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► Have you ever wanted to learn about meta-analysis 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.
Where should I start?
If you want to learn what is a meta-analysis...
If you want to learn how to start conducting a meta...
What is a meta-analysis?
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:
- 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?
- 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.
- 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:
- 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.
- 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.
- 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.
- 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 any meta-analysis book for all the statistical formulas.
- 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)).
Two (x Two) types of Variables
- In addition to variables being categorical (e.g., discrete categories) or continuous (e.g., assigned Likert scale value), there are:
- Ojbective Variables – These are study characteristics objectively identifiable such as type of IV, type of DV, publication type (e.g., articles, books, dissertation, technical reports, unpublished, etc), design features (e.g., experimental, correlational, survey, field-study, laboratory-based, etc), sample features (e.g., sample size, demographics like sex, age, education, ethnicity, etc). For more information see any article/book about meta-analysis or see actual published meta-analyses for the types of variables coded.
- Subjective Variables – These are variables
There are two types of study variables: (a) objective variables -- such as type of IV or DV, ..., (b) subjective variables -- inferential judgements made by two or more judges....
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:
- Hedges & Olkin Approach – see (Hedges, 1981); (Hedges, 1982); (Hedges & Olkin, 1985)
- Rosenthal & Rubin Approach – see (Rosenthal, 1991); (Rosenthal & Rubin, 1978); (Rosenthal & Rubin, 1988)
- Hunter, Schmidt, & Jackson - see (Hunter, Schmidt, & Jackson, 1982); (Hunter & Schmidt, 1990)
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).
- 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.
- 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. Below are user opinions to help you identify which software is best for you!
- SPSS and SAS
- DSTAT by (Johnson, 1989) -
- Advanced Basic Meta-analysis by (Mullen, 1989) -
- Meta-Analysis by (Schwarzer, 1996) -
- MetaDOS by (Stauffer, 1996) -
- Metawin by (Rosenberg, Adams, Gurevitch, 1997)
see "practical meta analysis chapter 5 (page 91) which discusses pros and cons of different ways to... including...
For complete information and statistical formulas for all effect size indexes for each form of research, see (Lipsey & Wilson, 2001) (Practical Meta-Anlaysis).
DSTAT calculates all of this for you Can also use SPSS and macros from “Practical Meta-Analysis” Calculate Categorical variables – DSTAT using weighted ANOVA Calculate Continuous variables – SPSS using weighted Regression
If you want more detailed information about...
...the Hedges & Olkin approach...
- See (Lipsey & Wilson, 2001) (Practical Meta-Anlaysis) - which is relatively new book that provides a concise summary of all stages of the meta-analyses process, including providing ...
- See (Cooper & Hedges, 1994) (Handbook of Research Synthesis) - which is great in-depth articuluation of every step involved in designing, analyzing, and writing-up a meta-analysis.
- See (Hedges & Olkin, 1985) (Statistical Methods for Meta-Analysis) - which is the original source of information about the Hedges & Olkin approach.
...the Rosenthal & Rubin approach...
- See (Rosenthal, 1991) (Meta-analytic Procedures for Social Research) - which is the definitive source of information on the Rosenthal & Rubin approach.
- See (Rosenthal & DiMatteo, 2001) (Meta-Analysis: Recent Developments in Quantitative Methods for Literature Reviews) - which is an updated summary of the Rosenthal approach.
- See (Rosenthal, 1995) (Writing Meta-Analytic Reviews) - which is an excellent Psychological Bulletin article on how to write a meta-analysis.
...the Hunter, Schmidt, & Jackson approach...
...how to interpret your results?
...how to graphically present your results?
- What is the good number of studies to have bare minimum for a meta-analysis? A meta-analysis with 10 studies have been published before but is not recommended.
- In a meta-analysis, have judge rate each variable across studies, one moderator at a time, instead of rating all variables in a single study before moving on to next study.
- With meta-analysis coding with a high number of studies to code, such as 75+, can have some coders rate the entire set, but can also have some coders (undergrads) code only a subset as long there is overlap, so that more than 1 judge is rating each study.
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