Lindley’s Paradox
Article
Lindley’s Paradox is a recurring concept in the Astral Codex Ten archive, appearing 2 times across 2 issues between May 10, 2024 and May 29, 2024. The archive places it in contexts such as “Cremieux brought up a concern about Lindley’s Paradox”; “good discussion of Lindley’s Paradox”. It most often appears alongside FDA, Hanson, Twitter.
Metadata
- Category: Concepts
- Mention count: 2
- Issue count: 2
- First seen: May 10, 2024
- Last seen: May 29, 2024
Appears In
Related Pages
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- FDA (2 shared issues)
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- Hanson (2 shared issues)
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- Twitter (2 shared issues)
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- United Kingdom (2 shared issues)
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- United States (2 shared issues)
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- “Most Drugs Are Bad For You” (1 shared issues)
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- 1123581321 (1 shared issues)
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- @ElytraMithra (1 shared issues)
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- Aaron (1 shared issues)
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- ACX (1 shared issues)
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- Adderall (1 shared issues)
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- AI (1 shared issues)
External Links
Source Context
Recovered passages from the original issue text. When the raw archive preserved outbound links inside the source passage, they are listed directly under the quote.
I don't think it's a good general rule to say that just because you have a very large sample and a moderate p-value, you shouldn't reject the null hypothesis. On Lindley's Paradox, I'm not an expert but my understanding is that there's not really a paradox, it's just that a bayesian and frequentist approach are asking different questions, and whether you prefer the null hypothesis vs the alternative hypothesis can depend on your prior. More generally, even with millions of observations, it is very difficult to find statistically precise differences in mortality because mortality is such a rare event, and because the letters we sent didn't convince everyone in our treatment group to buy health insurance, and some of the people in the control group who did not receive a letter still chose to buy health insurance on their own. So it's not like one should automatically assume that any large sample size would generate a miniscule p-value if the null hypothesis was incorrect.
Cremieux brought up a concern about Lindley’s Paradox:
Inline links: Lindley’s Paradox
20: Related: good discussion of Lindley’s Paradox in the comments of the Hanson/medicine post, from Limelihood and Radford Neal. My understand: the paradox only causes problems if you assume the true effect is quite likely to be zero. Then if you get an effect of (let’s say) 0.1, you think “nah, it’s probably just zero with some noise”. This is a hackish way of representing the idea of “the null hypothesis”. But since the effect of health insurance is probably not exactly zero (it probably comes from some benefit of good treatments, minus some cost of bad treatments) we probably don’t have to worry. I might be explaining it wrong, read the comments.
Inline links: Limelihood, Radford Neal