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.
| 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. https://doi.org/10.1037/apl0000169 |
| 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 |
| Effect Size | Pearson's r | Cohen's d or Hedge's g |
| Small | .1 to .3 or -.1 to -.3 | 0.2 |
|
Medium |
.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 Calculator: Campbell 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.
How to read a forest plot:
Data Analysis Resources
Statistical resources:
- Meta Analysis using R
- Meta Analysis using Stata
- How to perform a meta-analysis with R: a practical tutorial
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.