levels will tend to be lower than the nominal $\alpha$).

There's also the possibility of a permutation test rather than either of the choices you mention - it would allow you to test a difference in means and have it be valid when the assumptions of the t-test are not satisfied.

Another possibility if you think that some exponential family distribution might suit better (such as a gamma distribution) would be to fit a GLM with a group factor representing the groups whose means you are comparing. An identity link will even give you a direct estimate of the difference in means.

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Glen_b
Glen_b
  • 290.5k
  • 37
  • 652
  • 1.1k

The derivation of the Mann Whitney assumes continuous data. When you have heavier-tailed than normal data, it's also typically more powerful than the t-test; if you assume only location shift alternatives, it's a test of difference in means; if that doesn't hold, it's testing something else.

That said, the t-test can tolerate moderate skewness and heavy-tailedness (though in the latter case your actual significance levels will tend to be lower than the nominal $\alpha$.

There's also the possibility of a permutation test rather than either of the choices you mention - it would allow you to test a difference in means and have it be valid when the assumptions of the t-test are not satisfied.

Another possibility if you think that some exponential family distribution might suit better (such as a gamma distribution) would be to fit a GLM with a group factor representing the groups whose means you are comparing. An identity link will even give you a direct estimate of the difference in means.