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Wilcox in his package WRS in R software managed to provide easily accessible robust techniques to conduct usual hypothesis testing like t-test, ANOVA etc.

I've two questions:

  1. Which is the preferred style: To use robust tests all the time without worrying about data distribution; or to check first the assumptions and decide to use robust or usual methods.

  2. How to report using robust methods in a scientific paper?

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    $\begingroup$ Rand Wilcox has invented numerous robust techniques. I don't know of any that have become in any sense standard in any field. None of the other texts on robust statistics that I've seen seems to quote his work extensively. More generally, note that your first sentence and your two questions are best kept separate. $\endgroup$ – Nick Cox Feb 12 '16 at 12:50
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For the first question, usually, in my experience, people use robust methods only when there is a reason to do so. I can see at least three reasons for this:

  1. They may not know about robust methods
  2. Robust methods are often less powerful when the assumptions are met
  3. Robust methods are less familiar and sometimes harder to explain

For the second question, you can report the test statistic, its df and its p-value together with some measure of the effect size. The particular test statistic and measure of effect size will depend on the particular method you are using.

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    $\begingroup$ This is an enormous topic and you'd agree that much. much more could be said. I'd add that just transforming the data and/or using a different model are often simpler, positive solutions. $\endgroup$ – Nick Cox Feb 12 '16 at 12:56
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    $\begingroup$ Sure, I'd agree with that. Entire books could be and have been written on this sort of thing. My own view is that data transformations should, in general, be done for substantive reasons. But I am a big fan of e.g. quantile regression, which makes very few assumptions. $\endgroup$ – Peter Flom - Reinstate Monica Feb 12 '16 at 13:07
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    $\begingroup$ The substantive reason for (e.g.) logarithmic transformation is that nature, or society, or whatever often behaves multiplicatively! But I suspect we'd agree on many more marginal cases: many ad hoc uses of transformations don't help much. Another thing to add is that robust statistics, for all the interest of its central problems and the ingenuity of its practitioners, is not obviously converging on agreed solutions. Wait a few years, and some quite different robust regression method appears to be in favour. (There are plenty of really good reasons why this is so.) $\endgroup$ – Nick Cox Feb 12 '16 at 13:13
  • $\begingroup$ I agree completely. And, in the two packages I use (R and SAS) I've seen problems. In R, the usual multiplicity of packages/methods is a big problem. How is the user to know which is best, or best for particular issues? And in SAS, I've found some issues with how the output is presented. That is one more reason I like quantile regression - it's a solved problem. $\endgroup$ – Peter Flom - Reinstate Monica Feb 12 '16 at 13:22

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