SPSS command: SPSS META BINARY
Meta-analysis of binary outcomes in your browser
A binary-outcome meta-analysis combines studies that each report events and non-events in a treatment and a control group.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS META BINARY procedure on your device: odds ratio, risk ratio, risk difference or Peto's odds ratio, Mantel-Haenszel or inverse-variance fixed effects, random effects with seven τ² estimators and optional Knapp-Hartung adjustment, heterogeneity statistics, Egger's test and a forest plot.
- The pooled treatment effect on the odds, risk or risk-difference scale, with a confidence interval and p value.
- Each study's effect, confidence interval and weight in the pooled estimate.
- How much the true effects vary between studies: Q test, τ², H² and I² with confidence intervals.
- Whether smaller studies report systematically larger effects (Egger's regression test for funnel asymmetry).
When to use it
Use it when
- Systematic reviews of trials or cohort studies reporting a yes/no outcome per arm.
- Combining several A/B tests of the same change that each report conversions out of visitors.
- Rare events with zero cells: Peto's odds ratio handles them without adding 0.5.
Use something else when
- Studies report means and SDs, not counts: use the continuous-outcome meta-analysis.
- You want to explain heterogeneity with study characteristics: compute log odds ratios and their SEs, then use meta-regression.
- You have individual-level data from all studies: a stratified or mixed logistic model uses more information.
How to run it in Crosstabs
- 01
Enter one row per study
Prepare a file with one row per study and four count columns: treatment successes and failures, control successes and failures. Open it and switch to Statistics mode.
- 02
Choose the binary meta-analysis
In the Agreement and diagnostics group, pick Meta-Analysis: Binary Outcomes (META BINARY).
- 03
Map the four counts
Set Treatment: successes, Treatment: failures, Control: successes and Control: failures, and optionally a Study label (optional); without one, the row number labels each study.
- 04
Pick the effect size and model
Set Effect size to Odds ratio, Risk ratio, Risk difference or Peto's odds ratio. Set Model to Random effects (choose the Between-study variance (τ²) estimator, optionally Knapp-Hartung adjustment) or Fixed effect (choose the Fixed-effect method: Mantel-Haenszel or Inverse variance).
- 05
Run
Set the Confidence level (%) and press Run. Any workspace weight is ignored, because each row is a study weighted by its inverse variance.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
Seven hypothetical randomized trials, each entered as one row with four counts: treatment events and non-events, control events and non-events. The event is an adverse outcome, so an odds ratio below 1 favours treatment. The counts are typed inputs; every statistic below is computed from them.
Input preview
| Study | Treatment: successes | Treatment: failures | Control: successes | Control: failures |
|---|---|---|---|---|
| Trial 1 | 14 | 86 | 22 | 78 |
| Trial 2 | 9 | 51 | 15 | 47 |
| Trial 3 | 31 | 169 | 42 | 160 |
| Trial 4 | 3 | 37 | 8 | 33 |
| Trial 5 | 20 | 130 | 21 | 125 |
| Trial 6 | 7 | 73 | 16 | 66 |
| Trial 7 | 25 | 95 | 28 | 94 |
“Successes” is the panel's name for the event column, here the adverse outcome.
| Study | Effect Size | Std. Error | 95% CI | Odds ratio | Weight % |
|---|---|---|---|---|---|
| Trial 1 | −0.550 | 0.376 | −1.286 – 0.187 | 0.577 | 13.7 |
| Trial 2 | −0.593 | 0.468 | −1.509 – 0.324 | 0.553 | 8.9 |
| Trial 3 | −0.358 | 0.261 | −0.870 – 0.154 | 0.699 | 28.4 |
| Trial 4 | −1.095 | 0.718 | −2.503 – 0.312 | 0.334 | 3.8 |
| Trial 5 | −0.088 | 0.337 | −0.748 – 0.572 | 0.916 | 17.1 |
| Trial 6 | −0.927 | 0.484 | −1.876 – 0.021 | 0.396 | 8.3 |
| Trial 7 | −0.124 | 0.311 | −0.734 – 0.486 | 0.883 | 20.0 |
Log scale; the exponentiated column is on the ratio scale. Weights are random-effects weights.
| Model | Effect Size | Std. Error | Z / t | Sig. | 95% CI | Odds ratio | 95% CI |
|---|---|---|---|---|---|---|---|
| Mantel-Haenszel | −0.393 | 0.138 | −2.85 | .004 | −0.664 – −0.123 | 0.675 | 0.515 – 0.884 |
| Random effects | −0.387 | 0.139 | −2.78 | .005 | −0.660 – −0.114 | 0.679 | 0.517 – 0.892 |
Random effects: τ² estimated by restricted maximum likelihood (REML).
| Q | df | Sig. | τ² | H² | I² (%) | I² 95% CI |
|---|---|---|---|---|---|---|
| 4.118 | 6 | .661 | 0.0000 | 0.686 | 0.0 | 0.0 – 57.5 |
Q is Cochran's homogeneity statistic for the common-effect estimate; H² = Q/df and I² = (Q − df)/Q.
How to read it
The random-effects pooled odds ratio is 0.679 (95% CI 0.517 – 0.892, p = .005): treatment lowers the odds of the adverse outcome by about 32%. The Mantel-Haenszel fixed-effect estimate (OR 0.675) is close, as expected when Q = 4.12 on 6 df (p = .661) and I² = 0.0% show little heterogeneity. With only seven trials, the I² interval (0.0% to 57.5%) is wide.
Output tables explained
- Effect Size Estimates
- Each study's effect on the log scale (or as a risk difference), standard error, confidence interval, the effect on the ratio scale and its percentage weight.
- Overall Effect Size
- The fixed-effect estimate (Mantel-Haenszel, inverse variance or Peto) and, for a random-effects model, the random-effects estimate, each with SE, Z or t, significance, interval and the back-transformed ratio with its bounds.
- Heterogeneity
- Cochran's Q with df and significance, τ², H² and I² with confidence intervals. I² is the share of total variation due to real differences between studies.
- Egger's Regression-Based Test
- Intercept, SE, t, df and significance from regressing effect/SE on 1/SE; shown with three or more studies. A non-zero intercept suggests funnel-plot asymmetry.
Assumptions and notes
- Studies estimate comparable effects of the same intervention on the same outcome.
- Studies with a zero cell get 0.5 added to every cell (not for Peto); studies with no events or all events in both arms are excluded for ratio measures.
- Random effects assume the true study effects are normally distributed around the pooled mean.
- At least two usable studies are needed; with few studies τ² and I² are very imprecise.
How the results are validated
On an eight-study reference set, odds ratio, risk ratio and risk difference effect sizes and variances match R metafor 5.2.1 escalc to 1e-12; Mantel-Haenszel estimates match rma.mh to 1e-10 (the MH risk-difference SE, where metafor uses a different variance formula, matches an independent implementation of the SPSS form); inverse-variance fixed effects and Q match to 1e-10; all seven τ² estimators match rma to 1e-6 for interior solutions; Peto matches rma.peto to 1e-10. Validation evidence
Questions
Odds ratio or risk ratio?
Risk ratios are easier to explain and are preferred when events are common. Odds ratios have better mathematical properties and match logistic regression and case-control designs. With rare events the two are nearly equal.
Fixed or random effects?
Fixed effect assumes one true effect shared by all studies; random effects allow the true effect to vary. When studies differ in population or protocol, random effects is the usual choice, and Knapp-Hartung gives more honest intervals with few studies.
Which τ² estimator should I pick?
REML is the default and a sound general choice. DerSimonian-Laird is the classic method many older reviews report; Empirical Bayes, Sidik-Jonkman and the others in the list are useful as sensitivity checks.
Why is I² 0% when the forest plot looks scattered?
With wide study intervals, the scatter is no larger than sampling error predicts, so Q is at or below its df and I² is truncated at 0. Its confidence interval usually shows that substantial heterogeneity cannot be ruled out.
Related procedures
- Meta-Analysis: Continuous OutcomesMETA CONTINUOUS
- Meta-RegressionMETA REGRESSION
- Crosstabs StatisticsCROSSTABS /STATISTICS
- Binary Logistic RegressionLOGISTIC REGRESSION
- Free SPSS alternative: full coverage list
Run Meta-Analysis: Binary Outcomes on your own data
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