Abstract

In this lecture I will survey the history of meta-analysis, provide an introduction to common meta-analytic techniques, explore some controversies, and discuss several ecological applications.

Definition

``... the statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings.''
(Glass 1976)

Related Terms

• Quantitative research synthesis
• Research reviews / overviews

Measures of Effect Size

• Often want to combine estimates of effect of some treatment e.g. drug, rehabilitation program, teaching method.
  
  
• Measure of effect size depends on problem and even customs of different fields of research. (Hall et al. 1994)
  
  
• Near-replicate studies may use different scales of measurement. Need an index of effect size that does not depend on abitrary scaling of dependent variable. (Hedges & Olkin 1985, p.6)
  
  
• Two scale-free indices are commonly used:
  
  
  1. The std. mean difference.
     Most commonly used index of effect size.
     
     
  2. Product-moment correlation coefficient.
     
     

  Combining Effect Size Estimates

  Assume that we have k studies to review, which we will index by i . In each study we estimate a mean for the experiment, which will have an E superscript, and a mean for the control, which will have a C superscript. The standarized mean difference d_i is the mean for the experiment minus the mean for the control divided by the standard deviation within each population (The observed standard deviation is denoted by s , while the theoretical is denoted by the Greek letter sigma).

  Summary

  Thus, when you hear the term "meta-analysis" you can simply interpret as a "weighted mean of experimental results".

  Alternative viewpoints

  • Meta-analysis is ``... an exercise in mega-silliness'' (H.J. Eysenck).
    
    
  • ``I simply cannot imagine any great contribution to knowledge from combining statistical results.'' (Peer reviewer of a meta-analysis by H. Cooper)
    
    

  References (For your information, not needed for exam)

  Cooper, H. and L.V. Hedges, eds. 1994. The Handbook of Research Synthesis. New York: Russell Sage Foundation.
  Glass, G.V. 1976. Primary, secondary, and meta-analysis. Educational Researcher, 5: 3-8.
  Hall, J. A., L. Tickle-Degnen, R. Rosenthal, and F. Mosteller. 1994. Hypotheses and problems in research synthesis. In Cooper, H. and L. V. Hedges, eds. The Handbook of Research Synthesis. New York: Russell Sage Foundation.
  Hedges, L.V., and I. Olkin. 1985. Statistical Methods for Meta-analysis. San Diego: Academic Press.

  The Details