Unravelling the gender productivity gap in science
Question 1a - Gender productivity gap (individual-based)
Camila de Toledo Castanho
May 13, 2019
Installing required packages
install.packages (c("metafor", "rmarkdown", "knitr")Loading required packages
library (metafor)## Loading required package: Matrix## Loading 'metafor' package (version 2.0-0). For an overview
## and introduction to the package please type: help(metafor).library(knitr)
library(rmarkdown)Loading data
Q1a<-read.table("Q1a.txt", header=TRUE, sep="\t")
str(Q1a)## 'data.frame': 18 obs. of 12 variables:
## $ ID_article : int 68 69 69 218 239 395 396 435 441 486 ...
## $ ID_observation : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Reference : Factor w/ 14 levels "Addessi et al. 2012",..: 6 1 1 11 2 12 10 8 7 13 ...
## $ Time : Factor w/ 3 levels "20th","21st",..: 3 2 2 3 3 1 1 NA NA 2 ...
## $ Research_field : Factor w/ 14 levels "Behavioral and educational sciences ",..: 3 9 9 4 7 11 8 2 13 5 ...
## $ Research_field.2: Factor w/ 4 levels "Biological science",..: 1 1 1 1 1 3 3 1 4 4 ...
## $ N_men : int 233 72 88 129 305 2276 6230 262 255 71 ...
## $ N_wom : int 183 98 61 39 136 731 2937 138 162 27 ...
## $ Mean_men : num 3.02 1.25 1.71 28.26 12.4 ...
## $ Mean_wom : num 2.18 1.11 1.22 20.23 9.1 ...
## $ SD_men : num 1.29 1.19 1.03 18.13 9.35 ...
## $ SD_wom : num 0.95 0.79 0.13 11.27 6.25 ...Calculating effect sizes (yi) and variances (vi)
Q1a<-escalc(measure="SMD", m1i=Mean_men, m2i=Mean_wom, sd1i=SD_men, sd2i=SD_wom, n1i=N_men, n2i=N_wom, data=Q1a, vtype="UB")
Q1a## ID_article ID_observation Reference Time
## 1 68 1 Krista et al. 2012 Mix
## 2 69 2 Addessi et al. 2012 21st
## 3 69 3 Addessi et al. 2012 21st
## 4 218 4 Symonds et al. 2006 Mix
## 5 239 5 Braisher et al. 2005 Mix
## 6 395 6 Xie & Shauman 1998 20th
## 7 396 7 Sax et al. 2002 20th
## 8 435 8 Long et al. 1993 <NA>
## 9 441 9 Leahey 2006 <NA>
## 10 486 10 van den Besselaar & Sandstrom 2016 21st
## 11 486 11 van den Besselaar & Sandstrom 2016 21st
## 12 486 12 van den Besselaar & Sandstrom 2016 21st
## 13 625 13 Henderson et al. 2014 21st
## 14 781 14 Mueller et al. 2017 <NA>
## 15 781 15 Mueller et al. 2017 <NA>
## 16 781 16 Mueller et al. 2017 <NA>
## 17 854 17 Frandsen et al. 2015 Mix
## 18 1001 18 Cikara et al. 2012 21st
## Research_field Research_field.2
## 1 Biology Biological science
## 2 Primatology Biological science
## 3 Primatology Biological science
## 4 Ecology and Evolution Biological science
## 5 Life science Biological science
## 6 Several Mix
## 7 Not informed, but we supposes all universities areas Mix
## 8 Biochemistry Biological science
## 9 Sociology and linguistics Social science
## 10 Economics Social science
## 11 Behavioral and educational sciences Social science
## 12 Psychology Social science
## 13 Health Health
## 14 Surgery Health
## 15 Surgery Health
## 16 Surgery Health
## 17 Several Mix
## 18 Social Psicology Social science
## N_men N_wom Mean_men Mean_wom SD_men SD_wom yi vi
## 1 233 183 3.02 2.18 1.29 0.95 0.7272 0.0104
## 2 72 98 1.25 1.11 1.19 0.79 0.1423 0.0242
## 3 88 61 1.71 1.22 1.03 0.13 0.6119 0.0290
## 4 129 39 28.26 20.23 18.13 11.27 0.4756 0.0341
## 5 305 136 12.40 9.10 9.35 6.25 0.3868 0.0108
## 6 2276 731 4.02 3.05 5.45 4.46 0.1855 0.0018
## 7 6230 2937 2.79 2.47 1.20 1.09 0.2744 0.0005
## 8 262 138 1.41 1.61 0.98 1.08 -0.1966 0.0111
## 9 255 162 14.60 9.10 13.30 8.20 0.4736 0.0104
## 10 71 27 8.82 5.81 5.13 3.77 0.6222 0.0532
## 11 17 28 23.24 16.86 11.31 18.25 0.3912 0.0964
## 12 40 50 25.60 16.10 19.23 17.19 0.5197 0.0466
## 13 335 98 327.00 263.00 1373.71 785.05 0.0505 0.0132
## 14 51 23 23.47 16.56 22.58 14.21 0.3353 0.0639
## 15 45 10 45.69 25.50 32.07 11.85 0.6718 0.1266
## 16 59 18 85.78 61.83 66.60 44.85 0.3803 0.0735
## 17 63 78 0.88 0.77 2.17 3.11 0.0401 0.0287
## 18 30 23 28.20 15.50 6.30 2.90 2.4446 0.1375Hierarchical mixed effect meta-analysis
m.Q1a<-rma.mv(yi,vi, random=~1|ID_article/ID_observation,data=Q1a)
m.Q1a##
## Multivariate Meta-Analysis Model (k = 18; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.1767 0.4203 13 no ID_article
## sigma^2.2 0.0210 0.1450 18 no ID_article/ID_observation
##
## Test for Heterogeneity:
## Q(df = 17) = 100.0047, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.4177 0.1287 3.2449 0.0012 0.1654 0.6700 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1forest (m.Q1a, slab=Q1a$Reference, xlim=c(-5,6), cex=0.8, xlab = "Hedges'd", mlab = "Overall effect (18)")
text(-5,20, "Author(s) and Year", pos=4, font=2, cex=1)
text(6,20, "Hedges'd [95% CI]", pos=2, font=2, cex=1)
Heterogeneity
Heterogeneity I^2 for hierarchical models is not provided by metafor. We calculate total heterogeneity using the formulas provided by Nakagawa & Santos 2012. 1) Calculate sampling variance of the dataset (we use precision of effect size); 2) Use the variance components of the model associated with random factors (those summarized in the sigma2 structure components).
Sampling variance of the dataset
Q1a$wi <- 1/Q1a$vi
sv.mQ1a <- sum(Q1a$wi*(length(Q1a$wi)-1))/(sum(Q1a$wi)^2-sum(Q1a$wi^2))
sv.mQ1a## [1] 0.008995005Total heterogeneity
I2.total = (m.Q1a$sigma2[1]+m.Q1a$sigma2[2])/(m.Q1a$sigma2[1]+m.Q1a$sigma2[2] + sv.mQ1a) * 100
I2.total## [1] 95.64836Publication bias
Egger’s regression
Egger’s regression using the meta-analytic residuals as the response variable and the precision as the moderator, as proposed by Nakagawa & Santos 2012 for hierarchical models. If the intercept of Egger’s regression is significantly different from zero, there is evidence of publication bias.
egger.Q1a<-lm(residuals.rma(m.Q1a)~Q1a$vi)
summary(egger.Q1a)##
## Call:
## lm(formula = residuals.rma(m.Q1a) ~ Q1a$vi)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.54079 -0.31719 0.03689 0.18078 1.16122
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3102 0.1473 -2.106 0.05133 .
## Q1a$vi 8.5531 2.4945 3.429 0.00344 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4296 on 16 degrees of freedom
## Multiple R-squared: 0.4236, Adjusted R-squared: 0.3875
## F-statistic: 11.76 on 1 and 16 DF, p-value: 0.003444Sensitivity analysis
If residual standard >3 AND hatvalue >2 times the average of hatvalues, run analysis with those cases deleted to test for sensitivity (from Habeck & Schultz 2015).
rs.Q1a.me<-rstandard (m.Q1a)
hat.Q1a.me<-hatvalues(m.Q1a)/mean(hatvalues(m.Q1a))
plot(hat.Q1a.me, rs.Q1a.me$resid, xlab="hat / average hat value", ylab= "standard residuals",xlim=c(0,2.5), ylim=c(-3,3), cex.lab=1.2)
abline (h=-3)
abline (h=3)
abline (v=(2))