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

• Ties-corrected Spearman

  Using method="spearman" gives you the ties-corrected Spearman. Spearman's rho, according to the definition, is simply the Pearson's sample correlation coefficient computed for ranks of sample data. So it works both in presence and in absence of ties. You can see that after replacing your original data with their ranks (midranks for ties) and using method="pearson", you will get the same result:

  > cor.test(rank(c(1,2,3,4,5,6,7,8)), rank(c(0,0,0,0,0,0,7,8)), method="pearson")
  
  Pearson's product-moment correlation
  
  data:  rank(c(1, 2, 3, 4, 5, 6, 7, 8)) and rank(c(0, 0, 0, 0, 0, 0, 7, 8))
  t = 2.8983, df = 6, p-value = 0.0274
  alternative hypothesis: true correlation is not equal to 0
  95 percent confidence interval:
   0.1279559 0.9546436
  sample estimates:
    cor 
  0.7637626 
  

  Notice, there exists a simplified no-ties Spearman version, that is in fact used in cor.test() implementation in absence of ties, but it is equivalent to the definition above.

• P-value

  In case of ties in data, exact p-values are not computed neither for Spearman nor for Kendall measures (within cor.test() implementation), hence the warning. As mentioned in Eduardo's post, for not to get a warning you should set exact=FALSE,