Measurement error in home scales, with a worked standard deviation — the long version posts 91–106

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.

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".

Coming back to post #91, because the follow-up matters more than the original answer.

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.

Picking up post #91: that is the part I would want checked first.

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.

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.

This follows post #95 rather than contradicting it.

Thank you for the correction. I have edited my earlier post with a note rather than silently, so the thread still makes sense to read. The error was mine and it was the kind that comes from remembering a figure instead of looking it up.

On post #95 — agreed on the reasoning, with one qualification.

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.

post #99 answers the question as asked. The question underneath it is different.

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 #99, because the follow-up matters more than the original answer.

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.

Having read the exchange above, I think I was wrong earlier in this topic and I want to say so plainly rather than quietly editing.

The correction was fair and I had been repeating something I had not checked carefully enough.

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.