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Why am I getting different results for Pearson and Spearman correlation, although I am already comparing ranks?
a <- c(1,2,3,1,2,3)
b <- c(1,2,2,1,2,3)
cor(a, b, method="pearson")
# [1] 0.8911328
cor(a, b, method="spearman")
# [1] 0.9036961
Formula to use when there are tied ranks seems identical to formula for pearson correlation.
As far as I understand, spearman correlation is just pearson correlation on the ranks. Right?
As pointed out by @mdewey I am not already using ranks. If I use the correct ranks results are identical as expected.
a <- c(1,2,3,3)
b <- c(1,2,2,1)
cor(a, b, method="spearman")
# [1] 0.2357023
rank(a)
# [1] 1.0 2.0 3.5 3.5
rank(b)
# [1] 1.5 3.5 3.5 1.5
cor(rank(a), rank(b), method="spearman")
# [1] 0.2357023
aas if it represented positions in a race among six people: two people tied for each position. There are various ways to assign ranks with ties, but typically the ranks that would be given to the top two places--namely 1 and 2--would be averaged, giving a rank of 1.5 to the first two finishers. Similarly, the next two would have equal ranks of 3.5 and the last two would have ranks of 5.5. $\endgroup$ – whuber♦ Jun 4 '18 at 15:03