Fixed-effect vs Random-effects Models

Two assumptions for pooling

In meta-analysis, two main models govern how study results are pooled. The fixed-effect model assumes all studies estimate a single common true effect size; observed differences arise from sampling error alone. The random-effects model assumes the true effect varies across studies and estimates the distribution of those effects. In most real-world settings, the random-effects model is considered the more realistic default assumption.

Defining the Concept

The pooling model in meta-analysis determines how effect sizes from individual studies are weighted and interpreted. The fixed-effect model assumes a single true effect size exists in the universe; each study estimates the same value with differing precision. Larger studies receive more weight because they contain less sampling error. The random-effects model acknowledges that studies conducted in different populations, under different conditions, or with different operationalizations may each have their own true effect size. This model accounts for both sampling error and the genuine variance across studies, estimated as tau-squared.

How It Works: Weighting and Confidence Intervals

The weighting logic differs between the two models. In the fixed-effect model, each study receives a weight equal to the inverse of its sampling variance alone, granting substantially more influence to large-sample studies. In the random-effects model, the weight incorporates both sampling variance and the estimated between-study variance, giving smaller studies relatively more weight. Consequently, the random-effects model typically yields wider confidence intervals, more honestly reflecting the underlying uncertainty. Heterogeneity statistics such as I-squared are used to measure the degree of inconsistency across studies and inform model choice.

A Concrete Example

Consider ten studies examining the effect of a drug treatment on blood pressure. If those studies were conducted in different countries, in different age groups, and at different doses, it is reasonable to assume each has its own underlying true effect size. Here the random-effects model is the appropriate choice. In contrast, if the studies are replications following an identical protocol in homogeneous populations, the fixed-effect model may be defensible. The pooled mean effect might be 0.45 under fixed effects and 0.38 under random effects, with the confidence interval being notably wider in the latter, more accurately capturing the between-study uncertainty.

Common Pitfalls and Good Practice

The most frequent error is choosing a model based solely on whether the heterogeneity test reaches statistical significance; that test has very low power when the number of studies is small. Choosing the random-effects model does not simply mean artificially widening the fixed-effect confidence interval; the two models rest on different conceptual foundations. Good practice requires researchers to justify model selection before the analysis, investigate sources of heterogeneity through moderator analyses, and report both tau-squared and I-squared. Presenting both models as a sensitivity analysis promotes transparency and allows readers to assess robustness.

Key terms

Fixed-effect Model: A pooling approach assuming all studies estimate one common true effect size.
Random-effects Model: A meta-analysis model that acknowledges and estimates true variance in effects across studies.
Tau-squared: Estimated between-study variance of true effects in the random-effects model.
I-squared: Percentage of observed variation attributable to true heterogeneity rather than sampling error.
Heterogeneity: Variation in true effect sizes across studies included in a meta-analysis.