The Anatidae Principle

If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family Anatidae on our hands.
- Douglas Adams

I like to teach my students how they can apply to their data-analysis what I call the Anatidae Principle (or the Principle of the Duck). (The name is obviously inspired by the above quote from Douglas Adam's Dirk Gently's Holistic Detective Agency).

For the purpose of data-analysis, the Anatidae Principle simply boils down to the following: If it looks like you found a relation, difference, or effect in your sample you should at least consider the possibility that there indeed is a relation, difference or effect. That is, look at your data, summarize, make figures, and think (hard) about what your data potentially mean for the answer to your research question, hypotheses, hunches, whatever you like. Do this before you start calculating p-values, confidence intervals, Bayes Factors, Posterior distributions, etc., etc.

In my experience, researchers too often violate the Anatidae Principle: they calculate a p-value, and if it is not significant they simply ignore their sample results. Never mind that, as they predicted, group A  outperforms group B, if it is not significant, they will claim they found no effect. And, worse still, believe it.

Kline (2013) ) (p. 117) gives solid advice:

"Null hypothesis rejections do not imply substantive significance, so researchers need other frames of reference to explain to their audiences why the results are interesting or important. A start is to learn to describe your results without mention of statistical significance at all. In its place, refer to descriptive statistics and effect sizes and explain why those effect sizes matter in a particular context. Doing so may seem odd at first, but you should understand that statistical tests are not generally necessary to detect meaningful or noteworthy effects, which should be obvious to visual inspection of relatively simple kinds of graphical displays (Cohen, 1994). The description of results at a level closer to the data may also help researchers to develop better communication skills."

Planning with assurance, with assurance

Planning for precision requires that we choose a target Margin of Error (MoE; see this post for an introduction to the basic concepts) and a value for assurance, the probability that MoE will not exceed our target MoE.  What your exact target MoE will be depends on your research goals, of course.

Cumming and Calin-Jageman (2017, p. 277) propose a strategy for determining target MoE. You can use this strategy if your research goal is to provide strong evidence that the effect size is non-zero. The strategy is to divide the expected value of the difference by two, and to use that result as your target MoE.

Let's restrict our attention to the comparison of two means. If the expected difference between the two means is Cohens's d = .80, the proposed strategy is to set your target MoE at f = .40, which means that your target MoE is set at .40 standard deviations. If you plan for this value of target MoE with 80% assurance, the recommended sample size is n = 55 participants per group. These results are guaranteed to be true, if it is known for a fact that Cohen's d is .80 and all statistical assumptions apply.

But it is generally not known for a fact that Cohen's d has a particular value and so we need to answer a non-trivial question: what effect size can we reasonably expect? And, how can we have assurance that the MoE will not exceed half the unknown true effect size? One of the many options we have for answering this question is to conduct a pilot study, estimate the plausible values of the effect size and use these values for sample size planning.  I will describe a strategy that basically mirrors the sample size planning for power approach described by Anderson, Kelley, and Maxwell (2017).

The procedure is as follows. In order to plan with approximately 80% assurance, estimate on the basis of your pilot the 80% confidence interval for the population effect size and use half the value of the lower limit for sample size planning with 90% assurance. This will give you 81% assurance that assurance MoE is no larger than half the unknown true effect size.