[Feature] cor_diff() : test for differences between correlations

[DominiqueMakowski]

Simple function with parametric vs. bootstrapped approaches. I ran some simulations and it seems to nicely work.

correlation::cor_diff(iris, c("Sepal.Length", "Sepal.Width"), c("Sepal.Length", "Petal.Width"))
#> Correlation Difference Test
#> 
#> Method     |      t |      p
#> ----------------------------
#> parametric | -10.00 | < .001

^{Created on 2025-01-29 with reprex v2.1.1}

[DominiqueMakowski]

@bwiernik @mattansb do you know of any way to compute a Bayes factor for that?
It uses psych::r.test() internally for the parametric test

[strengejacke]

[mattansb]

I'm unfamiliar with a Bayes factor for such a comparison.

[DominiqueMakowski]

bayestestR::p_to_bf() go brrrrrr

[bwiernik]

Didn't look into code yet.

The straightforward approach to these tests is to do a Fisher z transform and then do a z test for the difference (potentially accounting for covariance).

So BF methods analogous to a z test would work

[DominiqueMakowski]

Test:

library(ggplot2)
library(correlation)

rez <- data.frame()
for(r in seq(0, 0.6, length.out=200)) {
  for(n in seq(20, 100, by=30)) {
    
    data <- bayestestR::simulate_correlation(
      n = n, 
      r = matrix(c(
        1.0, r, 0.0,
        r, 1.0, 0.0,
        0.0, 0.0, 1.0), nrow = 3))
    
    rez <- cor_diff(data, x="V1", y="V2", x2="V1", y2="V3", method = "parametric") |>
      datawizard::data_rename("t", "z") |> 
      rbind(cor_diff(data, x="V1", y="V2", x2="V1", y2="V3", method = "bootstrapping", iterations=2000)) |>  
      datawizard::data_modify(n = n, r = r) |> 
      rbind(rez)
  }
}

rez |> 
  datawizard::reshape_longer(select=-c("r", "n", "Method")) |>
  datawizard::data_modify(type = ifelse(name %in% c("p"), "p-value", "z-value")) |> 
  ggplot(aes(x=r, y=value)) +
  geom_smooth(aes(group=interaction(Method, n), color=n), method="loess", se=FALSE, formula = 'y ~ x') +
  geom_point(aes(color=n), alpha=0.1) +
  facet_grid(type~Method, scales="free_y", switch="y") +
  theme_minimal()