Why one randomization does not a successful experiment make

Based on a PsyArXiv preprint with the admittedly slightly provocative title “Why most experiments in psychology failed: sample sizes required for randomization to generate equivalent groups as a partial solution to the replication crisis” a modest debate erupted on Facebook (see here; you need to be in the PsychMAP group to access the link, though) and Twitter (see here, here, and here) regarding randomization.

John Myles White was nice enough to produce a blog post with an example of why Covariate-Based Diagnostics for Randomized Experiments are Often Misleading (check out his blog; he has other nice entries, e.g. about why you should always report confidence intervals over point estimates).

I completely agree with the example he provides (except that where he says ‘large, finite population of N people’ I assume he means ‘large, finite sample of N people drawn from an infinite population’). This is what puzzled me about the whole discussion. I agreed with (almost all) arguments provided; but only a minority of the arguments seemed to concern the paper. So either I’m still missing something, or, as Matt Moehr ventured, we’re talking about different things.

So, hoping to get to the bottom of this, I’ll also provide an example. It probably won’t be as fancy as John’s example, but I have to work with what I have 🙂

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On the obsession with being normal

In statistics, one of the first distributions that one learns about is usually the normal distribution. Not only because it’s pretty, also because it’s ubiquitous.

In addition, the normal distribution is often the reference that is used when discussion other distributions: right skewed is skewed to the right  compared to the normal distribution; when looking at kurtosis, a leptokurtic distribution is relatively spiky compared to the normal distribution: and unimodality is considered the norm, too.

There exist quantitative representations of skewness, kurtosis, and modality (the dip test), and each of these can be tested against a null hypothesis, where the null hypothesis is (almost) always that the skewness, kurtosis, or dip test value of the distribution is equal to that of a normal distribution.

In addition, some statistical tests require that the sampling distribution of the relevant statistic is approximately normal (e.g. the t-test), and some require an even more elusive assumption called multivariate normality.

Perhaps all these bit of knowledge mesh together in people’s minds, or perhaps there’s another explanation: but for some reason, many researchers and almost all students operate on the assumption that their data have to be normally distributed. If they are not, they often resort to, for example, converting their data into categorical variables or transforming the data.

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Why one-sided tests in psychology are practically indefensible

This post is a response to a post by Daniel Lakens, “One-sided tests: Efficient and Underused“, whom I greatly respect and, apparently up until now, always vehemently agreed with. So this post is partly an opportunity for him and others to explain where I’m wrong, so dear reader, if you would take this time to point that out, I would be most grateful. Alternatively, telling me I’m right is also very much appreciated of course 🙂 In any case, if you haven’t done so yet, please read Daniel’s post first (also, see below this post for an update with more links and the origin of this discussion).

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