# Shape the Science to the Statistics, Not the Statistics to the Science

In theatre, and more generally in writing, the advice is always to “show, don’t tell”. You could just tell your audience that Long John Silver is a ruthless pirate, but it works a lot better to show him marching a prisoner off the plank. Rather than just informing with words, you want to make things as concrete as possible, with actions.

There is a similar rule in pedagogy. Pedagogy courses teach you to be explicit about your goals, planning a course by writing down Intended Learning Outcomes. (They never seem amused when I ask about the Unintended Learning Outcomes.) At first, you’d want to write down outcomes like “students will understand calculus” or “students will know what a sine is”. These, however, are hard to judge, and thus hard to plan around. Instead, the advice is to write outcomes that correspond to actions you want the students to take, things you want them to be capable of doing: “students can perform integration by parts” “students can decide correctly whether to use a sine or cosine”. Again and again, the best way to get the students to know something is to get them to do something.

Jay Daigle recently finished a series of blog posts on how scientists use statistics to test hypotheses. I recommend it, it’s a great introduction to the concepts scientists use to reason about data, as well as a discussion of how they often misuse those concepts and what they can do better. I have a bit of a different perspective on one of the “takeaways” of the post, and I wanted to highlight that here.

The center of Daigle’s point is a tool, widely used in science, called Neyman-Pearson Hypothesis Testing. Neyman-Pearson is a tool for making decisions involving a threshold for significance: a number that scientists often call a p-value. If you follow the procedure, only acting when you find a p-value below 0.05, then you will only be wrong 5% of the time: specifically, that will be your rate of false positives, the percent of the time you conclude some action works when it really doesn’t.

A core problem, from Daigle’s perspective, is that scientists use Neyman-Pearson for the wrong purpose. Neyman-Pearson is a tool for making decisions, not a test that tells you whether or not a specific claim is true. It tells you “on average, if I approve drugs when their p-value is below 0.05, only 5% of them will fail”. That’s great if you can estimate how bad it is to deny a drug that should be approved, how bad it is to approve a drug that should be denied, and calculate out on average how often you can afford to be wrong. It doesn’t tell you anything about the specific drug, though. It doesn’t tell you “every drug with a p-value below 0.05 works”. It certainly doesn’t tell you “a drug with a p-value of 0.051 almost works” or “a drug with a p-value of 0.001 definitely works”. It just doesn’t give you that information.

In later posts, Daigle suggests better tools, which he argues map better to what scientists want to do, as well as general ways scientists can do better. Section 4. in particular focuses on the idea that one thing scientists need to do is ask better questions. He uses a specific example from cognitive psychology, a study that tests whether describing someone’s face makes you worse at recognizing it later. That’s a clear scientific question, one that can be tested statistically. That doesn’t mean it’s a good question, though. Daigle points out that questions like this have a problem: it isn’t clear what the result actually tells us.

Here’s another example of the same problem. In grad school, I knew a lot of social psychologists. One was researching a phenomenon called extended contact. Extended contact is meant to be a foil to another phenomenon called direct contact, both having to do with our views of other groups. In direct contact, making a friend from another group makes you view that whole group better. In extended contact, making a friend who has a friend from another group makes you view the other group better.

The social psychologist was looking into a concrete-sounding question: which of these phenomena, direct or extended contact, is stronger?

At first, that seems like it has the same problem as Daigle’s example. Suppose one of these effects is larger: what does that mean? Why do we care?

Well, one answer is that these aren’t just phenomena: they’re interventions. If you know one phenomenon is stronger than another, you can use that to persuade people to be more accepting of other groups. The psychologist’s advisor even had a procedure to make people feel like they made a new friend. Armed with that, it’s definitely useful to know whether extended contact or direct contact is better: whichever one is stronger is the one you want to use!

You do need some “theory” behind this, of course. You need to believe that, if a phenomenon is stronger in your psychology lab, it will be stronger wherever you try to apply it in the real world. It probably won’t be stronger every single time, so you need some notion of how much stronger it needs to be. That in turn means you need to estimate costs: what it costs if you pick the weaker one instead, how much money you’re wasting or harm you’re doing.

You’ll notice this is sounding a lot like the requirements I described earlier, for Neyman-Pearson. That’s not accident: as you try to make your science more and more clearly defined, it will get closer and closer to a procedure to make a decision, and that’s exactly what Neyman-Pearson is good for.

So in the end I’m quite a bit more supportive of Neyman-Pearson than Daigle is. That doesn’t mean it isn’t being used wrong: most scientists are using it wrong. Instead of calculating a p-value each time they make a decision, they do it at the end of a paper, misinterpreting it as evidence that one thing or another is “true”. But I think that what these scientists need to do is not chance their statistics, but change their science. If they focused their science on making concrete decisions, they would actually be justified in using Neyman-Pearson…and their science would get a lot better in the process.