statsmodels.stats.meta_analysis.combine_effects(effect, variance, method_re='iterated', row_names=None, use_t=False, alpha=0.05, **kwds)[source]

combining effect sizes for effect sizes using meta-analysis

This currently does not use np.asarray, all computations are possible in pandas.


mean of effect size measure for all samples


variance of mean or effect size measure for all samples

method_re{“iterated”, “chi2”}

method that is use to compute the between random effects variance “iterated” or “pm” uses Paule and Mandel method to iteratively estimate the random effects variance. Options for the iteration can be provided in the kwds “chi2” or “dl” uses DerSimonian and Laird one-step estimator.

row_nameslist of strings (optional)

names for samples or studies, will be included in results summary and table.

alphafloat in (0, 1)

significance level, default is 0.05, for the confidence intervals


Contains estimation results and intermediate statistics, and includes a method to return a summary table. Statistics from intermediate calculations might be removed at a later time.


Status: Basic functionality is verified, mainly compared to R metafor package. However, API might still change.

This computes both fixed effects and random effects estimates. The random effects results depend on the method to estimate the RE variance.

Scale estimate In fixed effects models and in random effects models without fully iterated random effects variance, the model will in general not account for all residual variance. Traditional meta-analysis uses a fixed scale equal to 1, that might not produce test statistics and confidence intervals with the correct size. Estimating the scale to account for residual variance often improves the small sample properties of inference and confidence intervals. This adjustment to the standard errors is often referred to as HKSJ method based attributed to Hartung and Knapp and Sidik and Jonkman. However, this is equivalent to estimating the scale in WLS. The results instance includes both, fixed scale and estimated scale versions of standard errors and confidence intervals.


Borenstein, Michael. 2009. Introduction to Meta-Analysis.

Chichester: Wiley.

Chen, Ding-Geng, and Karl E. Peace. 2013. Applied Meta-Analysis with R.

Chapman & Hall/CRC Biostatistics Series. Boca Raton: CRC Press/Taylor & Francis Group.