It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.

The quotes

Here’s one: “You have no choice but to accept that the major conclusions of these studies are true.”

Ahhhh, but we do have a choice!

First, the background. We have two quotes from this paper by E. J. Wagenmakers, Ruud Wetzels, Denny Borsboom, Rogier Kievit, and Han van der Maas.

Here’s Alan Turing in 1950:

I assume that the reader is familiar with the idea of extra-sensory perception, and the meaning of the four items of it, viz. telepathy, clairvoyance, precognition and psycho-kinesis. These disturbing phenomena seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming.

Wow! Overwhelming evidence isn’t what it used to be.

In all seriousness, it’s interesting that Turing, who was in some ways an expert on statistical evidence, was fooled in this way. After all, even those psychologists who currently believe in ESP would not, I think, hold that the evidence for telepathy as of 1950 was overwhelming. I say this because it does not seem so easy for researchers to demonstrate ESP using the protocols of the 1940s; instead there is continuing effort to come up with new designs

How could Turing have thought this? I don’t know much about Turing but it does seem, when reading old-time literature, that belief in the supernatural was pretty common back then, lots of mention of ghosts etc. And at an intuitive level there does seem, at least to me, an intuitive appeal to the idea that if we just concentrate hard enough, we can read minds, move objects, etc. Also, remember that, as of 1950, the discovery and popularization of quantum mechanics was not so far in the past. Given all the counterintuitive features of quantum physics and radioactivity, it does not seem at all unreasonable that there could be some new phenomena out there to be discovered. Things feel a bit different in 2014 after several decades of merely incremental improvements in physics.

To move things forward a few decades, Wagenmakers et al. mention “the phenomenon of social priming, where a subtle cognitive or emotional manipulation influences overt behavior. The prototypical example is the elderly walking study from Bargh, Chen, and Burrows (1996); in the priming phase of this study, students were either confronted with neutral words or with words that are related to the concept of the elderly (e.g., ‘Florida’, ‘bingo’). The results showed that the students’ walking speed was slower after having been primed with the elderly-related words.”

They then pop out this 2011 quote from Daniel Kahneman:

When I describe priming studies to audiences, the reaction is often disbelief . . . The idea you should focus on, however, is that disbelief is not an option. The results are not made up, nor are they statistical flukes. You have no choice but to accept that the major conclusions of these studies are true.

And that brings us to the beginning of this post, and my response: No, you don’t have to accept that the major conclusions of these studies are true. Wagenmakers et al. note, “At the 2014 APS annual meeting in San Francisco, however, Hal Pashler presented a long series of failed replications of social priming studies, conducted together with Christine Harris, the upshot of which was that disbelief does in fact remain an option.”

Where did Turing and Kahneman go wrong?

Overstating the strength of empirical evidence. How does that happen? As Eric Loken and I discuss in our Garden of Forking Paths article (echoing earlier work by Simmons, Nelson, and Simonsohn), statistically significant comparisons are not hard to come by, even by researchers who are not actively fishing through the data.

The other issue is that when any real effects are almost certainly tiny (as in ESP, or social priming, or various other bank-shot behavioral effects such as ovulation and voting), statistically significant patterns can be systematically misleading (as John Carlin and I discuss here).

Still and all, it’s striking to see brilliant people such as Turing and Kahneman making this mistake. Especially Kahneman, given that he and Tversky wrote the following in a famous paper:

People have erroneous intuitions about the laws of chance. In particular, they regard a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics. The prevalence of the belief and its unfortunate consequences for psvchological research are illustrated by the responses of professional psychologists to a questionnaire concerning research decisions.

Indeed.

Having an open mind

It’s good to have an open mind. Psychology journals publish articles on ESP and social priming, even though these may seem implausible, because implausible things sometimes are true.

It’s good to have an open mind. When a striking result appears in the dataset, it’s possible that this result does not represent an enduring truth or even a pattern in the general population but rather is just an artifact of a particular small and noisy dataset.

One frustration I’ve had in recent discussions regarding controversial research is the seeming unwillingness of researchers to entertain the possibility that their published findings are just noise. Maybe not, maybe these are real effects being discovered, but you should at least consider the possibility that you’re chasing noise. Despite what Turing and Kahneman say, you can keep an open mind.

P.S. Some commenters thought that I was disparaging Alan Turing and Daniel Kahneman. I wasn’t. Turing and Kahneman both made big contributions to science, almost certainly much bigger than anything I will ever do. And I’m not criticizing them for believing in ESP and social priming. What I am criticizing them for is their insistence that the evidence is “overwhelming” and that the rest of us “have no choice” but to accept these hypotheses. Both Turing and Kahneman, great as they are, overstated the strength of the statistical evidence.

And that’s interesting. When stupid people make a mistake, that’s no big deal. But when brilliant people make a mistake, it’s worth noting.