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How can you find r correlation coefficient for ordinal data in a table - in R?

I am wondering how to find r, the correlation coefficient for a contingency table of an ordinal dataset. My text gives the following formula: formula attached

Is there an R package or function that does this calculation?

For example, if my table was

T <- as.table(rbind(
     c(9, 44, 13, 10), 
     c(11, 52, 23, 22), 
     c(9, 41, 12, 27)))

dimnames(T) <- list(Var1 = c("A","B","C"), 
                     Var2 = c("W","X","Y","Z"))

Can R calculate r of this example data set for me quickly? The answer in this case should be r = 0.14

Solution

  • the polycor R package should be able to get to the correct solution:

    T
##     Var2
## Var1  W  X  Y  Z
##    A  9 44 13 10
##    B 11 52 23 22
##    C  9 41 12 27

# install.packages("polycor")
library(polycor)
polychor(T)
## [1] 0.148935