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Shen-yi Liao

Very interesting! I'll email you for the full paper.

I want to ask about one comment in the post:

"This means studies that only looking at “averaged” responses are probably not worth doing—they create strange fictions. Most bimodal/multi-modal distributions are poorly approximated with unimodal models".

I am not sure whether the criticism here is just statistical or deeply theoretical.

Before running any tests, we should certainly check whether the normality assumption is met.

It is true that parametric tests assume normal distribution, but a fair number of them are robust under wide variety of circumstances. (Though, as usual, there are debates about this amongst statisticians.) With each individual study, we can dispute whether the test used is sufficiently robust even though the normality assumption is violated. But I am not sure how that translates to a general criticism of studies that use parametric tests (and, in particular, studies that look at averaged responses).

And, as I'm sure you know, there are plenty of nonparametric tests that can detect differences between samples. So if the aim of a statistical test in the experiment is null-hypothesis-testing a manipulation, then nonparametric tests can do the job too in many cases.

So, in the end, I'm not sure whether the comment is just calling for: (a) checking normality assumption, (b) checking a parametric test's robustness, or (c) using nonparametric tests... or is there some deeper theoretical criticism that I'm missing?

Dan Jones

Sounds like a great paper, Adam. I think I've got access to it - but, if not, expect an email!

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3QD Prize 2012: Wesley Buckwalter