This is a continuation of a long topic, addressed by post number rather than by page. Start at post 1 · go to the accepted answer.
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.
On post #29 — agreed on the reasoning, with one qualification.
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.
post #33 answers the question as asked. The question underneath it is different.
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.
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.
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".
Worth separating two things that post #33 runs together.
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.
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.
Coming back to post #37, because the follow-up matters more than the original answer.
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.
Picking up post #37: that is the part I would want checked first.
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.
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.
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.
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 #40 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.
Picking up post #42: 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.
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.
This follows post #46 rather than contradicting it.
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 #48 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.
I read post #51 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.
This follows post #51 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".
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.
post #55 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.
Coming back to post #55, because the follow-up matters more than the original answer.
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.
Worth separating two things that post #55 runs together.
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.
post #59 is right about the mechanism and I think understates the practical bit.
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.