Meta-analysis calculator

A single trial answers a narrow question: did this intervention work in this sample, at this site, over this follow-up window? A meta-analysis asks a broader and more useful question. Across every comparable study that has been run, what is the best single estimate of the effect, and how much does that effect vary from one context to another? The pooled estimate is a precision-weighted average, so it borrows strength from every included study and produces a tighter confidence interval than any one trial could on its own.

The weighting is the heart of the method. Each study contributes in proportion to the inverse of its variance, which means large, precise trials dominate and small, noisy ones contribute little. This is far more defensible than a simple average of the reported effects, which would let a tiny pilot study count as much as a multi-thousand-patient randomised controlled trial. Our companion guide on how to plan and run a meta-analysis walks through every stage from protocol to pooled result.

When pooling is appropriate, and when it is not

Pool studies only when they are estimating something close to the same underlying effect. The studies should share a comparable population, a comparable intervention and comparator, and an outcome that means the same thing across trials. If a set of studies measures wildly different interventions or incompatible outcomes, a single pooled number is misleading no matter how clean the arithmetic looks. In those situations a structured narrative synthesis is the more truthful route.

The decision between models matters too. The fixed-effect model assumes one true effect shared by all studies, so the only reason results differ is sampling error. The random-effects model assumes the true effect varies and estimates that variation as tau-squared. Because real studies almost always differ in population and delivery, the random-effects model is the default in most reviews. Our explainer on choosing between fixed-effect and random-effects models covers the trade-off in depth.

Interpreting the output

Read three things together: the pooled point estimate, its 95 per cent confidence interval, and the heterogeneity statistics. The point estimate tells you the average direction and size of the effect. The interval tells you how precisely that average is pinned down; if it crosses the line of no effect (zero for a difference, one for a ratio), the pooled result is compatible with no benefit. The heterogeneity statistics tell you whether a single average even makes sense. As a rough guide, I-squared near 25 per cent is low, near 50 per cent is moderate, and 75 per cent or above is high, but always read it beside Cochran’s Q and tau-squared rather than in isolation. You can probe variation in more detail with the dedicated heterogeneity statistics calculator.

A worked example

Suppose five trials of a behavioural intervention report risk ratios of 0.82, 0.91, 0.75, 0.88, and 0.79, with the largest trial (the 0.88) carrying by far the most weight because of its narrow interval. Pooling on the log scale, the random-effects estimate might land at a risk ratio of about 0.84 with a 95 per cent confidence interval of 0.77 to 0.92. That interval sits entirely below one, so the pooled evidence points to a genuine reduction in risk of roughly 16 per cent. If I-squared came back at 18 per cent and tau-squared near zero, the studies are telling a consistent story and the single pooled figure is a fair summary. Had I-squared been 80 per cent, you would report the pooled value cautiously and explore the variation through subgroup and sensitivity work on heterogeneity.

Common mistakes

• Pooling apples with oranges. Combining studies that measure fundamentally different things produces a number that is precise and meaningless. Define the comparison before you collect a single effect size.
• Averaging the effects unweighted. A plain mean of the reported effects throws away precision information and lets small studies distort the result. Inverse-variance weighting exists for a reason.
• Ignoring heterogeneity. Reporting a pooled estimate with I-squared at 85 per cent as if it were a clean summary hides the most important finding, which is that the effect is not constant.
• Treating a wide interval as a null result. An interval that crosses no effect means the data are inconclusive, not that the intervention definitely does nothing.
• Forgetting small-study effects. A neat pooled estimate can still be biased if smaller studies were never published. Inspect a funnel plot and consider how publication bias distorts pooled estimates before you trust the number.