Which statistic is used to test for heterogeneity in meta-analysis, often reported alongside I^2?

• A. Cochran's Q
• B. R-squared
• C. p-value
• D. t-statistic

Answer: (A)

In meta-analysis, you want to know whether the study results vary more than would be expected from random sampling error. The statistic used to test this is Cochran’s Q, a chi-square type test of heterogeneity. It works by weighting each study’s effect estimate by its precision, then summing the squared differences between each study’s effect and the overall pooled effect. Under the assumption that all studies share a common true effect (no real heterogeneity), this Q statistic follows a chi-square distribution with degrees of freedom equal to the number of studies minus one.

If Q is large and the p-value is small, it suggests that the observed differences among study results are unlikely due to chance alone, indicating heterogeneity. However, Q’s ability to detect heterogeneity depends on how many studies you have: it can miss real differences when there are few studies, and it can flag trivial differences as significant when there are many. That’s why I^2 is often reported alongside Q — I^2 quantifies the proportion of total variation that is due to real differences between studies (heterogeneity) rather than sampling error, giving a sense of how substantial the heterogeneity is.