Correlation between effect sizes

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library(tidyverse)
library(here)

DATA_PATH <- here("data/processed/syntactic_bootstrapping_tidy_data.csv") 
d <- read.csv(DATA_PATH)

calculate raw effect size

d <- d %>% 
  mutate(
    d_calc_raw = case_when(
      !is.na(x_2_raw) & !is.na(sd_2_raw) ~ (x_1 - x_2_raw) / sqrt((sd_1^2 + sd_2_raw^2)/2),
      TRUE ~  NA_real_ 
    ), 
    d_var_calc_raw = case_when(
      !is.na(x_2_raw) & !is.na(sd_2_raw) ~  (1 / n_1) + (d_calc_raw ^ 2 / (2 * n_1)), 
      TRUE ~ NA_real_
    )) 

d_with_raw <- d %>% filter(!is.na(d_calc_raw))

cor.test(d_with_raw$d_calc,
         d_with_raw$d_calc_raw)

    Pearson's product-moment correlation

data:  d_with_raw$d_calc and d_with_raw$d_calc_raw
t = 0.74497, df = 11, p-value = 0.4719
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.3774018  0.6871646
sample estimates:
      cor 
0.2191553 

d_with_raw %>% ggplot(aes(x = d_calc, y = d_calc_raw, color = unique_id)) + 
  geom_point()