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, experts on meta-analysis provide their suggesstions on which 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) which provides a concise overview of everything you need to know, including the history, advantages, criticisms, and basic steps involved in a meta-analysis.
    • then see (Johnson & Eagly, 2000) which is a chapter from the "Handbook of Research Methods in Social and Personality Psychology" that provides a more detailed explanation of each stage in the meta-analysis process including statistical forumlas for analyzing effect sizes from various indexes and study designs.
    • 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.
    • based upon which meta-analytic approach you choose to use, you may want to also 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 individual participants in order to answer a specific research question (e.g., each participant is a separate data point), a meta-analysis summarizes data from individual studies that concern a specific research question (e.g., each data point is each individual study).


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.
  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. 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, one variable relationships, 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.


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 - the David 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. DSTAT (by (Johnson, 1989)) -
  3. Advanced Basic Meta-analysis (by (Mullen, 1989)) -
  4. Meta-Analysis by ((Schwarzer, 1996)) -
  5. MetaDOS (by (Stauffer, 1996)) -
  6. Metawin (by (Rosenberg, Adams, & Gurevitch, 1997)) -


SPSS and SAS


DSTAT

Advanced Basic Meta-analysis

Meta-Analysis

MetaDOS

Metawin

websites you may find interesting or helpful...

  1. For an online slide-show of how to conduct a meta-analysis, see...












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