Results from 9 studies on the reliability of the Center for Epidemiologic Studies Depression (CES-D) Scale administered to children providing care to an elderly parent.

dat.bonett2010

Format

The data frame contains the following columns:

studynumericstudy number
sourcecharactersource of data
ninumericsample size
minumericnumber of items in the scale
ainumericobserved value of Cronbach's alpha
caregiverscharactergender of the children in the sample

Details

The Center for Epidemiologic Studies Depression (CES-D) Scale is a 20-item questionnaire assessing various symptoms of depression, with each item scored on a 4-point scale. The scale has been used in several studies to examine depressive symptoms in children providing care to an elderly parent. The dataset includes information on the reliability of the scale as measured with Cronbach's alpha in 9 such studies. Also, the gender composition of the children in each sample is indicated.

Source

Bonett, D. G. (2010). Varying coefficient meta-analytic methods for alpha reliability. Psychological Methods, 15(4), 368--385. https://doi.org/10.1037/a0020142

References

Bonett, D. G. (2002). Sample size requirements for testing and estimating coefficient alpha. Journal of Educational and Behavioral Statistics, 27(4), 335--340. https://doi.org/10.3102/10769986027004335

Hakstian, A. R., & Whalen, T. E. (1976). A k-sample significance test for independent alpha coefficients. Psychometrika, 41(2), 219--231. https://doi.org/10.1007/BF02291840

Examples

### copy data into 'dat' and examine data
dat <- dat.bonett2010
dat
#>   study                           source  ni   ai mi caregivers
#> 1     1 Atienza & Parris Stephens (2000) 103 0.93 20      women
#> 2     2             Hooker et al. (2002)  64 0.91 20      mixed
#> 3     3            Martire et al. (1997) 118 0.94 20      women
#> 4     4               Bass et al. (1996) 401 0.89 20      mixed
#> 5     5             Miller et al. (1995) 215 0.90 20      mixed
#> 6     6             Hooker et al. (1992)  51 0.89 20      mixed
#> 7     7             Hooker et al. (2000) 175 0.86 20      mixed
#> 8     8              Brody et al. (1990) 311 0.91 20      mixed
#> 9     9              Brody et al. (1995) 492 0.90 20      women

# \dontrun{

### load metafor package
library(metafor)

### meta-analysis using the raw alpha values
res <- rma(measure="ARAW", ai=ai, mi=mi, ni=ni, data=dat)
res
#> 
#> Random-Effects Model (k = 9; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 0.0004 (SE = 0.0003)
#> tau (square root of estimated tau^2 value):      0.0199
#> I^2 (total heterogeneity / total variability):   81.02%
#> H^2 (total variability / sampling variability):  5.27
#> 
#> Test for Heterogeneity:
#> Q(df = 8) = 37.9808, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se      zval    pval   ci.lb   ci.ub     ​ 
#>   0.9052  0.0077  118.2471  <.0001  0.8902  0.9202  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### meta-analysis using transformed alpha values (using the
### transformation suggested by Hakstian & Whalen, 1976)
res <- rma(measure="AHW", ai=ai, mi=mi, ni=ni, data=dat)
res
#> 
#> Random-Effects Model (k = 9; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 0.0011 (SE = 0.0007)
#> tau (square root of estimated tau^2 value):      0.0328
#> I^2 (total heterogeneity / total variability):   81.43%
#> H^2 (total variability / sampling variability):  5.39
#> 
#> Test for Heterogeneity:
#> Q(df = 8) = 35.1131, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se     zval    pval   ci.lb   ci.ub     ​ 
#>   0.5440  0.0125  43.4201  <.0001  0.5195  0.5686  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
predict(res, transf=transf.iahw)
#> 
#>    pred  ci.lb  ci.ub  pi.lb  pi.ub 
#>  0.9052 0.8891 0.9197 0.8555 0.9420 
#> 

### meta-analysis using transformed alpha values (using the
### transformation suggested by Bonett, 2002)
res <- rma(measure="ABT", ai=ai, mi=mi, ni=ni, data=dat)
res
#> 
#> Random-Effects Model (k = 9; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 0.0461 (SE = 0.0302)
#> tau (square root of estimated tau^2 value):      0.2147
#> I^2 (total heterogeneity / total variability):   81.40%
#> H^2 (total variability / sampling variability):  5.38
#> 
#> Test for Heterogeneity:
#> Q(df = 8) = 33.3957, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se     zval    pval   ci.lb   ci.ub     ​ 
#>   2.3561  0.0824  28.6085  <.0001  2.1947  2.5175  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
predict(res, transf=transf.iabt)
#> 
#>    pred  ci.lb  ci.ub  pi.lb  pi.ub 
#>  0.9052 0.8886 0.9193 0.8512 0.9396 
#> 

### forest plot
forest(res, slab=dat$source, header=TRUE, atransf=transf.iabt, refline=coef(res))


### examine whether female/mixed samples yield different alphas (with raw alphas)
res <- rma(measure="ARAW", ai=ai, mi=mi, ni=ni, mods = ~ caregivers, data=dat)
res
#> 
#> Mixed-Effects Model (k = 9; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of residual heterogeneity):     0.0003 (SE = 0.0002)
#> tau (square root of estimated tau^2 value):             0.0159
#> I^2 (residual heterogeneity / unaccounted variability): 71.80%
#> H^2 (unaccounted variability / sampling variability):   3.55
#> R^2 (amount of heterogeneity accounted for):            36.19%
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 7) = 26.6797, p-val = 0.0004
#> 
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 4.3519, p-val = 0.0370
#> 
#> Model Results:
#> 
#>                  estimate      se      zval    pval   ci.lb   ci.ub     ​ 
#> intrcpt            0.8949  0.0083  107.7806  <.0001  0.8786  0.9111  *** 
#> caregiverswomen    0.0277  0.0133    2.0861  0.0370  0.0017  0.0536    * 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
predict(res, newmods=c(0,1), digits=2)
#> 
#>   pred   se ci.lb ci.ub pi.lb pi.ub 
#> 1 0.89 0.01  0.88  0.91  0.86  0.93 
#> 2 0.92 0.01  0.90  0.94  0.89  0.96 
#> 

# }