Skip to Main Content

Evidence Synthesis in the Social Sciences

Data Analysis in Meta Analysis

Meta Analysis is primarily the statistical analysis of the data from independent primary studies focused on the same question, which aims to generate a quantitative estimate of the studied phenomenon, for example, the effectiveness of the intervention.

Effect Size

Effect size tells you how meaningful the relationship between variables or the difference between groups is. It indicates the practical significance of a research outcome. The effect size is the key component of a meta-analysis because it encodes the results in a numeric value that can then be aggregated.

Types of Effect Size
Effect Size Measure of Effect Size Description Example in Social Sciences 
Correlation coefficients Pearson’s r Pearson’s r measures the strength of the relationship between two variables. Litwiller, B., Snyder, L. A., Taylor, W. D., & Steele, L. M. (2017). The relationship between sleep and work: A meta-analysis. Journal of Applied Psychology, 102(4), 682–699.
Standardized mean differences Cohen's d

Cohen’s d is designed for comparing two groups. It takes the difference between two means and expresses it in standard deviation units. It tells you how many standard deviations lie between the two means. 

It is subject to non negligible bias for small sample sizes.

Kim J, Castelli DM. Effects of Gamification on Behavioral Change in Education: A Meta-Analysis. Int J Environ Res Public Health. 2021 Mar 29;18(7):3550. 10.3390/ijerph18073550
Standardized mean differences Hedge's g

Hedge’s g is also designed for comparing two groups. It takes the difference between two means and expresses it in standard deviation units.

It removes the non negligible bias for small sample sizes with a correction factor.

Hilll DC, Moss RH, Sykes-Muskett B, Conner M, O'Connor DB. Stress and eating behaviors in children and adolescents: Systematic review and meta-analysis. Appetite. 2018 Apr 1;123:14-22. doi: 10.1016/j.appet.2017.11.109
Interpreting Effect Size
Effect Size Pearson's r Cohen's d or Hedge's g
Small .1 to .3 or -.1 to -.3 0.2


.3 to .5 or -.3 to -.5 0.5
Large .5 or greater or -.5 or less > 0.8

A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.

Effect Size CalculatorCampbell Collaboration web-based effect size calculator for meta analysis. 

Graphical Presentations in Meta Analysis

Graphical presentations in meta analysis allows readers to see the information from the individual studies that went into the meta-analysis at a glance. It provides a simple visual representation of the amount of variation between the results of the studies, as well as an estimate of the overall result of all the studies together.

Forest plots are popularly used in depicting this information in meta analysis.

(1) Roberts BW, Walton KE, Viechtbauer W. Patterns of mean-level change in personality traits across the life course: a meta-analysis of longitudinal studies. Psychol Bull. 2006 Jan;132(1):1-25. doi: 10.1037/0033-2909.132.1.1.

How to read a forest plot: 

Dettori JR, Norvell DC, Chapman JR. Seeing the Forest by Looking at the Trees: How to Interpret a Meta-Analysis Forest Plot. Global Spine J. 2021 May;11(4):614-616. doi: 10.1177/21925682211003889

Lewis S, Clarke M. Forest plots: trying to see the wood and the trees. BMJ. 2001 Jun 16;322(7300):1479-80. doi: 10.1136/bmj.322.7300.1479

Data Analysis Resources

Statistical resources: 

Softwares to support your Meta Analysis:

  • MetaXL is a free tool for conducting meta-analyses and meta-regression analyses, designed to work as an add-on for Microsoft Excel.
  • Meta-Essentials is a free tool for meta-analysis. It facilitates the integration and synthesis of effect sizes from different studies.
  • OpenMeta[Analyst] is an open-source tool for conducting meta-analyses and other statistical analyses, available for free to researchers.
  • Comprehensive Meta-Analysis (CMA): Although not free, CMA offers a free trial version that allows users to conduct a meta-analysis during the trial period.

© , Rutgers, The State University of New Jersey

Rutgers is an equal access/equal opportunity institution. Individuals with disabilities are encouraged to direct suggestions, comments, or complaints concerning any accessibility issues with Rutgers websites to or complete the Report Accessibility Barrier / Provide Feedback form.