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."

Decisions are not evidence

The thinking that lead to this post began with trying to write something about what Kline (2013) calls the filter myth. The filter myth is the arguably - in the sense that it depends on who you ask - mistaken belief in NHST practice that the p-value discriminates between effects that are due to chance (null-hypothesis not rejected) and those that are real (null-hypothesis rejected). The question is whether decisions to reject or not reject can serve as evidence for the existence of an effect.

Reading about the filter myth made me wonder whether NHST can be viewed as a screening test (diagnostic test), much like those used in medical practice. The basic idea is that if the screening test for a particular condition gives a positive result, follow-up medical research will be undertaken to figure out whether that condition is actually present. (We can immediately see, by the way, that this metaphor does not really apply to NHST, because the presumed detection of the effect is almost never followed up by trying to figure out whether the effect actually exists, but the detection itself is, unlike the screening test, taken as evidence that the effect really exists; this is simply the filter myth in action).