Don’t Change The p-value Threshold

Personally, I think the proposal to ‘change’ the p-value for significant results from .05 to .005 is a mistake. The only sense in which this proposal has any real bite is if journals and hiring committees respond by treating research that doesn’t meet p < .005 as less important but all that does is make the incentives for the kind of behavior causing all the problems much stronger.

I’d much rather have a well designed (ideally pre-registered) trial at p < .05 than a p < .005 result that is cherry picked as a result of after the fact choice of analysis. Rather than making the distinction between well designed appropriate methodology and dangerous potentially misleading methodology more apparent this further obscures it and tells any scientist who was standing on principle they need to stop hoping their better methodology will be appreciated and do something to compete on p-value with papers published using problematic data analysis.

In particular, I think this kind of proposal doesn’t take sufficient account of the economics and incentives of researchers. Yes, p < .005 studies would be more convincing but they also cost more (both in $ and time) so by telling fledgling researchers they need p < .005 you force them to put all their eggs in one basket making dubious data analysis choices that much more tempting when their study fails to meet the threshold.

What we need is more results blind publication processes (in which journals publish the results based merely on a description of the experimental process without knowledge of what the results found). That would both help combat many of these biases and truly evaluate researchers on their ability not their luck. Ideally such studies would be pre-accepted before results were actually analyzed. Of course there still needs to be a place for merely suggestive work that invites further research but it should be regarded as such without any particular importance assigned to p-value.

However, as these are only my brief immediate thoughts I’m quite open to potential counterarguments.

Rejecting Rationality

I felt I would use this first post to explain this blog’s title. It is not, despite appearances to the contrary, meant to suggest any animosity toward the rationality community nor sympathy with the idea that when evaluating claims we should ever favor emotions and intuition over argumentation and evidence. Rather, it is intended as a critique of the ambiguous overuse of the term `rationality’ by the rationality community in general (and Yudkowsky specifically).

I want to suggest that there are two different concepts we use the word rationality to describe and that the rationality community overuses the term in a way that invites confusion. Both conceptions of rationality are judgements of epistemic virtue but the nature of that virtue differs.

Rationality As Ideal Evaluation Of Evidence

The first conception of rationality reflects the classic idea that rationality is a matter of a priori theoretical insight. This makes intuitive sense as rationality, in telling us how we should respond to evidence, shouldn’t depend on the particular way the evidence turns out. On this conception rationality constrains how one reaches judgements from arbitrary data and something is rational just if we expect it to maximize true beliefs in the face of a completely unknown/unspecified fact pattern1. In other words this is the kind of rationality you want if you are suddenly flung into another universe where the natural laws, number of dimensions or even the correspondence between mental and physical states might differ radically from our own.

On this conception having logically coherent beliefs and obeying the axioms of probability can be said to be rationally required (as doing so never forces you to belief less truths) but it’s hard to make a case for much else. Carnap (among others) suggested at one point that there might be something like a rationally (in this sense) preferable way of assigning priors but the long history of failed attempts and conceptual arguments suggests this isn’t possible.

Note that on this conception of rationality it is perfectly appropriate to criticize a belief forming method for how it might perform if faced with some other set of circumstances. For instance, we could appropriately criticize the rule: never believe in ghosts/psychics on the grounds that it would have lead us to the wrong conclusions in a world where these things were real.

Rationality As Heuristic

The second conception of rationality is simpler. Rationality is what will lead human beings like us to true beliefs in this world. Thus, this notion of rationality can take into account things that happen to be true. For instance, consider the rule that when asked a question on a math test (written by humans in the usual circumstances) that calls for a numerical answer you should judge that 0 is the most probable answer. This rule is almost certainly truth-conducive but only because it happens to be true that human psychology tends to favor asking questions whose answer is 0.

Now a heuristic like this might, at first, seem pretty distant from the kind of things we usually mean by rationality but think about some of the rules that are frequently said to be rationally required/favored. For instance, one should steelman2 your opponents arguments, try to consider the issue in the most dispassionate way you can manage and you should break up complex/important events.

For instance, suppose that humans were psychologically disposed to be overly deferential so it was far more common to underestimate the strength of your argument than it was to underestimate your opponent’s argument. In this case steelmanning would make us even more likely to reach the wrong conclusions not less. Similarly, our emotions could have reflected useful information available to our subconscious minds but not our concuss minds in such a way that they provided a good guide to truth. In such a world trying to reach probability judgements via dispassionate consideration wouldn’t be truth conducive.

Thus, on this conception of rationality whether or not a belief forming method is rational depends only on how well it does in the actual world.

The Problematic Ambiguity

Unfortunately, when people in the rationality community talk about rationality they tend to blur these two concepts together. That is they advocate belief forming mechanisms that could only be said to be rational in the heuristic sense but assume that they can determine matters of rationality purely by contemplation without empirical evidence.

For instance, consider these remarks by Yudkowsky or this lesswrong post. Whether or not they come out and assert it they convey the impression that there is some higher discipline or lifestyle of rationality which goes far beyond simply not engaging in logical contradiction or violating probability axioms. Yet they seem to assume that we can determine what is/isn’t rational by pure conceptual analysis rather than empirical validation.

This issue is even more clear when we criticize others for the ways they form beliefs. For instance, we are inclined to say that people who adopt the rule ‘believe what my community tells me is true’ or ‘believe god exists/doesn’t exist regardless of evidence’ are being irrational since such rules would yield incorrect results if they had been born in a community with crazy beliefs or in a universe with/without deities. Yet, as I observed above the very rules we take to be core rational virtues have the very same property.

The upshot of this isn’t that we should give up on finding good heuristics for truth. Not at all. Rather, I’m merely suggesting we take more care, especially in criticizing other people’s belief forming methods, to ensure we are applying coherent standards.

A Third Way

One might hope that there was yet another concept of rationality that someone split the difference of the two I provided here. A notion that allows us to take into account things like our psychological makeup or seemingly basic (if contingent) properties our universe has, e.g., we experience it as predictable rather than being an orderless succession of experiential states, but doesn’t let us build in facts like Yeti’s don’t exist into supposedly rational belief forming mechanisms. Frankly, I’m skeptical that any such coherent notion can be articulated but don’t currently have a compelling argument for that claim.

Finally, I’d like to end by pointing out there is another issue we should be aware of regarding the term rationality (though hardly unique to it). That is rationality is ultimately a property of belief forming rules while in the actual world what we get is instances of belief formation and some vague intentions about how we will form beliefs in the future. Thus there is the constant temptation to simply find some belief forming rule that qualifies as sufficiently rational and use it to justify this instance of our belief. However, it’s not generally valid to infer that you are forming beliefs appropriately just because each belief you form agrees with some sufficiently rational (in the heuristic sense) belief forming mechanism.

For instance, suppose there are a 100 different decent heuristics for forming a certain kind of belief. We know that each one is imperfect and gets different cases wrong but any attempt to come up with a better rule doesn’t yield anything humans (with our limited brains) can usefully apply. It is entirely plausible that almost any particular belief of this kind matches up with 1 of these 100 different heuristics thus allowing you to always cite a justification for your belief even though you underperform every single one of these heuristics.



  1. I’m glossing over the question of whether there is a distinction between an arbitrary possible world and a `random’ possible world. For instance, suppose that some belief forming rule is true in all but finitely many possible worlds (out of some hugely uncountable set of possible worlds). That rule is not authorized in an arbitrary possible world (choose the counterexample world and it leads to falsehood) but intuitively it seems justified and any non-trivial probability measure (i.e. one that doesn’t concentrate on any finite set of worlds) on the space of possible worlds would assign probability 1 to the validity of the belief forming procedure. However, this won’t be an issue in this discussion. 
  2. The opposite of strawmannirg. Rendering your opponents argument in the strongest fashion possible.