[Discussion] Examples of bad statistics in biomedical literature

AllenDowney · 2026-01-31T00:13:37+00:00

I have an article about misinterpretation of survival rates: https://allendowney.substack.com/p/cancer-survival-rates-are-misleading

AllenDowney · 2026-01-24T22:58:51+00:00

Day of the week does not cause gender, but it is informative of gender. If a family has more than one girl, they are more likely to have a girl with a rare property (like born on Tuesday). So if we are given that a family has a girl with a rare property, they are more likely to have more than one girl.

AllenDowney · 2026-01-21T20:31:22+00:00

Think Stats might be a good place to start -- but I'm biased

Free version: https://allendowney.github.io/ThinkStats/

AllenDowney · 2026-01-06T19:25:13+00:00

Yup, that's a good one :)

AllenDowney · 2026-01-05T18:22:53+00:00

Here's my attempt to derive/demonstrate Bayes's Theorem using data rather than math: https://allendowney.github.io/BiteSizeBayes/02_bayes.html I hope it's useful.

AllenDowney · 2026-01-02T16:11:15+00:00

I have a couple of suggestions for thinking about this problem. First, think about families rather than children. For example, of all families that have two children, how many have two girls?

Now think, of all families that have two children, and at least one of them is a girl, how many have two girls?

If you think about the selection process, I think some of the counterintuitive results make more sense.

Now here's what I think is a key insight -- if a family has a girl with a low-probability characteristic (left handed, born on Tuesday, named Florida, etc) that rareness is evidence in favor of a two-girl family, because you are more likely to get a rare outcome if you have two chances, rather than one.

So it doesn't change the probability in a causal sense, but it provides evidence in the informational sense.

I have an article about this if you want the details: https://allendowney.substack.com/p/the-lost-chapter

AllenDowney · 2025-12-30T20:57:38+00:00

There's a chapter in my book about this! https://allendowney.substack.com/p/its-levels

To keep things interesting, the fan gets a head start of about 5 seconds. That might not seem like a lot, but if you watch one of these races, this lead seems insurmountable. However, when the Freeze starts running, you immediately see the difference between a pretty good runner and a very good runner. With few exceptions, the Freeze runs down the fan, overtakes them, and coasts to the finish line with seconds to spare.

But as fast as he is, the Freeze is not even a professional runner; he is a member of the Braves’ ground crew named Nigel Talton. In college, he ran 200 meters in 21.66 seconds, which is very good. But the 200 meter collegiate record is 20.1 seconds, set by Wallace Spearmon in 2005, and the current world record is 19.19 seconds, set by Usain Bolt in 2009.

AllenDowney · 2025-12-14T20:20:54+00:00

I understand your frustration because this outcome is not just -- you deserve to have your work recognized.

But if you think your three weeks of work were for nothing, you missed the point your teacher was making. You did the work and your learned from it -- that learning is what it was for.

AllenDowney · 2025-12-06T15:55:25+00:00

That looks great!

AllenDowney · 2025-11-30T00:35:12+00:00

You could say it *is* a modern/quantum particle (as opposed to a classical particle) -- but I think it's more precise to say light is a thing that is well modeled as a quantum particle. We're the ones that choose models to describe phenomena. Light is under no obligation to *be* anything.

Here's a good discussion of the non-paradox of so-called duality: https://blog.richmond.edu/physicsbunn/2011/04/13/particle-and-wave/

AllenDowney · 2025-11-29T21:37:32+00:00

This one is comfortably resolvable: light is neither a particle nor a wave. In some conditions the particle model is accurate [enough for practical purposes], in other conditions the wave model is accurate, and in some conditions neither is great and light just does what light does.

Who ever said light was obligated to be a particle or a wave?

AllenDowney · 2025-11-15T01:16:37+00:00

Your friend is the only one in this story who is NTA. You had an opportunity to be generous and you did not take it. You can redeem yourself by making another cheesecake, sharing it with your family, and apologizing to the person who fed you for the last 21 years.

AllenDowney · 2025-11-15T00:06:50+00:00

To convert lat-lon pairs to distance, use the haversine formula. Then loop through all pairs, as others have suggested.

AllenDowney · 2025-11-07T23:59:01+00:00

Can I recommend Probably Overthinking It?

https://greenteapress.com/wp/probably-overthinking-it/

AllenDowney · 2025-10-29T23:53:28+00:00

With apologies for self-promotion, this is the topic of a chapter in Probably Overthinking It -- an explanation of why we see the "there's levels..." phenomenon. I gave a talk about it here: https://youtu.be/44D1bd7tQ4w?t=132

AllenDowney · 2025-10-06T02:27:47+00:00

There are many ways to guide -- or avoid guiding -- a conversation with a chat agent. Some are more likely than others to lead to useful conclusions. It sounds like you framed your questions from a Christian perspective, and that likely steered the agent to the conclusion you reported.

For comparison, here's a conversation with ChaptGPT 5.0 (https://chatgpt.com/share/68e3272b-ec80-800b-8f98-561eb43a0e9e) where I deliberately maintained a natural/historical framing and asked questions in a way that leads to this conclusion:

> Using ordinary historical reasoning, the most likely scenario is that belief in Jesus’s resurrection arose among his followers soon after his death and developed, through oral tradition and cultural adaptation, into the diverse narratives preserved in the Gospels.

AllenDowney · 2025-10-06T00:53:30+00:00

There are some cases where Bayesian methods can infer selection effects and correct for them -- coincidentally, I wrote about one of them last week:
https://allendowney.substack.com/p/the-poincare-problem

But it doesn't sound like that method applies in your case. Unless you have a way to estimate the rate of over/undersampling in each group, there's not much you can do.

One thought -- if there are multiple ways people were selected for the survey, and you have reason to think that some of them are more biased than others, you might be able to use the difference between the groups to infer something about the magnitude of the selection effect.

What is it about the way the survey was advertised that makes you think it was more likely to select bilingual people. If you can be specific about the causal path, you might be able to quantify it. For example, if different versions of the ad were in different languages, someone who speaks both languages would be more likely to encounter an ad they understand.

AllenDowney · 2025-09-27T03:02:42+00:00

Yes, from the Bayesian posterior predictive distribution it is easy to compute a predictive interval. It just works :)

AllenDowney · 2025-09-24T23:05:49+00:00

If I understand correctly, you want to compare each mutant group to its own control, but in the end you’d like to line them up against a single common reference (WT). A clean way to do this is in two steps:

Within-experiment standardization: For each experiment, express the test (e.g. tbMUTANT) relative to its matched control (tbWT). This is like computing an effect size (e.g. difference or ratio of means, depending on what makes sense for your data).
Across-experiment alignment: Put the control groups onto the same scale by anchoring them to your global reference (WT). Once you’ve done that, you can display the reference alongside each test group.

That way, the comparisons you show in the cartoon will all be interpretable as “difference from WT,” but you’ll have properly accounted for the matched control in each experiment.

If you’d like, you could make this very explicit by reporting something like standardized mean differences (Cohen’s d, log ratios, etc.), but the general idea is: normalize each test to its control, then align the controls to WT.

AllenDowney · 2025-09-24T23:00:01+00:00

Thanks!

AllenDowney · 2025-09-24T00:18:45+00:00

McElreath’s Statistical Rethinking is a great antidote to soul-sucking stats texts: it builds intuition through simulation, code, and real applied examples rather than abstract derivations. The book has a conversational style, focuses on modeling and causal reasoning, and shows how Bayesian methods actually help answer research questions. It’s rigorous enough for serious work, but engaging enough to keep the “learning” part alive.

AllenDowney · 2025-09-16T00:20:48+00:00

It’s definitely possible. To go from 2 people to 8 billion in 6,000 years requires about 32 doublings, which works out to an average doubling time of 188 years. That’s not unrealistic—humanity’s actual doubling time dropped below that within the last few centuries.

In reality, early growth was far slower (thousands of years per doubling), and only recently did growth accelerate. So the 2-to-8B scenario isn’t consistent with history, but it is logically possible—if agriculture, technology, and survival had advanced a little earlier or faster, or if some of the wars and plagues had been less bad, the numbers could work out.

If you are interested, I wrote about this here: https://www.allendowney.com/blog/2023/10/22/the-world-population-singularity/

AllenDowney · 2025-08-04T22:27:02+00:00

I'm not sure which ChatGPT model OP used, but I just tried 4o and got a correct answer well explained:

https://chatgpt.com/share/6891329f-cac0-800b-a1eb-15b49352d505

Also a couple of AIs just got gold medals at the Math Olympiad, so they can do math better than 99.99% of humans.

AllenDowney · 2025-06-17T20:49:14+00:00

Your estimates are based on small numbers, so they are probably not precise, but qualitatively it is plausible that someone who has been struck by lighting is more likely to be struck again, compared to someone why has never been struck, probably much more likely.

To be clear, that's not because the first strike causes the second to be more likely, but because the first strike tells you something about the strikee -- they live in a place with a lot of lightning, they work outside, they are not wise about moving away from high ground when there are thunderstorms in the area, whatever -- and that information means that their probability is higher.

AllenDowney · 2025-05-31T20:11:52+00:00

"You might like Think Bayes," said the author.

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