Answering R4DS learning community question on whether stratified sampling. Generally probably don't need to worry about biasing parameter estimates.

stratified-sampling-parameter-estimates.R

library(tidyverse)

sim_params <- function(n_a = 100, n_b = 400, suffix = ""){
  
  tibble(id = c(rep("a", n_a), rep("b", n_b)), 
         vals = c(rnorm(n_a, 5), rnorm(n_b, 3))
  ) %>% 
    lm(vals ~ id, data = .) %>% 
    broom::tidy() %>% 
    select(term, estimate) %>% 
    rename_with(~paste0(.x, suffix))
}

comparing_estimates <- tibble(sim_id = 1:1000) %>% 
  mutate(imbalanced = map(sim_id, sim_params, suffix = "_imbalanced"),
         balanced = map(sim_id, ~sim_params(n_a = 250, n_b = 250, suffix = "_balanced"))) %>% 
  unnest(c(imbalanced, balanced))

comparing_estimates %>% 
  pivot_longer(cols = contains("estimate")) %>% 
  ggplot(aes(x = value, fill = name))+
  geom_density(alpha = 0.3)+
  facet_wrap(~term_balanced, ncol = 1, scales = "free_x")