On the subject in the title: Random versus fixed effects: choosing rather than defaulting — a second dataset Working notes rather than a conclusion.
Posting a small dataset on Random versus fixed effects. It is mine, it is uncontrolled, and the method is stated so it can be discounted appropriately.
What I would like is not agreement but a second dataset collected by someone with no stake in mine. If one exists I would rather read it than argue for this one.
Answering the question the opening post raises rather than the one it answers.
Fixed-effect and random-effects models answer different questions. The first assumes one true effect; the second assumes a distribution of them. Choosing between them is an assumption, not a technicality.
Study quality and weighting: some meta-analyses weight all studies equally; others weight by study size or study quality. The choice affects the result and should be stated and justified.
Filing this under things that are true until someone shows me otherwise.
Adding the measurement that post #2 says would settle it.
If you are new and reading this thread for the answer to Random versus fixed effects: the answer is conditional, the conditions are in the third reply, and the rest of the thread is worth skipping.
High heterogeneity is the finding rather than a nuisance to be minimised. If the effect genuinely differs across settings, an average of those settings is an average of things that should not have been averaged.
I would treat that as a working assumption and revisit it.
I had written a reply contradicting post #4 and deleted it. Here is what survived.
Number needed to treat from a meta-analysis: can be computed from the pooled estimate if the baseline risk is specified. More interpretable than pooled relative effects.
Double extraction with disagreement resolution is standard and is worth checking for, because single extraction errors are common and non-random.
Noting that the question and the thing people usually mean by it are different.
The claim about Random versus fixed effects upthread is stronger than its source supports. I have read the source. The source says "associated with" and the post says "causes".
The documentation on Random versus fixed effects is better than this thread and I say that as someone who has posted in the thread.
The reason Random versus fixed effects is hard to answer is that the obvious measurement and the relevant quantity are not the same thing, and substituting one for the other is silent.
Double extraction with disagreement resolution is standard and is worth checking for, because single extraction errors are common and non-random.
I have kept the units in throughout, for the obvious reason.
Answering the question post #15 raises rather than the one it answers.
Individual participant data pooling is a much stronger design than aggregate pooling and is rare because it requires cooperation rather than a search.
Small point, but it is the one that usually catches people.
The arithmetic in post #15 is right; the assumption feeding it is the part to check.
My understanding of Random versus fixed effects is a few years old and may have been superseded. If it has been, I would genuinely like to know rather than keep repeating it.
Worth separating two things that post #15 runs together.
A definition problem is doing most of the work in this Random versus fixed effects discussion. Once the term is pinned down I suspect the disagreement mostly goes away and what is left is small.
This is the sort of exchange that makes the archive worth searching.
Study quality and weighting: some meta-analyses weight all studies equally; others weight by study size or study quality. The choice affects the result and should be stated and justified.
If anyone has run this properly I would rather read that than my own guess.
I have no financial interest in anything named in this thread and I want to say so before I comment on Random versus fixed effects, because it is the sort of subject where it matters.
Fair, and the limits you put on it are the part I will remember.
I had written a reply contradicting post #22 and deleted it. Here is what survived.
Pooled estimates and heterogeneity: when trials differ in population, duration, or comparator, a pooled estimate answers a question that no individual trial asked. High heterogeneity means effects genuinely differ across studies. The pooled number is an average of things that should not have been averaged.
If someone has run Random versus fixed effects properly I would rather read that than my own reconstruction of it. Posting mine only because the thread has gone quiet.
Post #24 is the version of this I will quote in future. One addition.
Taking Random versus fixed effects seriously for a moment rather than deflecting: the honest position is that the community has observations and no controlled comparison, and those two things support very different sentences.
Fixed-effects versus random-effects models: fixed-effects assumes all studies are estimating the same thing and variation is sampling error. Random-effects assumes studies are estimating effects from different distributions and allows between-study variance. Choice matters if heterogeneity is high.
On balance I think that is right, and I would not bet much on it.
Answering the question post #26 raises rather than the one it answers.
Summarising the Random versus fixed effects thread so far, since it is long and the answer is buried: the first reply has the method, the fourth has the correction to it, and the rest is people agreeing at length.