Small Studies, Big Problems

Everyone knows that “good things come in small packages.” But in research evaluating practical educational programs, this saying does not apply. Small studies are very susceptible to bias. In fact, among all the factors that can inflate effect sizes in educational experiments, small sample size is among the most powerful. This problem is widely known, and in reviewing large and small studies, most meta-analysts solve the problem by requiring minimum sample sizes and/or weighting effect sizes by their sample sizes. Problem solved.

For some reason, the What Works Clearinghouse (WWC) has so far paid little attention to sample size. It has not weighted by sample size in computing mean effect sizes, although the WWC is talking about doing this in the future. It has not even set minimums for sample size for its reviews. I know of one accepted study with a total sample size of 12 (6 experimental, 6 control). These procedures greatly inflate WWC effect sizes.

As one indication of the problem, our review of 645 studies of reading, math, and science studies accepted by the Best Evidence Encyclopedia (www.bestevidence.org) found that studies with fewer than 250 subjects had twice the effect sizes of those with more than 250 (effect sizes=+0.30 vs. +0.16). Comparing studies with fewer than 100 students to those with more than 3000, the ratio was 3.5 to 1 (see Cheung & Slavin [2016] at http://www.bestevidence.org/word/methodological_Sept_21_2015.pdf). Several other studies have found the same effect.

Using data from the What Works Clearinghouse reading and math studies, obtained by graduate student Marta Pellegrini (2017), sample size effects were also extraordinary. The mean effect size for sample sizes of 60 or less was +0.37; for samples of 60-250, +0.29; and for samples of more than 250, +0.13. Among all design factors she studied, small sample size made the most difference in outcomes, rivaled only by researcher/developer-made measures. In fact, sample size is more pernicious, because while reviewers can exclude researcher/developer-made measures within a study and focus on independent measures, a study with a small sample has the same problem for all measures. Also, because small-sample studies are relatively inexpensive, there are quite a lot of them, so reviews that fail to attend to sample size can greatly over-estimate overall mean effect sizes.

My colleague Amanda Inns (2018) recently analyzed WWC reading and math studies to find out why small studies produce such inflate outcomes. There are many reasons small-sample studies may produce such large effect sizes. One is that in small studies, researchers can provide extraordinary amounts of assistance or support to the experimental group. This is called “superrealization.” Another is that when studies with small sample sizes find null effects, the studies tend not to be published or made available at all, deemed a “pilot” and forgotten. In contrast, a large study is likely to have been paid for by a grant, which will produce a report no matter what the outcome. There has long been an understanding that published studies produce much higher effect sizes than unpublished studies, and one reason is that small studies are rarely published if their outcomes are not significant.

Whatever the reasons, there is no doubt that small studies greatly overstate effect sizes. In reviewing research, this well-known fact has long led meta-analysts to weight effect sizes by their sample sizes (usually using an inverse variance procedure). Yet as noted earlier, the WWC does not do this, but just averages effect sizes across studies without taking sample size into account.

One example of the problem of ignoring sample size in averaging is provided by Project CRISS. CRISS was evaluated in two studies. One had 231 students. On a staff-developed “free recall” measure, the effect size was +1.07. The other study had 2338 students, and an average effect size on standardized measures of -0.02. Clearly, the much larger study with an independent outcome measure should have swamped the effects of the small study with a researcher-made measure, but this is not what happened. The WWC just averaged the two effect sizes, obtaining a mean of +0.53.

How might the WWC set minimum sample sizes for studies to be included for review? Amanda Inns proposed a minimum of 60 students (at least 30 experimental and 30 control) for studies that analyze at the student level. She suggests a minimum of 12 clusters (6 and 6), such as classes or schools, for studies that analyze at the cluster level.

In educational research evaluating school programs, good things come in large packages. Small studies are fine as pilots, or for descriptive purposes. But when you want to know whether a program works in realistic circumstances, go big or go home, as they say.

The What Works Clearinghouse should exclude very small studies and should use weighting based on sample sizes in computing means. And there is no reason it should not start doing these things now.

References

Inns, A. & Slavin, R. (2018 August). Do small studies add up in the What Works Clearinghouse? Paper presented at the meeting of the American Psychological Association, San Francisco, CA.

Pellegrini, M. (2017, August). How do different standards lead to different conclusions? A comparison between meta-analyses of two research centers. Paper presented at the European Conference on Educational Research (ECER), Copenhagen, Denmark.

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.