Varying coefficient meta-analytic methods for alpha reliability.

Bonett, Douglas G.

doi:10.1037/a0020142

Cited by 77 publications

(133 citation statements)

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“…Such a model is most accurately called a constant-coefficient model (Bonett, 2010), given that all studies included in the meta-analysis are assumed to reflect a single, constant, common effect size. In other words, there is only one "true" value of the relationship in question (e.g., the link between smoking and lung cancer is the same for everyone across all settings and periods of time), and the purpose of the meta-analytic technique is to infer the best estimate of this common effect size.…”

Section: Constant-coefficient Modelsmentioning

confidence: 99%

“…In other words, there is only one "true" value of the relationship in question (e.g., the link between smoking and lung cancer is the same for everyone across all settings and periods of time), and the purpose of the meta-analytic technique is to infer the best estimate of this common effect size. Bonett (2010) provides the following mathematical expression for a constant-coefficient model:…”

Section: Constant-coefficient Modelsmentioning

confidence: 99%

“…However, they assume that studies that are meta-analyzed have been randomly sampled from a clearly defined superpopulation that follows a normal distribution. Bonett (2010) provides the following mathematical expression for a randomcoefficient model:…”

Section: Random-coefficient Modelsmentioning

confidence: 99%

“…If strong moderating factors are hypothesized, certain linear contrasts of j would be of more interest. Varying-coefficient models have been used for meta-analytic confidence intervals of Pearson correlations and their differences (Bonett, 2008), meta-analytic confidence intervals of standardized and unstandardized mean differences (Bonett, 2009), and meta-analytic confidence intervals of internal consistency estimates (Bonett, 2010). Additional information about varyingcoefficient models can be found in Judge, Griffiths, Hill, Lutkepohl, and Lee (1985, chap.…”

Section: Introducing a Varying-coefficient Modelmentioning

confidence: 99%

“…Given the important limitations of constant-and random-coefficient models, on many occasions it would be advisable to employ a varying-coefficient model (e.g., Bonett, 2008Bonett, , 2009Bonett, , 2010, which does not assume a common effect or random sampling of study populations from a normally distributed, well-defined superpopulation of studies. Bonett (2010) provided the following expression for a varying-coefficient model:…”

Section: Introducing a Varying-coefficient Modelmentioning

confidence: 99%

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Synthesizer 1.0: A varying-coefficient meta-analytic tool

Križan

2010

Behavior Research Methods

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Around the turn of the 20th century, communicable infectious diseases were a great threat to human populations. It was only with the advent of vaccination protocols that many of such modern "plagues" were successfully controlled-indeed, today's children are routinely vaccinated against diseases such as measles and smallpox. Karl Pearson, one of the fathers of modern statistics, lived during this period. Given the controversies that existed at the time, he too was interested in the efficacy of newly developed inoculation procedures for combating vulnerability to such infections. In what can probably be called the first metaanalysis, Pearson (1904) collected correlation coefficients to examine whether inoculation against smallpox predicted survival. Furthermore, he quantitatively aggregated these correlations, yielding an unweighted average correlation of .63, a truly massive effect size with enormous real-world significance. Although it took a hiatus for a large part of the 20th century, due to seminal work of pioneers such as Bob Rosenthal (1976) and Gene Glass (1976), meta-analysis became a critical tool for reaching accurate conclusions about empirical findings and resolving sticky questions about whether and when particular effects manifest. Today, meta-analysis is one of the most popular methods for conducting secondary research and literature reviews-a search of the PsycINFO database revealed that 630 publications with the term "meta-analysis" in the abstract were published in 2008, but only 11 were published in 1980.Although there is no denying that quantitative synthesis of empirical findings is both prevalent and desirable (see, e.g., Cooper & Hedges, 1994), there is much less agreement about how to best statistically aggregate research results. Answering this question involves everything from fairly high-level considerations (e.g., how to conceptualize the research question, how to define relevant research findings, how to determine what qualifies as an appropriate test of relevant hypotheses) to lower level considerations of how to choose a relevant metric and what statistical models to use for aggregation of the metrics (e.g., Cooper, Hedges, & Valentine, 2009). Perhaps the most contentious issues revolve around the last question: What statistical procedures are the most appropriate when aggregating effect sizes? In this article, I briefly review the two dominant statistical models employed in metaanalyses, emphasize their limitations, and describe a new, no-cost statistical software tool that employs novel statistical techniques (Bonett, 2008(Bonett, , 2009 and overcomes some of the limitations of traditionally used meta-analytic techniques. STATISTICAL MODELS IN META-ANALYSISIn order for a researcher to infer "true" values of a particular effect size (e.g., how strong is the link between smoking and lung cancer in an actual population) based on inherently limited empirical data, he or she must specify a "scheme" (generally a mathematical function) for how a given empirical finding relates to the act...

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Section: Constant-coefficient Modelsmentioning

confidence: 99%

Section: Constant-coefficient Modelsmentioning

confidence: 99%

Section: Random-coefficient Modelsmentioning

confidence: 99%