Estimating IQ means from Hegelund et al 2020
04 July, 2024
- Hegelund, E. R., Flensborg-Madsen, T., Dammeyer, J., Mortensen, L. H., & Mortensen, E. L. (2019). The influence of familial factors on the association between IQ and educational and occupational achievement: A sibling approach. Personality and Individual Differences, 149, 100-107. https://www.sciencedirect.com/science/article/pii/S0191886919303411
Based on this paper, we can estimate the mean IQ of immigrants, approximately, by simulating data in order to arrive at the proportions seen in the study.
Init
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theme_set(theme_bw())
options(
digits = 3
)Functions
run_simulations = function(danish_n, nondanish_n, step_size = 0.1, lower_limit = 80, upper_limit = 90, replicates = 5) {
#generate range of nondanish means
nondanish_means = seq(lower_limit, upper_limit, by = step_size) %>% rep(replicates)
#loop across
results = map_dfr(nondanish_means, ~{
nondanish_mean = .x
#simulate data
dd = bind_rows(
tibble(
group = "danish",
IQ = rnorm(danish_n, 100, 15)
),
tibble(
group = "nondanish",
IQ = rnorm(nondanish_n, nondanish_mean, 15)
)
) %>%
#bands
mutate(
IQ_band = cut(IQ, breaks = c(-Inf, 85, 115, Inf), labels = c("low", "middle", "high"))
)
#proportions of nondanes in bands
results = dd %>%
group_by(IQ_band) %>%
summarise(
prop_nondanish = mean(group == "nondanish")
)
#return
tibble(
nondanish_low = results$prop_nondanish[results$IQ_band == "low"],
nondanish_middle = results$prop_nondanish[results$IQ_band == "middle"],
nondanish_high = results$prop_nondanish[results$IQ_band == "high"],
danish_n = danish_n,
nondanish_n = nondanish_n,
nondanish_mean = nondanish_mean
)
})
}Analysis
#sample sizes
danish_sizes = c(
30892, 173649, 39891
)
nondanish_sizes = c(
4860, 8059, 440
)
#true nondanish proportions
true_nondanish_props = nondanish_sizes / (danish_sizes + nondanish_sizes)
#run simulations
set.seed(1)
results = run_simulations(
danish_n = danish_sizes %>% sum(),
nondanish_n = nondanish_sizes %>% sum()
)
#calculate deviations from expectation
results %<>%
mutate(
deviation = abs(nondanish_low - true_nondanish_props[1]) +
abs(nondanish_middle - true_nondanish_props[2]) +
abs(nondanish_high - true_nondanish_props[3])
)
#deviation as function of immigrant mean
results %>%
ggplot(aes(nondanish_mean, deviation)) +
geom_point() +
#make smooth line fit but increase smoothness
geom_smooth(span = 0.2) +
scale_x_continuous(breaks = seq(0, 100, 1)) +
labs(
x = "Assumed IQ mean of non-Danes, relative to Danish 100",
y = "Sum of absolute deviations from true proportions"
)## [1m[22m`geom_smooth()` using method = 'loess' and formula = 'y ~ x'
Meta
#versions
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