misspecified estimand explains result

estimand_sex_diff.R

library(dplyr)
N = 10000
people <- tibble(
  male = sample(0:1, N, TRUE),
  trait = rnorm(N) + male)
true_means <- people %>% 
  group_by(male) %>% 
  summarise(sex_mean = mean(trait))
people <- people %>% left_join(true_means) %>% 
  left_join(true_means %>% rename(opposite_sex_mean = sex_mean) %>% mutate(male = 1-male)) %>% 
  mutate(unspecified = trait,
         same_sex = trait - sex_mean,
         opposite_sex = trait - opposite_sex_mean)

effsize::cohen.d(unspecified ~ male, people)
#> Cohen's d
#> 
#> d estimate: -1.043947 (large)
effsize::cohen.d(opposite_sex ~ male, people)
#> Cohen's d
#> 
#> d estimate: -2.087894 (large)
effsize::cohen.d(same_sex ~ male, people)
#> Cohen's d
#> 
#> d estimate: -9.587134e-17 (negligible)