# Spearman's rho to correlate discrete with binary variables

Is it ok to use the Spearman's rho if one has to correlate a binary and a discrete (from 0 to 100) variable? Or Kendall's tau b would be a better choice?

• Since binary scale has only one interval it cannot be named "interval" or "ordinal"; rather, it is on its own. Both interval (such as Pearson r) or ordinal (such as Spearman or Kendall) association measures are valid for it. Now, if you think that the other, 0-100, variable is equiinterval (i.e. distance between 5-10 = distance 25-30 = distance 95-100) you may use Pearson r. If you don't, use Spearman or Kendall. Some differences between the latter two are described e.g. here. – ttnphns Jan 14 '14 at 11:52
• Thanks. I was also worried by the potentially high number of ties one may encounter when dealing with a binary variable. For this reason I'm also in doubt about using Spearman's rho. – Forinstance Jan 14 '14 at 11:56
• Ties are not as awful as they might seem to you. Well, if you are scared, add tiny random fractional noise to your values, to put away ties. You'll see that this doesn't affect Spearman greatly. – ttnphns Jan 14 '14 at 12:02

Since binary scale has only one interval it cannot be named "interval" or "ordinal"; rather, it is on its own. Both interval (such as Pearson $$r$$) or ordinal (such as Spearman or Kendall) association measures are valid for it. Now, if you think that the other, 0-100, variable is equiinterval (i.e. distance between 5-10 = distance 25-30 = distance 95-100) you may use Pearson $$r$$. If you don't, use Spearman or Kendall. Some differences between the latter two are described e.g. How do the Goodman-Kruskal gamma and the Kendall tau or Spearman rho correlations compare?. – ttnphns