Qrbar: Meta-Analytic Q statistic for r-bar

In psychometric: Applied Psychometric Theory

Meta-Analytic Q statistic for r-bar

Description

Provides a chi-square test for significant variation in sample weighted correlation, rbar

Usage

Qrbar(x)
aprox.Qrbar(x)

Arguments

x	A matrix or data.frame with columns Rxy and n: see EnterMeta

Details

Q is distributed as chi-square with df equal to the number of studies - 1. Multiple equations exist presumably because of a need to do the calculations ‘by hand’ in the past. A significant Q statistic implies the presence of one or more moderating variables operating on the observed correlations.

Value

A table containing the following items:

CHISQ	Chi-square value
df	degrees of freedom
p-val	probabilty value

Warning

The test is presented by Hunter et al. 1982, but is NOT recommended nor mentioned by Hunter & Schmidt (2004). The test is sensitive to the number of studies included in the meta-analysis. Large meta-analyses may find significant Q statistics when variation in the population is not present, and small meta-analyses may find lack of significant Q statistics when moderators are present. Hunter & Schmidt (2004) recommend the credibility inteval, CredIntRho, or the 75% rule, pvse, as determinants of the presence of moderators.

Note

Qrbar is computed as: sum((((n-1)*(r-rb)^2)/(1-rb^2)^2),na.rm=TRUE)
aprox.Qrbar is computed as: (N/(1-rb^2)^2)*vr

where n is sample size of study i, N is total sample size across studies, rb is rbar, r is the correlation of study i, and vr is varr.

Author(s)

Thomas D. Fletcher [e-mail]

References

Arthur, Jr., W., Bennett, Jr., W., and Huffcutt, A. I. (2001) Conducting Meta-analysis using SAS. Mahwah, NJ: Erlbaum.

Hunter, J.E. and Schmidt, F.L. (2004). Methods of meta-analysis: Correcting error and bias in research findings (2nd ed.). Thousand Oaks: Sage Publications.

Hunter, J.E., Schmidt, F.L., and Jackson, G.B. (1982). Meta-analysis: Cumulating research findings across studies. Beverly Hills: Sage Publications.

See Also

varr, vare, rbar, CredIntRho, pvse

Examples

# From Arthur et al
data(ABHt32)
aprox.Qrbar(ABHt32)

# From Hunter et al
data(HSJt35)
Qrbar(HSJt35)
aprox.Qrbar(HSJt35)

psychometric documentation built on Nov. 6, 2023, 1:06 a.m.