Second pass at: Absence of evidence and evidence of absence

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

P-values and significance: p<0.05 means the data would be surprising if the null hypothesis were true, not that the null hypothesis is false. A non-significant p-value does not mean "no effect".

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.

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.

Worth separating two things that post #15 runs together.

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.

post #19 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.

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.

Picking up post #20: that is the part I would want checked first.

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.

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.

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.

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.

This follows post #24 rather than contradicting it.

P-values and significance: p<0.05 means the data would be surprising if the null hypothesis were true, not that the null hypothesis is false. A non-significant p-value does not mean "no effect".

I read post #26 twice before replying, because I had assumed the opposite.

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.

post #28 answers the question as asked. The question underneath it is different.

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.

On post #26 — agreed on the reasoning, with one qualification.

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.