Pitfalls of meta-analysis19 April, 2016 at 10:28 | Posted in Statistics & Econometrics | 1 Comment
Including all relevant material – good, bad, and indifferent – in meta-analysis admits the subjective judgments that meta-analysis was designed to avoid. Several problems arise in meta-analysis: regressions are often non -linear; effects are often multivariate rather than univariate; coverage can be restricted; bad studies may be included; the data summarised may not be homogeneous; grouping different causal factors may lead to meaningless estimates of effects; and the theory-directed approach may obscure discrepancies. Meta-analysis may not be the one best method for studying the diversity of fields for which it has been used …
Glass and Smith carried out a meta-analysis of research on class size and achievement and concluded that “a clear and strong relationship between class size and achievement has emerged.”10 The study was done and analysed well; it might almost be cited as an example of what meta-analysis can do. Yet the conclusion is very misleading, as is the estimate of effect size it presents: “between class-size of 40 pupils and one pupil lie more than 30 percentile ranks of achievement.” Such estimates imply a linear regression, yet the regression is extremely curvilinear, as one of the authors’ figures shows: between class sizes of 20 and 40 there is absolutely no difference in achievement; it is only with unusually small classes that there seems to be an effect. For a teacher the major result is that for 90% of all classes the number of pupils makes no difference at all to their achievement. The conclusions drawn by the authors from their meta-analysis are normally correct, but they are statistically meaningless and particularly misleading. No estimate of effect size is meaningful unless regressions are linear, yet such linearity is seldom investigated, or, if not present, taken seriously.
Systematic reviews in sciences are extremely important to undertake in our search for robust evidence and explanations — simply averaging data from different populations, places, and contexts, is not.