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Are 'mixed effects' and 'random effects' moderator analyses (meta regression and ANOVAs) used interchangeably? Lipsey and Wilson in 'Practical meta analysis' seem to describe 'mixed effects meta regression' as what others called 'random effects meta regression' and random effects models as having an unexplainable 'random' component alongside the variance due to standard error, in which case you wouldn't do moderator analysis at all as by its nature it is saying there are no observable systematic differences to try and understand?

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The term mixed-effects is usually used for a meta-analysis with a moderator or moderators. Since the underlying model is likely to ave been a random effects meta-analysis it is understandable that some people call this a random effects moderator analysis although I have not seen the term myself. It is perfectly possible to have more variability between studies than can be accounted for my the moderator(s) so your last statement is a bit hard to support.

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