Meta-Analysis and Its Discontents

Everyone loves meta-analyses. We did an analysis of the most frequently opened articles on Best Evidence in Brief. Almost all of the most popular were meta-analyses. What’s so great about meta-analyses is that they condense a lot of evidence and synthesize it, so instead of just one study that might be atypical or incorrect, a meta-analysis seems authoritative, because it averages many individual studies to find the true effect of a given treatment or variable.

Meta-analyses can be wonderful summaries of useful information. But today I wanted to discuss how they can be misleading. Very misleading.

The problem is that there are no norms among journal editors or meta-analysts themselves about standards for including studies or, perhaps most importantly, how much or what kind of information needs to be reported about each individual study in a meta-analysis. Some meta-analyses are completely statistical. They report all sorts of statistics and very detailed information on exactly how the search for articles took place, but never say anything about even a single study. This is a problem for many reasons. Readers may have no real understanding of what the studies really say. Even if citations for the included studies are available, only a very motivated reader is going to go find any of them. Most meta-analyses do have a table listing studies, but the information in the table may be idiosyncratic or limited.

One reason all of this matters is that without clear information on each study, readers can be easily misled. I remember encountering this when meta-analysis first became popular in the 1980s. Gene Glass, who coined the very term, proposed some foundational procedures, and popularized the methods. Early on, he applied meta-analysis to determine the effects of class size, which by then had been studied several times and found to matter very little except in first grade. Reducing “class size” to one (i.e., one-to-one tutoring) also was known to make a big difference, but few people would include one-to-one tutoring in a review of class size. But Glass and Smith (1978) found a much higher effect, not limited to first grade or tutoring. It was a big deal at the time.

I wanted to understand what happened. I bought and read Glass’ book on class size, but it was nearly impossible to tell what had happened. But then I found in an obscure appendix a distribution of effect sizes. Most studies had effect sizes near zero, as I expected. But one had a huge effect size, of +1.25! It was hard to tell which particular study accounted for this amazing effect but I searched by process of elimination and finally found it.

It was a study of tennis.

blog_6-7-18_tennis_500x355

The outcome measure was the ability to “rally a ball against a wall so many times in 30 seconds.” Not surprisingly, when there were “large class sizes,” most students got very few chances to practice, while in “small class sizes,” they did.

If you removed the clearly irrelevant tennis study, the average effect size for class sizes (other than tutoring) dropped to near zero, as reported in all other reviews (Slavin, 1989).

The problem went way beyond class size, of course. What was important, to me at least, was that Glass’ presentation of the data made it very difficult to find out what was really going on. He had attractive and compelling graphs and charts showing effects of class size, but they all depended on the one tennis study, and there was no easy way to find out.

Because of this review and several others appearing in the 1980s, I wrote an article criticizing numbers–only meta-analyses and arguing that reviewers should show all of the relevant information about the studies in their meta-analyses, and should even describe each study briefly to help readers understand what was happening. I made up a name for this, “best-evidence synthesis” (Slavin, 1986).

Neither the term nor the concept really took hold, I’m sad to say. You still see meta-analyses all the time that do not tell readers enough for them to know what’s really going on. Yet several developments have made the argument for something like best-evidence synthesis a lot more compelling.

One development is the increasing evidence that methodological features can be strongly correlated with effect sizes (Cheung & Slavin, 2016). The evidence is now overwhelming that effect sizes are greatly inflated when sample sizes are small, when study durations are brief, when measures are made by developers or researchers, or when quasi-experiments rather than randomized experiments are used, for example. Many meta-analyses check for the effects of these and other study characteristics, and may make adjustments if there are significant differences. But this is not sufficient, because in a particular meta-analysis, there may not be enough studies to make any study-level factors significant. For example, if Glass had tested “tennis vs. non-tennis,” there would have been no significant difference, because there was only one tennis study. Yet that one study dominated the means anyway. Eliminating studies using, for example, researcher/developer-made measures or very small sample sizes or very brief durations is one way to remove bias from meta-analyses, and this is what we do in our reviews. But at bare minimum, it is important to have enough information available in tables to enable readers or journal reviewers to look for such biasing factors so they can recompute or at least understand the main effects if they are so inclined.

The second development that makes it important to require more information on individual studies in meta-analyses is the increased popularity of meta-meta-analyses, where the average effect sizes from whole meta-analyses are averaged. These have even more potential for trouble than the worst statistics-only reviews, because it is extremely unlikely that many readers will follow the citations to each included meta-analysis and then follow those citations to look for individual studies. It would be awfully helpful if readers or reviewers could trust the individual meta-analyses (and therefore their averages), or at least see for themselves.

As evidence takes on greater importance, this would be a good time to discuss reasonable standards for meta-analyses. Otherwise, we’ll be rallying balls uselessly against walls forever.

References

Cheung, A., & Slavin, R. (2016). How methodological features affect effect sizes in education. Educational Researcher, 45 (5), 283-292

Glass, G., & Smith, M. L. (1978). Meta-Analysis of research on the relationship of class size and achievement. San Francisco: Far West Laboratory for Educational Research and Development.

Slavin, R.E. (1986). Best-evidence synthesis: An alternative to meta-analytic and traditional reviews. Educational Researcher, 15 (9), 5-11.

Slavin, R. E. (1989). Class size and student achievement:  Small effects of small classes. Educational Psychologist, 24, 99-110.

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.

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4 thoughts on “Meta-Analysis and Its Discontents

  1. This blog post and paper are very relevant: http://documents.worldbank.org/curated/en/516191468172488103/What-really-works-to-improve-learning-in-developing-countries-an-analysis-of-divergent-findings-in-systematic-reviews.

    Here is the abstract from the paper:

    In the past two years alone, at least six systematic reviews or meta-analyses have examined the interventions that improve learning outcomes in low- and middle-income countries. However, these reviews have sometimes reached starkly different conclusions: reviews, in turn, recommend information technology, interventions that provide information about school quality, or even basic infrastructure (such as desks) to achieve the greatest improvements in student learning. This paper demonstrates that these divergent conclusions are largely driven by differences in the samples of research incorporated by each review. The top recommendations in a given review are often driven by the results of evaluations not included in other reviews. Of 227 studies with student learning results, the most inclusive review incorporates less than half of the total studies. Variance in classification also plays a role. Across the reviews, the three classes of programs that are recommended with some consistency (albeit under different names) are pedagogical interventions (including computer-assisted learning) that tailor teaching to student skills; repeated teacher training interventions, often linked to another pedagogical intervention; and improving accountability through contracts or performance incentives, at least in certain contexts. Future reviews will be most useful if they combine narrative review with meta-analysis, conduct more exhaustive searches, and maintain low aggregation of intervention categories.

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  2. Bob, another brilliant blog! Standards for conducting,analyzing and reporting data from meta analyses are still an important need!

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  3. Thank you unpacking this complex issue, Bob. It is so easy to be blinded by neat-looking statistics, but you have demonstrated the importance of maintaining a critical lens.

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