Question

Comparison between Spearman’s rho and Kendall’s tau

23 Apr 2024
Answer :
Word Count : 634
Feature/Aspect Spearman’s Rho Kendall’s Tau
Definition Measures rank correlation, assessing how well the relationship between two variables can be described using a monotonic function. Measures rank correlation, focusing on the ordinal association between two quantities.
Calculation Based on the difference between ranks of each pair of observations. Based on the number of concordant and discordant pairs.
Formula ρ=1−6∑di2n(n2−1)\rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}ρ=1−n(n2−1)6∑di2​​ where did_idi​ is the difference in ranks and nnn is the number of observations. τ=2(P−Q)n(n−1)\tau = \frac{2(P - Q)}{n(n-1)}τ=n(n−1)2(P−Q)​ where PPP is the number of concordant pairs and QQQ is the number of discordant pairs.
Range -1 to +1 -1 to +1
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