Introduction to Quantitative Meta-Analysis

Chapter 1. Introduction
1.1 Introduction to Quantitative Meta-Analysis

Chapter 2. Calculating Standardized Mean Difference Estimates
2.1 Calculating the Standardized Mean Difference
2.2 Calculating the Variance of the Standardized Mean Difference

Chapter 3. Pooling Standardized Mean Differences
3.1 Fixed-Effects Pooling of Effect Size Estimates
3.2 Random-Effects Pooling of Effect Size Estimates
3.3 Demonstration of Pooling SMDs with escalc

Chapter 4. Meta-Regression Models
4.1 Regression and Meta-Regression
4.2 Using rma to estimate fixed- & mixed-effects meta-regression models
4.3 Meta-Regression Models: An Example

Chapter 5. Handling Within-Study Dependence in SMDs
5.1 Dependent Effects Introduction
5.2 Using GLS to handle within-study dependence in effect sizes
5.3 Using Robust Variance Estimation to handle within-study dependence in effect sizes

Chapter 6. Missing Data and Publication Bias
6.1 Assessing Publication Bias
6.2 Correcting for Publication Bias

Chapter 7. Meta-Analysis of Correlations
7.1 Pooling Correlation Estimates
7.2 Meta-Regression with Correlation Estimates as the effect size type
7.3 Testing publication bias in meta-analysis of correlations

Chapter 8. Meta-Analysis of Treatment Effects on Dichotomous Outcomes
8.1 Categorical Effect Size Measures
8.2 Meta-Regression with Categorical Effect Sizes as the effect size type
8.3 Final Hurrah of Equations and Stuff

Appendix
A.1 Transforming Inferential Statistics to Obtain the SMD
A.2 Calculating the SMD from repeated measures design data

This workshop is designed for graduate students, post-doctoral fellows, faculty, and research scientists from the behavioral, social, and health sciences. It is recommended that participants have a working knowledge of the general multiple regression model. Relevant core statistical concepts will be reviewed at the beginning of the workshop. Participants who would benefit from a more in-depth refresher on linear regression prior to attending may wish to watch our (no cost) Linear Regression Playlist on YouTube.

Live demonstrations of analyses will be presented using the R software program because it is the software that is most rapidly and frequently updated with the latest methodological innovations in meta-analysis. Where possible, supplemental materials demonstrating use of SPSS statistical software will be provided. Note that R can be downloaded for free.  While it is helpful to have some familiarity with R, it is not necessary.  The lectures which constitute the majority of the workshop are software-independent.  Note that while code will be shared for all analyses demonstrated in the workshop, the majority of the pedagogy will focus on the concepts and content rather than use of software.

The goal of the workshop is to cover the core skills needed to conduct a quantitative meta-analysis. While a good portion of the content has to include statistical formulas and models, the teaching will include demonstrations, explanations and interpretations to connect real data and methodological dilemmas with concepts, formulas and models. Because it is not possible for all methodological dilemmas as well as data and research question challenges to be covered, the understanding and skills learned in this class are intended to be generalized to new scenarios encountered by the learners in their future applied meta-analyses.

Tasha Beretvas will teach the workshop via Zoom. Participants will receive complete PDF copies of the course notes and the computer demonstrations as well as data for all examples. The PDFs are not time-limited and may be retained indefinitely but should not be distributed to others without obtaining prior permission.