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Meta-analysis: correlation

Next selectMeta-analysis
Next selectCorrelation


For a short overview of meta-analysis in MedCalc, see Meta-analysis: introduction.

MedCalc uses the Hedges-Olkin (1985) method for calculating the weighted summary Correlation coefficient under the fixed effects model, using a Fisher Z transformation of the correlation coefficients. Next the heterogeneity statistic is incorporated to calculate the summary Correlation coefficient under the random effects model (DerSimonian and Laird, 1986).

How to enter data

The data of different studies can be entered as follows in the spreadsheet:

Meta-analysis: correlation - how to enter data

Required input

The dialog box for "Meta-analysis: correlation" can then be completed as follows:

Meta-analysis: correlation - dialog box

Studies: a variable containing an identification of the different studies.


Number of cases: a variable containing the total number of cases included in the different studies.

Correlation coefficients: a variable containing the correlation coefficient reported in the different studies.

Filter: a filter to include only a selected subgroup of cases in the graph.



Meta-analysis: correlation - results

The program lists the results of the individual studies included in the meta-analysis: number of cases, the correlation coefficient with 95% CI.

The pooled correlation coefficient with 95% CI is given both for the Fixed effects model and the Random effects model.

The random effects model will tend to give a more conservative estimate (i.e. with wider confidence interval), but the results from the two models usually agree where there is no heterogeneity. See Meta-analysis: introduction for interpretation of the heterogeneity statistics Cochran's Q and I2. When heterogeneity is present the random effects model should be the preferred model.

See Meta-analysis: introduction for interpretation of the different publication bias tests.

Forest plot

The results of the different studies, with 95% CI, and the pooled correlation coefficients with 95% CI are shown in a forest plot:

Meta-analysis: correlation - forest plot


See also

Recommended book

Book cover

Introduction to Meta-Analysis
Michael Borenstein, Larry V. Hedges, Julian P. T. Higgins, Hannah R. Rothstein

Buy from Amazon

This book provides a clear and thorough introduction to meta-analysis, the process of synthesizing data from a series of separate studies. Meta-analysis has become a critically important tool in fields as diverse as medicine, pharmacology, epidemiology, education, psychology, business, and ecology.