The use of meta-analysis in medicine and epidemiology really took off in the 1970s. However, in high-energy physics, the Particle Data Group has been carrying out meta-analyses of measurements of particle masses and other properties since 1957. Curiously, there has been virtually no interaction between those working inside and outside particle physics. In this paper, we use statistical models to study two major differences in practice. The first is the usefulness of systematic errors, which physicists are now beginning to quote in addition to statistical errors. The second is whether it is better to treat heterogeneity by scaling up errors as do the Particle Data Group or by adding a random effect as does the rest of the community. Besides fitting models, we derive and use an exact test of the error-scaling hypothesis. We also discuss the other methodological differences between the two streams of meta-analysis. Our conclusion is that systematic errors are not currently very useful and that the conventional random effects model, as routinely used in meta-analysis, has a useful role to play in particle physics. The moral we draw for statisticians is that we should be more willing to explore "grassroots" areas of statistical application, so that good statistical practice can flow both from and back to the statistical mainstream.