Example of how selecting top 10% of papers can induce negative correlation between positively associated desired features

berkson_journal.R

# berkson's paradox journal example

library(rethinking)

n <- 500
rho <- 0.25
y <- rmvnorm2( n , Mu=c(0,0) , sigma=c(1,1) , Rho=matrix( c(1,rho,rho,1) , 2 , 2 ) )
b <- 1
score <- y[,1] + b*y[,2]
theshold <- quantile( score , 0.9 )
pass <- ( score > theshold )

plot( y  , xlab="rigorous" , ylab="innovative" ) 

plot( y  , xlab="rigorous" , ylab="innovative" , 
    pch=ifelse(pass,16,1) , 
    col=ifelse(pass,"orange","black") ) 
abline( a=theshold/b , b=-1/b , lwd=0.5 )

cor( y )
cor( y[pass,] )