The Statistician's Fallacy

Essentially all scientific fields rely heavily on statistics.

This is true in a technical sense but misses a crucial distinction. Hard sciences (basically physics and its relatives), are far less vulnerable to statistical pitfalls because practitioners in those fields have the ability to generate effectively unlimited quantities of data by simply repeating experiments as many times as necessary. This makes statistical reasoning largely irrelevant: in the limit of infinite data, you don't need to do Bayesian updates because the weight of the prior is insignificant compared to the weight of the observations. Rutherford, for example, did not bother to state a prior probability for the plum pudding model of the atom compared to the planetary model; he just amassed a bunch of experimental data, and showed that the plum pudding model could not explain it. This large-data-generation ability of physics is largely why that field has succeeded in spite of continuing debates and confusion about the fundamentals of statistical philosophy. Researchers in fields like economics, nutrition, and medicine simply cannot obtain data on the same scale that physicists can.

Thank you for taking our ability to dismiss experts we don't like up one meta-level.

The professor had a background in statistics, and as far as I could tell knew her stuff in that area (though she dismissed Bayesianism in favor of orthodox statistics).

Bayesians will realize that, since there's a good chance that of happening even when the conclusion is correct and well- supported by the evidence, finding mistakes in the statistics is only weak evidence that the conclusion is wrong.

Wow, lesswrong, you just never fail to do this at every opportunity. Bayesianity is not a minority view anymore. Bayesians do not have a monopoly on correct reasoning with probabilities. Seriously, knock it off, please.

The professor had a background in statistics

Do you have a background in statistics, Chris?

edit: One of the areas I am working on is "causal discovery," which is learning the structure of graphs from observational data. One problem I have worked on a lot is causal discovery in the presence of hidden variables. It turns out there is a very interesting statistical model that recovers all independence constraints that a hidden variable DAG imposes on the observed margin. It also turns out that there is a way to write down the likelihood for this model in the case of discrete state spaces, while doing the same for continuous state spaces is currently unknown. This suggests that a search and score method (e.g. Bayesian method, or at least a method with a Bayesian justification) is natural for the discrete case, while a method based on hypothesis testing (e.g. a frequentist method, although Bayesian versions are possible here, they are less satisfactory because there is no global posterior) is natural for the continuous case. After all, we can't very well figure out what the posterior is if we can't even write the likelihood down.

Did the above paragraph make sense to you? These are the kinds of consideration people have in mind when thinking about B vs F. If you aren't working in ML/stats I am not sure what the point even is of having an opinion on this topic, other than "belief as attire."

It's completely bizarre. Somehow when it comes to B vs F, LW is willing to tell experts what they should be doing in their area of expertise.

Microwaves are almost certainly safe, but just FYI, the point about there being 'no plausible mechanism' is wrong, and a common misconception. Photons don't need to have enough energy to directly cause DNA breakage, in order to be dangerous. Microwaves seem have effects on proteins beyond that caused by thermal excitation, which means they could plausibly be carcinogenic, e.g. if they interfere with DNA repair enzymes. There's some evidence that pumping enough microwaves at cells in culture can turn them cancerous.

The epidemiological evidence though, is that they don't cause cancer.

http://www.ncbi.nlm.nih.gov/pubmed/11088227

But when a solid majority of the experts agree on a conclusion, and you see flaws in their statistics, I think the default assumption should be that they still know the issue better than you and very likely the sum total of the available evidence does support the conclusion, even if the specific statistical arguments youv'e seen from them are wrong.

Experts have perverse incentives to overstate the value of their expertise. An academic paper concluding "the tools of our profession are more powerful than we thought because...." is much more likely to get published than one concluding the reverse. The flaws you see in expert opinions might mostly be pushing the conclusions in the direction that makes the experts' advice seem more important.

Because of political correctness in academia, you can't much generalize from how academics treat IQ to how we handle most other topics.

Excellent article. Another example of how the skill of arguing, whether it involves verbal eloquence or math/stats literacy, doesn't help and often actually harms the skill of changing your mind.

Aside: I can no longer read about cancer and cell phones without thinking of this and bursting out laughing.

So if you go scrutinizing their papers, there's a good chance you'll find clear mistakes in their stats, and an even better chance you'll find arguable ones.

Call it the statistician's fallacy: thinking that finding a mistake in the statistics is sufficient grounds to dismiss a finding.

I've observed something similar in regard to conspiracies, specifically JFK and 9/11. There are, of course, mistakes in the official commission reports... because they are huge reports with tons of detailed stuff to potentially get wrong. Enter the Conspiracy Theorist, who will insist these mistakes are strong evidence that the official story is wrong. They often cite experts in physics, ballistics, aeronautics, acoustics, etc. who state some aspect of the official report is not supported by science. And it just snowballs into the strangest stuff...

I'd say this sort of "missing the forest for the trees" reasoning is very common, evidenced by the healthy percentage of people who believe in grand conspiracies surrounding these two events. I think there are psychological reasons people end up believing in conspiracies -- and keep believing in them despite all the evidence -- but It seems well-supported conclusions get discarded by lots of people due to some faulty reasoning based on some tiny mistake, and this is how conspiracy thinking might often get started.

Call it the statistician's fallacy: thinking that finding a mistake in the statistics is sufficient grounds to dismiss a finding.

I love it. (I'm a statistician by trade.)

A field taken as a whole usually musters multiple lines of evidence.

Bayesians will realize that, since there's a good chance that of happening even when the conclusion is correct and well-supported by the evidence, finding mistakes in the statistics is only weak evidence that the conclusion is wrong.

I'm not sure why you think this conclusion is particularly Bayesian.

she dismissed Bayesianism in favor of orthodox statistics

You mean frequentism right? Then just say so. At this point Bayesianism is so widespead and so many statisticians use in practice both frequentist and Bayesian techniques such using frequentism as intechangeable with "orthodox" seems off.

One hypothesis is that most science is mostly coming up with decent hypotheses via unbiased human intuition about already-well-understood mechanisms, or in less fortunate cases via social/political/rent-seeking necessity; the testing the hypothesis part is usually very easy to the point where the statistics are superfluous, or it's very hard to the point where statistics are grant-justifyingly rigorous-looking but woefully lacking in power. Thus by the time you're actually looking at the statistics they can be good or bad or point one way or the other and it really doesn't matter much, what matters is the intelligent-person-unbiased-apolitical-common-sense-appraised plausibility of the hypothesis and the epistemological soundness of the methodology. Edit: Daniel Burfoot's comment jibes well with this one.

Not defending the conclusions of his article, but Shalizi does address at least one of the points you say he doesn't. In the section titled "How to make 2766 independent abilities look like one g factor" he explains why he's not impressed by correlations between performance on different tests. I don't know enough to properly judge the quality of his argument, but it is there.

It would be fair to shout a warning about correspondance bias before inferring anything from these cases.

Spelling nitpick: correspondence.

Going a little farther.

If you say you've proved hypothesis H, but you don't do the statistics right, then that means there's some possibility E, distinct from H, that can account for your results. I call it E because it's the possibility in which the conclusion is an error.

Therefore, disbelieving the study is the same as believing E. But E might be just as unlikely as H, which is something you've got to consider before rejecting the study.

It gets even worse for you if they've got 10 studies confirming H, with decorrelated error. What that means is that H accounts for all of them (that's why they're all studies confirming H), and the "decorrelated error" part means there's no single possibility E in which all their bad statistical analyses would fail. Instead, there's E1, E2, E3...

At that point, the chance that E1 through E10 are all true is way less likely than H.

This is part of why different kinds of evidence are important: to decorrelate the error in imperfect analyses.

An example: the criticism that a conclusion H is based on studies of WEIRD subjects (Western, Educated, Industrialized, Rich, and Democratic) is serious, because it's a single circumstance E that accounts for all the studies. The errors are correlated. However, you've still got to consider, is the hypothesis E, "H is true for WEIRD people", more likely than what the scientists believe, that H is true for everybody? Disbelieving the conclusion because the subjects are WEIRD still commits you to a pretty specific belief.

Essentially all scientific fields rely heavily on statistics.

What does this mean?
If they need statistics to reach the truth, then undermining the statistics is a very big deal.

I can see only a few possibilities:

1. They really need statistics, but they are making random errors in their statistics and getting random results. The field is worthless.

2. They are reaching the correct conclusions through non-statistical scientific methods and the statistics is window-dressing. (or perhaps they real method is statistical, but much simpler and more robust than they claim)

3. They are reaching wrong conclusions through unspecified wrong methods and the statistics is window dressing. (How can you distinguish this from the previous?)

4. The leaders of the field do correct statistics and reach the correct conclusions. Everyone else copies their conclusions and messes up the statistics. It should be easy to find the leaders and check their statistics.