A meta-analysis is only as good as its bookkeeping: turning each study into a comparable effect size, weighting them, and being honest about how much they disagree. Magic Stat computes the effect sizes from the numbers in your table, fits fixed and random-effects models, and draws the forest and funnel plots.
You give the app one row per study in the form the paper reports — means and SDs, events and totals, a correlation, an F, a chi-square, a hazard ratio, or a ready effect size with its confidence interval — and it converts each to a common scale: Hedges' g or mean difference, log odds ratio, log risk ratio, risk difference, Fisher's z, and more. It then combines them with fixed-effect (inverse-variance) and random-effects (DerSimonian–Laird) models, reporting τ², Cochran's Q, I², H² and a prediction interval.
The random-effects estimate is the one to read when the studies are not measuring exactly the same thing — which is the usual case. I² tells you how much of the spread is real heterogeneity rather than chance, and the prediction interval says where a future study's effect might fall, which the pooled confidence interval does not.
Two honest limits. The random-effects estimator is DerSimonian–Laird only; REML or Paule–Mandel are not offered, and metafor in R is the tool if you need them. And the publication-bias tools — funnel plot and Egger's regression — are diagnostics, not proof: with few studies they have little power, so a non-significant test is not evidence that there is no bias.
Input types: Continuous (mean ± SD) · Multiple groups (ANOVA F) · Binary (events/total) · Correlation (r) · Chi-square association (φ/V) · Proportion (events/total) · Survival (HR + CI) · Effect size + CI.
Effect measure: Hedges' g or mean difference · odds ratio, risk ratio or risk difference · Fisher's z · logit proportion · log hazard ratio · given effect size.
Model: random effects (DerSimonian–Laird) or fixed effect (inverse variance); both are always computed so the forest can show both diamonds.
Extras: funnel plot + Egger test · leave-one-out · subgroup analysis with the between-group Q.
Random effects if the studies are a sample of a broader population and their true effects plausibly differ — which is almost always. Fixed effect is only defensible when the studies share one true effect. Both are computed so you can see the difference, but the random-effects estimate is the one to report.
The metafor convention: the exact Hedges correction (a gamma ratio) for the point estimate and the Hedges (1982) variance. meta and Borenstein et al. use slightly different variances; all three are legitimate, and Magic Stat follows metafor because it is the most cited reference in R.
No — the random-effects estimator here is DerSimonian–Laird. If you want REML or Paule–Mandel with their respective confidence intervals, metafor in R is the right tool, and the app does not pretend to be a substitute.
It regresses the study effects on their precision to look for funnel asymmetry, with the caveat that asymmetry can come from heterogeneity as well as from publication bias. With few studies the test has low power, so a non-significant result is not evidence that there is no bias.
No. Everything is computed locally from the table you enter; nothing but an anonymous installation counter is transmitted.