Second pass at: Regression to the mean in progress reports

post #14 is right about the mechanism and I think understates the practical bit.

I disagree with the reply above, and I think the disagreement is substantive rather than terminological.

The distinction being drawn does not survive when you look at the published data for this specific question. I would be glad to be shown wrong on this, because the version I am arguing against is more convenient.

Multiplicity and multiple comparisons: if you test many hypotheses, the chance of finding a false positive by random chance increases. That is why pre-specifying the primary hypothesis matters.

Power and sample size: a study might be too small to detect a real effect (low power). Sample size calculations help determine how many participants are needed to detect an effect of a given magnitude.

I read post #16 twice before replying, because I had assumed the opposite.

Effect sizes: the magnitude of a difference, not just whether it is statistically significant. A difference that is significant (p<0.05) might be too small to matter. A large effect might not be significant if sample size is small.

Absence of evidence and evidence of absence: if a study is small and finds no effect, that is absence of evidence, not evidence of absence. A larger study might find an effect that a small study missed.

Number needed to treat: how many people need to be treated to prevent one bad outcome or achieve one good outcome. More intuitive than relative risk reduction.

Regression to the mean: if you select people with extreme values (very high or very low), their next measurement is often less extreme just by chance. This can look like a treatment effect when it is just statistics.

post #21 is right about the mechanism and I think understates the practical bit.

I disagree with the reply above, and I think the disagreement is substantive rather than terminological.

The distinction being drawn does not survive when you look at the published data for this specific question. I would be glad to be shown wrong on this, because the version I am arguing against is more convenient.

I read post #21 twice before replying, because I had assumed the opposite.

Relative risk and odds ratios: both compare the rate in one group to the rate in another. Relative risk is easier to understand. Odds ratios are standard in many analyses but can be misinterpreted.

Confounding: a third variable explains an apparent association. In randomised data, randomisation balances confounders. In observational data, confounders can be adjusted for but unknown ones cannot.

Practical note that does not fit anywhere else. Whatever you conclude from this topic, write down what you did and when. The single most useful thing in your own records is not any individual result; it is that they are dated and consecutive.

Confidence intervals: rather than a single point estimate, a range of plausible values. A narrow interval means precise measurement; a wide interval means measurement is imprecise. Wider intervals (more uncertainty) are honest about limitation.

Coming back to post #25, because the follow-up matters more than the original answer.

Multiplicity and multiple comparisons: if you test many hypotheses, the chance of finding a false positive by random chance increases. That is why pre-specifying the primary hypothesis matters.

Picking up post #25: that is the part I would want checked first.

Confidence intervals: rather than a single point estimate, a range of plausible values. A narrow interval means precise measurement; a wide interval means measurement is imprecise. Wider intervals (more uncertainty) are honest about limitation.

Effect sizes: the magnitude of a difference, not just whether it is statistically significant. A difference that is significant (p<0.05) might be too small to matter. A large effect might not be significant if sample size is small.

Power and sample size: a study might be too small to detect a real effect (low power). Sample size calculations help determine how many participants are needed to detect an effect of a given magnitude.