dat.bornmann2007.RdResults from 21 studies on gender differences in grant and fellowship awards.
dat.bornmann2007The data frame contains the following columns:
| study | character | study reference |
| obs | numeric | observation within study |
| doctype | character | document type |
| gender | character | gender of the study authors |
| year | numeric | (average) cohort year |
| org | character | funding organization / program |
| country | character | country of the funding organization / program |
| type | character | fellowship or grant application |
| discipline | character | discipline / field |
| waward | numeric | number of women who received a grant/fellowship award |
| wtotal | numeric | number of women who applied for an award |
| maward | numeric | number of men who received a grant/fellowship award |
| mtotal | numeric | number of men who applied for an award |
The studies in this dataset examine whether the chances of receiving a grant or fellowship award differs for men and women. Note that many studies provide multiple comparisons (e.g., for different years / cohorts / disciplines). A multilevel meta-analysis model can be used to account for the multilevel structure in these data.
Bornmann, L., Mutz, R., & Daniel, H. (2007). Gender differences in grant peer review: A meta-analysis. Journal of Informetrics, 1(3), 226–238. https://doi.org/10.1016/j.joi.2007.03.001
Marsh, H. W., Bornmann, L., Mutz, R., Daniel, H.-D., & O'Mara, A. (2009). Gender effects in the peer reviews of grant proposals: A comprehensive meta-analysis comparing traditional and multilevel approaches. Review of Educational Research, 79(3), 1290–1326. https://doi.org/10.3102/0034654309334143
sociology, odds ratios, multilevel models
### copy data into 'dat' and examine data
dat <- dat.bornmann2007
head(dat, 16)
#> study obs doctype gender year org country type discipline
#> 1 Ackers (2000) 1 Grey M&F 1996.0 MSCA Europe Fellowship Physical Sciences
#> 2 Ackers (2000) 2 Grey M&F 1996.0 MSCA Europe Fellowship Physical Sciences
#> 3 Ackers (2000) 3 Grey M&F 1996.0 MSCA Europe Fellowship Physical Sciences
#> 4 Ackers (2000) 4 Grey M&F 1996.0 MSCA Europe Fellowship Physical Sciences
#> 5 Ackers (2000) 5 Grey M&F 1996.0 MSCA Europe Fellowship Social Sciences / Biology
#> 6 Ackers (2000) 6 Grey M&F 1996.0 MSCA Europe Fellowship Physical Sciences
#> 7 Ackers (2000) 7 Grey M&F 1996.0 MSCA Europe Fellowship Life Sciences / Biology
#> 8 Allmendinger (2002) 1 Article M&F 1993.0 DFG Europe Grant Social Sciences / Biology
#> 9 Allmendinger (2002) 2 Article M&F 1994.0 DFG Europe Grant Social Sciences / Biology
#> 10 Allmendinger (2002) 3 Article M&F 1995.0 DFG Europe Grant Social Sciences / Biology
#> 11 Allmendinger (2002) 4 Article M&F 1996.0 DFG Europe Grant Social Sciences / Biology
#> 12 Allmendinger (2002) 5 Article M&F 1997.0 DFG Europe Grant Social Sciences / Biology
#> 13 Allmendinger (2002) 6 Article M&F 1998.0 DFG Europe Grant Social Sciences / Biology
#> 14 Allmendinger (2002) 7 Article M&F 1999.0 DFG Europe Grant Social Sciences / Biology
#> 15 Bazeley (1998) 1 Article F 1995.0 ARC Australia Grant Multidisciplinary
#> 16 Bornmann (2005) 1 Article M 1992.5 BIF Europe Fellowship Life Sciences / Biology
#> waward wtotal maward mtotal
#> 1 139 711 274 1029
#> 2 45 258 166 908
#> 3 44 236 219 928
#> 4 63 251 96 507
#> 5 157 910 252 1118
#> 6 114 589 460 2244
#> 7 381 2027 489 2275
#> 8 8 13 53 72
#> 9 5 8 53 82
#> 10 6 8 63 97
#> 11 8 16 53 94
#> 12 4 11 43 92
#> 13 20 44 55 93
#> 14 5 15 70 116
#> 15 11 56 82 344
#> 16 204 1085 430 1612
### load metafor package
library(metafor)
### calculate log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=waward, n1i=wtotal, ci=maward, n2i=mtotal, data=dat)
### fit multilevel meta-analysis model
res <- rma.mv(yi, vi, random = ~ 1 | study/obs, data=dat)
res
#>
#> Multivariate Meta-Analysis Model (k = 66; method: REML)
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2.1 0.0161 0.1268 21 no study
#> sigma^2.2 0.0038 0.0613 66 no study/obs
#>
#> Test for Heterogeneity:
#> Q(df = 65) = 221.2850, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> -0.1010 0.0417 -2.4196 0.0155 -0.1828 -0.0192 *
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### estimated average odds ratio (with 95% CI/PI)
predict(res, transf=exp, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 0.90 0.83 0.98 0.68 1.21
#>
### test for a difference between fellowship and grant applications
res <- rma.mv(yi, vi, mods = ~ type, random = ~ 1 | study/obs, data=dat)
res
#>
#> Multivariate Meta-Analysis Model (k = 66; method: REML)
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2.1 0.0045 0.0670 21 no study
#> sigma^2.2 0.0035 0.0596 66 no study/obs
#>
#> Test for Residual Heterogeneity:
#> QE(df = 64) = 133.4811, p-val < .0001
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 11.2312, p-val = 0.0008
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt -0.2010 0.0429 -4.6816 <.0001 -0.2852 -0.1169 ***
#> typeGrant 0.1890 0.0564 3.3513 0.0008 0.0785 0.2995 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
predict(res, newmods=0:1, transf=exp, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 1 0.82 0.75 0.89 0.67 0.99
#> 2 0.99 0.92 1.06 0.82 1.20
#>