Correlation in a self-tracked dataset: what it can support posts 151–167

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 #151 answers the question as asked. The question underneath it is different.

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.

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.

For anyone arriving from a search: the marked solution above is the direct answer, and the replies underneath it add the caveats that make it safe to use.

Worth separating two things that post #151 runs together.

Two things before anyone answers the substance.

First, the context in the first post is clear and specific. Second, the question is framed so that an answer can actually address it. Both are the norm here and both matter more than they sound.

post #155 is right about the mechanism and I think understates the practical bit.

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.

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.

On post #155 — agreed on the reasoning, with one qualification.

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.

For anyone arriving from a search: the marked solution above is the direct answer, and the replies underneath it add the caveats that make it safe to use.

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.

I read post #162 twice before replying, because I had assumed the opposite.

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.