R Notebook

Meta-analysis of the IQ~income correlation. The previous Strenze meta-analysis is deflated by the fact that he frequently used samples of young adults or ones that were selected for educational attainment – this meta-analysis uses roughly representative datasets such as the PIAAC, NLSY, CFPS, and UK Biobank to avoid this issue, and also corrects for test reliability.

Data cleaning

im <- imeta
im$se <- sqrt(1-im$r^2)/sqrt(im$n-2)

im$cohort <- im$year - im$age

im$code <- countrycode(im$country, origin='country.name', destination='iso3c')
im$code[im$country=='North Ireland'] <- 'IRL'

im$corrr <- im$r/sqrt(im$testreliability*.85)

Data quality check.

plot(im$corrr, im$r)

Meta-analysis + funnel plot

metaobj <- metafor::rma(yi=corrr, sei=se, data=im)
summary(metaobj)

Random-Effects Model (k = 41; tau^2 estimator: REML)

  logLik  deviance       AIC       BIC      AICc   
 47.0673  -94.1347  -90.1347  -86.7569  -89.8104   

tau^2 (estimated amount of total heterogeneity): 0.0049 (SE = 0.0012)
tau (square root of estimated tau^2 value):      0.0699
I^2 (total heterogeneity / total variability):   95.26%
H^2 (total variability / sampling variability):  21.10

Test for Heterogeneity:
Q(df = 40) = 463.1361, p-val < .0001

Model Results:

estimate      se     zval    pval   ci.lb   ci.ub      
  0.3700  0.0115  32.1495  <.0001  0.3474  0.3926  *** 

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

funnel(metaobj, xlab='Correlation between IQ and income', cex = .7, cex.lab = 1.25)
text(im$corrr, im$se, labels = im$country, cex = .88, pos = 1)

Differences by country

metaobj <- metafor::rma(yi=corrr, sei=se, data=im, mods = ~ country)
summary(metaobj)

Mixed-Effects Model (k = 41; tau^2 estimator: REML)

   logLik   deviance        AIC        BIC       AICc   
  11.3512   -22.7023    47.2977    45.4045  2567.2977   

tau^2 (estimated amount of residual heterogeneity):     0.0019 (SE = 0.0012)
tau (square root of estimated tau^2 value):             0.0437
I^2 (residual heterogeneity / unaccounted variability): 87.10%
H^2 (unaccounted variability / sampling variability):   7.75
R^2 (amount of heterogeneity accounted for):            61.02%

Test for Residual Heterogeneity:
QE(df = 7) = 56.3170, p-val < .0001

Test of Moderators (coefficients 2:34):
QM(df = 33) = 81.7865, p-val < .0001

Model Results:

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1