Meta-analysis

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► Have you ever wanted to learn about meta-analyses or conduct a meta-analysis but didn't know where to start? This webpage is devoted to providing you expert opinion on what you need to know to start your own meta-analysis.

► With the thousands of meta-analyses conducted in all areas of psychology over the past few decades, there has been an ever-increasing number of articles, books, and software programs devoted to how to conduct meta-analyses. Below, you can find out which of the many sources of information are the most useful and why -- so that the user has an easy-to-use starting place for learning everything about meta-analyses.



Contents



Where should I start?

If you want to learn what is a meta-analysis...

  1. For the basics, see below where we lay out:

  2. For more in-depth discussion and explanations...
    • start first with (Rosenthal & DiMatteo, 2001) (an Annual Review article) which provides a concise overview of everything you need to know, including the history, advantages, criticisms, and basic steps involved in a meta-analysis. (see the Annual Review website here)
    • then try (Johnson & Eagly, 2000) (a chapter in Handbook of Research Methods in Social and Personality Psychology which can be downloaded here) and (Lipsey & Wilson, 2001) (a book called Practical Meta-Analysis) for more detailed explanation of each stage in the meta-analysis process.
    • then for even more in-depth descriptions see (Cooper & Hedges, 1994) (Handbook of Research Synthesis) which provides a separate chapter on every step involved in designing, analyzing, and writing-up a meta-analysis.

If you want to learn how to start conducting a meta...

  1. For the basics, see below were we lay out:

  2. For more in-depth discussion and explanations...
    • start first with (Johnson, Mullen, & Salas, 1995) which provides a statistical comparision of the three major meta-analytic approaches using actual datasets, as well as the statistical formulas for each approach and the methodological differences between each approach.
    • if you want more information on each specific approach, see (Hedges & Olkin, 1985) for the Hedges/Olkin approach, see (Rosenthal, 1991) for the information on the Rosenthal/Rubin approach, or see (Hunter, Schmidt, & Jackson, 1982) for the Hunter/Schmidt/Jackson approach.
    • then for user-friendly step-by-step instructions for conducting all the different steps of a meta-anlaysis, see (Lipsey & Wilson, 2001) (Practical Meta-Analysis) which provides information on all three approaches including the statistical formulas for effect size indexes from each approach.




What is a meta-analysis?

Definition

A meta-analysis statistically combines the results of several studies that address a shared research hypotheses.

Just as individual studies summarize data collected from many participants in order to answer a specific research question (e.g., each participant is a separate data-point in the analysis), a meta-analysis summarizes data from individual studies that concern a specific research question (e.g., each study is a separate data-point in the analysis).


Three Basic Questions

A meta-analysis answers three general questions:
  1. Central tendency – The central purpose of a meta-analysis is to test the relationship between two variables such that X causes Y. Central tendency refers to identifying whether X affects Y via statistically summarizing signficance levels, effect sizes, and/or confidence intervals. You are trying to answer whether X affects Y, is the effect significant, and how strong is that effect?
  2. Variability – There is always going to be some degree of variation between the outcomes of the individual studies that compose the meta-analysis. The question is whether the degree of variablity is signficantly different than what we would expect by chance alone. If so, then its called heterogeneity. (for more info on heterogeneity, see here and here and here)
  3. Prediction – If there is heterogeneity (variability), then we look for moderating variables that explain the variability. In other words, does the effect of X on Y differ with moderator variables?


Five Basic Steps

There are generally five separate steps in conducting a meta-analysis:
  1. Define your Hypothesis – First you must have a well-defined statement of the relationship between the variables under investigation so that you can carefully define the inclusion and exclusion criteria when locating potential studies. For more information see Chapter 2 of (Lipsey & Wilson, 2001) (Practical Meta-Anlaysis) for a thorough examination of this step.
  2. Locate the Studies – A meta-analysis is only informative if it adequately summarizes the existing literature, so a thorough literature search is critical to retrieve every relevant study, such as database searches, ancestry approach, descendancy approach, hand searching, and the invisible college (e.g., network of researchers who know about unpublished studies, conference proceedings, etc). For more information see (Johnson & Eagly, 2000) (Handbook of Research Methods in Social and Personality Psychology) which details five general ways to retrieve relevant articles.
  3. Input data – Gather empiricial findings from primary studies (e.g., p-value, effect size, etc) and input into statistical database. Not every study provides sufficient statistical information to calculate the effect size statistic. For more information see below about choosing your statistical software.
  4. Cacluate Effect Sizes – Calculate the overall effect by converting all statistics to a common metric, making adjustments as necessary to correct for issues like sample-size or bias, and then calculating central tendency (e.g., mean effect size and confidence intervals around that effect size) and variablity (e.g., heterogeneity analysis). For more information see below about choosing which effect size index to calculate and see (Lipsey & Wilson, 2001) (Practical Meta-Anlaysis) for all the different statistical formulas.
  5. Analyze Variables – If heterogeneity exists, you may want to analyze moderating variables by coding each variable in the database and analyzing either mean differences (for categorical variables) or weighted regression (for continuous variables) to see if the variable accounts for the variability in the effect size. Note - even if heterogeneity does not exist, some argue analyzing moderating variables is appropriate ((Rosenthal, 1995)). FYI - (Rosenthal, 1995) is also an excellent Psychological Bulletin article on how to write a meta-analysis.


How do I conduct a meta-analysis?

First, choose which statistical approach suits your needs

There are generally three different statistical approaches to conduct a meta-analysis so first you need to choose which approach best fits your needs. For an excellent detailed comparison of these three approaches, see (Johnson, Mullen, & Salas, 1995) (Comparison of Three Major Meta-Analytic Approaches. Journal of Applied Psychology, 80, 94-106). Some basic information from that article is posted below to get you started:
  1. Hedges & Olkin Approach – see (Hedges, 1981); (Hedges, 1982); (Hedges & Olkin, 1985)
  2. Rosenthal & Rubin Approach – see (Rosenthal, 1991); (Rosenthal & Rubin, 1978); (Rosenthal & Rubin, 1988)
  3. Hunter, Schmidt, & Jackson - see (Hunter, Schmidt, & Jackson, 1982); (Hunter & Schmidt, 1990)
Table1JMS2.gif


Second, choose which effect size index to calculate

The commonly used effect size indexes are "the "r" family and the "d" family" of effect sizes (see (Rosenthal, 1994); (Rosenthal and Dimatteo, 2001)). Since "r" and "d" can be transformed into each other statistically you may wonder why it matters which metric you choose. Empirical research can take many forms (e.g., dichotomous and/or continuous IV, dichotomous and/or continuous DV, two variables relationships, etc) and the form of research you are analyzing helps determine which metric may be best to use (see below). For complete information and statistical formulas for all effect size indexes for each form of research, see (Lipsey & Wilson, 2001) (Practical Meta-Anlaysis).
  1. The r family – Correlation Coefficient - The "r" family includes all types of correlation coefficients (e.g., r, phi, rho, etc) and (Johnson & Eagly, 2000) suggest using r when the studies composing the meta-analysis primarily report the correlation between variables, but also see (Rosenthal & DiMatteo, 2001) for a discussion of the advantages of using r over d.
  2. The d family – Standardized Difference - The "d" family includes Cohen's d (unweighted) and Hedges g (weighted), and (Johnson & Eagly, 2000) suggest using d when the studies composing the meta-analysis primarily report ANOVAs and t-tests comparisons between groups.

(for an online effect size calculator for both "r" and "d", see the Larry C. Lyons and Wendy A. Morris website)


Third, choose your statistical software

You have two basic options -- use specialized software designed to conduct meta-analyses, or use standard statistical software such as SPSS and SAS. There are pros/cons to whichever option you use, so how do you choose? What you need are opinions/suggestions from those who have already used each type of software, which is where PsychWiki comes in. Directly below we have a quick summary of each approach, and then posted below are user opinions to help you identify which software is best for you!
  1. SPSS and SAS (free) – the David B. Wilson website provides an excel spreadsheet for calcuating effect sizes, and SPSS and SAS macros for perfoming meta-analyses after you have imported your effect sizes from the spreadsheet. These tools accompany the (Lipsey and Wilson, 2001) book Practical Meta-Analysis.
  2. Meta-Analysis (free) – Developed by (Schwarzer, 1996), it can be found on the Ralf Schwarzer website and each of the three meta-analytic approaches discussed above here can be selected (e.g., Hedges/Olkin approach, Rosenthal approach, or Hunter/Schmidt/Jackson approach.
  3. META (Meta-Analysis Easy to Answer) (free) – Developed by David Kenny, a description of the software can be found on the David Kenny website here and the program can be found on his website here.
  4. CMA (Comprehensive Meta-Analysis) (free demo, academic pricing) – Developed by many of the experts in meta-analyses (see here for a list), it includes an array of sophisticated options, and a comparison between CMA and other meta-analytic sofware can be found here.
  5. DSTAT – Developed by (Johnson, 1989) ...
  6. Advaned Basic Meta-analysis – Developed by (Mullen, 1989) ...
  7. Metawin (free demo, student discounts) – Developed by (Rosenberg, Adams, & Gurevitch, 1997), see the Metawin homepage for more information including a description of Metawin here and download a free demo here.
  8. MetaDOS – Developed by (Stauffer, 1996) ...


SPSS and SAS


Meta-Analysis

META (Meta-Analysis Easy to Answer)

CMA (Comprehensive Meta-Analysis)

DSTAT

Advanced Basic Meta-analysis

Metawin

MetaDOS

websites you may find interesting or helpful...

  1. For an online slide-show of how to conduct a meta-analysis,
    see the University of Pittsburgh's Supercourse on how to conduct a meta-analysis.
  2. For a powerpoint presentation summary of the (Lipsey and Wilson, 2001) book Practical Meta-analysis,
    see the David B. Wilson website.
  3. For a concise depiction of the meta-analytic process,
    see the Systematic Review webiste for a powerpoint presentation.
    see the Cochrane Collaboration website for an online booklet.
  4. For a truly engaging and informative paper on the history of meta-analyses written by the person who coined the term "meta-analysis"
    see Gene V. Glass website.
  5. For a discussion of how a meta-analysis fits into the research process,
    see the CMA (Comprehensive Meta-Analysis) website.
  6. For a listing of various commercial and freely available meta-analysis software,
    see the William R. Shadish website and
    see this page on the University of Leicester website.
    see this page on EpiVetNet.
  7. For a listing of articles that review/compare different meta-analytic software,
    see the William R. Shadish website and
    see this page on the University of Leicester website.
  8. For an online professional development course on how to conduct a meta-analysis,
    see the Statistics.com website.
  9. For the wikipedia webpage devoted to meta-analysis,
    see this page.
  10. For a Fail-Safe Number Calculator (and a paper describing the Fail-Safe Number issue),
    see the Michael S. Rosenthal website.






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