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Comment by whimsicalism | Hacker News Reader

I feel like a lot of these critiques are just straw-manning p-values consideration.

Consider effect sizes - this seems to be a completely different (yes important) question. Obviously the magnitude of the impact of the drug is important - but it isn't a replacement or "something to look at instead of p-value" because the chance that the results you saw are due to random variation is still important! You can see a massive effect size but if that is totally expected within your null model, then it is probably not all that exciting!

Effect sizes are a complement to some sort of hypothesis testing, but they are not a replacement.

> Prior probability.

yes, when you can effectively encode your prior probability I would say the posterior probability of seeing what you did is at least as good as p-value.

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I agree that you shouldn't look only at effect sizes any more than you should look only at p-values. (What I would actually prefer you to do, where you can figure out a good way to do it, is to compute a posterior probability distribution and look at the whole distribution. Then you can look at its mean or median or mode or something to get a point estimate of effect size, you can look at how much of the distribution is > 0 to get something a bit like a p-value but arguably more useful, etc.

If anything I wrote appeared to be saying "just look at effect size, it's the only thing that matters" then that was an error on my part. I definitely didn't intend to say that.

But I was responding to an article saying "p<0.05 considered harmful" that never mentions effect sizes at all. I think that's enough to demonstrate that, in context, "it's bad to look at p-values and ignore effect sizes" is not in fact a straw man.

Incidentally, I am not convinced that the p-value as such is often a good way to assess how likely it is that your results are due to random chance. Suppose you see an effect size of 1 unit with p=0.05. OK, so there's a 5% chance of getting these results if the true effect size is zero. But you should also care what the chance is of getting these results if the true effect size is +0.1. (Maybe the distribution of errors is really weird and these results are very likely with a positive but much smaller effect size; then you have good evidence against the null hypothesis but very weak evidence for an effect size of the magnitude you measured.) In fact, what you really want to know is what the probability is for every possible effect size, because that gives you the likelihood ratios you can use to decide how likely you think any given effect size is after seeing the results. For sure, having the p-value is better than having nothing, but if you were going to pick one statistic to know in addition to (say) a point estimate of the effect size, it's not at all clear that the p-value is what you should choose.

Fair enough, I don’t disagree with anything you just said.

It would be cool if interfaces caught up so I could just draw a basic estimate of my prior and then see the posterior graph afterwards.

What I have discovered after working in medicine for pretty long is that many biologists and MDs think p-values are a measure of effect sizes. Even a reviewer from Nature thought that, which is incredibly disturbing.

p-values were created to facilitate rigorous inference with minimal computation, which was the norm during the first half of the 20th century. For those who work on a frequentist framework, inference should be done using a likelihood-based approach plus model selection, e.g. AIC. It's makes it much harder to lie.

AIC is an estimate of prediction error. I would caution against using it for selecting a model for the purpose of inference of e.g. population parameters from some dataset (without producing some additional justification that this is a sensible thing to do). Also, uncertainty quantification after data-dependent model selection can be tricky.

Best practice (as I understand it) is to fix the model ahead of time, before seeing the data, if possible (as in a randomized controlled trial of a new medicine, etc.).

And it is not uncommon that an intentionally bad model (low AIC) will be used for inference on a parameter when one wants to test the robustness of the parameter to covariates.

You can always encode the prior. If you take the frequentist approach and ignore bayesian concepts, it’s the same as just going bayesian but with an “uninformative prior” (constant distribution).

The only question is… would you rather be up front and explicit about your assumptions, or not?

An uninformative prior is an assumption, even if it’s the one that doesn’t bias the posterior (note that here “bias” is not a bad word).

There is potentially bias (of the bad word variant) introduced by the mismatch between the prior in your own mind and the distribution and params you choose to try to approximate that, especially if you're trying to pick out a distribution with a nice posterior conjugate.

I'm also not sure why everyone perceived my comment as anti-bayesian.

I did not perceive your comment as anti-bayesian, or at least not necessarily so! :)

But are you sure you know what I meant when I said “uninformative prior”? Because choosing an uninformative prior does not involve choosing any parameters: there is only one uninformative prior, and it’s the constant (flat) distribution which assigns equal probability to every value. It encodes no information and does not bias the posterior or result. It is the one and only mathematically-neutral prior. You can think of it as being a bit like an “identity function”.

Depending on the hypothesis space what you call the "uninformative prior" does not exist in the frequentist approach. If you search for a real value, then the uninformative prior is a uniform distribution on the infinite line. This distribution does not normalize and is off-limits to bayesians.

Ultimately, I think you are strawmanning frequentism here. Just because the log likelihood is sometimes the same as the map does not imply that they have the same meaning. This is why computed uncertainties of both approaches are often not the same and have a not-so-subtle difference in their interpretation. The one computes uncertainty in belief, the other imprecision of an experiment. You can't summarize that with "do you want to be explicit about assumptions".

Nobody normalizes an uninformative prior on its own. Normalization only happens when you get your posterior.

I am not straw-manning anything: bayesian methods are a generalization of frequentist methods. The equality / isomorphism to frequentist methods, in the special case of the uninformative prior, is commonly demonstrated in introductory (undergrad-level) bayesian textbooks and is in fact trivial. One need not even talk of any infinities: if you’re doing discrete observations, infinities never show up (and in that case the prior normalizes just fine). And if you’re curve-fitting (ie.: using parametric methods), the “infinite” line goes away as soon as you multiply your uninformative prior with your likelihood.

Indeed.

Ive worked with clinical trials and nobody says “oh, p < 0.05 so we should use this drug”.

Doctors do a much more sophisticated deep dive into the data and statistical significance is maybe 1 of a 10 factors they consider.

And hell, even if it is statistically significant, doctors may not use a drug for many other reasons.

It seems like the people who criticize p-values aren't that familiar with how they are actually used.

Yeah and it's super simple to roll significance and effect sizes in one with confidence (or credible) intervals.

Plus the interpretation is super straight forward: CI contains zero: Not significant. If nothing else, we should make CIs the primary default instead of p-values.

If you're not encoding your prior probability, you're just making stuff up. You almost always have some information, even if it's just sanity bounds.

Trying to fit your preconception into a mathematically convenient conjugate distribution is not as far afield from making stuff up as people want to believe. Maybe it is better with numerical approaches.

But yes, you usually do have some information and it is net better to encode when possible.

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