YuKangTu

library(psych)

"
Analyze the difference between change and initial value. 

Source:
Tu, Y. K. (2016). Testing the relation between percentage change 
and baseline value. Scientific reports, 6.
"

YuKangTu <- function(x, y){
  # ratio of the coefficients of variation
  cv_ratio = (sd(x) / mean(x)) / (sd(y) / mean(y))
  
  # observed correlation
  rho = cor(x, (y-x)/x)
  
  # correlation under the null hypothesis
  rho_H0 = cor(x, (y - x) / x) + sqrt((1 - cor(x, y)/2))
  
  # z-test
  z = (fisherz(rho) - fisherz(rho_H0)) / sqrt(1 / (length(x)-3))
  p_val = pnorm(z) / 2
  
  return(c(cv_ratio, z, p_val))
}