Spearman correlation and ties

Question

I\'m computing Spearman\'s rho on small sets of paired rankings. Spearman is well known for not handling ties properly. For example, taking 2 sets of 8 rankings, even if 6 a

Answer 1

cor.test with method="spearman" actually calculates Spearman coefficient corrected for ties. I've checked it by "manually" calculating tie-corrected and tie-uncorrected Spearman coefficients from equations in Zar 1984, Biostatistical Analysis. Here's the code - just substitute your own variable names to check for yourself:

ym <- data.frame(lousy, dors) ## my data

## ranking variables
ym$l <- rank(ym$lousy)
ym$d <- rank(ym$dors)


## calculating squared differences between ranks
ym$d2d <- (ym$l-ym$d)^2



## calculating variables for equations 19.35 and 19.37 in Zar 1984

lice <- as.data.frame(table(ym$lousy))

lice$t <- lice$Freq^3-lice$Freq

dorsal <- as.data.frame(table(ym$dors))

dorsal$t <- dorsal$Freq^3-dorsal$Freq

n <- nrow(ym)
sum.d2 <- sum(ym$d2d)
Tx <- sum(lice$t)/12
Ty <-sum(dorsal$t)/12


## calculating the coefficients

rs1 <- 1 - (6*sum.d2/(n^3-n))  ## "standard" Spearman cor. coeff. (uncorrected for ties) - eq. 19.35

rs2 <- ((n^3-n)/6 - sum.d2 - Tx - Ty)/sqrt(((n^3-n)/6 - 2*Tx)*((n^3-n)/6 - 2*Ty)) ## Spearman cor.coeff. corrected for ties - eq.19.37


##comparing with cor.test function
cor.test(ym$lousy,ym$dors, method="spearman") ## cor.test gives tie-corrected coefficient!