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Fixed effects model seems to differ from random effects model for a meta-analysis of sample correlations in terms of assumptions. What is key assumption for a fixed effect model?

marked as duplicate by amoeba, mdewey, Peter Flom Jan 31 at 13:17

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    I am having difficulties to understand your question. Why does your title refer to "multivariate ANOVA" but your question not? You might want to give more details and then we might be able to answer your question. – Bernd Weiss Jun 14 '12 at 12:19
  • I edited the title to ensure that the question makes sense. – Jeromy Anglim Jun 15 '12 at 3:54
  • Subhash, you've asked several vague questions and some that require significant amounts of clarification after you've already received an answer that appears to fully address the question as originally stated (e.g. this question). Also, the general content of this question (as originally stated) has been discussed on this site, as in the link I posted above. Perhaps you would benefit from consulting the section of the FAQ on how to ask questions as constructively as possible: stats.stackexchange.com/questions/how-to-ask – Macro Jul 9 '12 at 14:02
  • The question is a little different because the OP is asking only in the context of meta-analysis problems. Although that probably has no affect on the definitions. – Michael Chernick Jul 9 '12 at 14:17
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    Thanks @subhashdavar, my suggestion is as much to help you get useful answers as it is to help others find your questions (and the subsequent answers) useful in the future. Welcome to the site, by the way! – Macro Jul 9 '12 at 16:14
up vote 7 down vote accepted

In a fixed-effects model, you are assuming that the true correlation estimated in each study is the same. In the Random effects model you accept that there is variation in the true correlation being estimate in each study.

Thus, the fixed-effects model assumes that observed variation in estimated correlations is due only to effect of random sampling.

It deciding between the two, you would often use a combination of theoretical knowledge and observed data. Theory will often suggest that the true correlation should vary somewhat between studies. You can also examine various test statistics on the observed correlations to assess whether the variation appears more than you would expect based on random sampling (e.g., see this discussion about Cochran's Q and related indices).

  • Thanks. I am interested in a clear understandig of the assumptions in the context of ANOVA.It seems we have an assumption in ANOVA and same in case of meta-analyis of sample-correlations. The assumption of random scores at primary level generates a fixed r value for a study. The random distribution of scores rules out the effects of several moderator and or extraneous factors on the r-value of a particular study.That is the reason, we get a fixed quantity for r and there is no possibility of a range of values for r everytime you work on a sample. – Subhash C. Davar Jun 22 '12 at 3:14
  • @subhashdavar It sounds like you may have a separate question in that comment. I suggest asking a new question and perhaps including a link to this one. – Jeromy Anglim Jun 22 '12 at 3:35
  • My suggestion is that you press "ask question" and write up a separate question. You are more likely to get an answer to your question. – Jeromy Anglim Jun 22 '12 at 4:53
  1. Fixed-effect model

This model assumes that there is one true effect size; which underlies all the studies in the analysis, and that all differences in observed effects are due to sampling error. While we follow the practice of calling this a fixed-effect model, a more descriptive term would be a common-effect model. In either case, we use the singular (effect) since there is only one true effect.

  1. Random-effects model

Under this random-effects model we allow that the true effect could vary from study to study. For example, the effect size might be higher or lower in studies. Because studies will differ in the mixes of participants and in the implementations of interventions, among other reasons, there may be different effect sizes underlying different studies. If it were possible to perform an infinite number of studies (based on the inclusion criteria for analysis), the true effect sizes for these studies would be distributed about some mean. The effect sizes in the studies that actually were performed are assumed to represent a random sample of these effect sizes (hence the term random effects).

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