If, in a series, there are m items whose ranks are common, then which factor is added for correction for each repeating value in both series?

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Answer 1

Explanation

According to Spearman's rank correlation coefficient when ranks are repeated is as follows -

⇒ r_s = 1 - 6[(∑d² + (m₁³ - m₁)/12 + (m₂³ - m₂)/12 + -------)]/n(n² - 1)

m₁, m₂ ----- are the number of repetitions of the ranks

(m₁³ - m₁)/12 ----- are corresponding factors

∴ The factor is added for each repeating value in the both series is given by (m³ - m)/12 = m(m² - 1)/12 = m(m - 1)(m + 1)/12

Originally the spearsman rank correlation is denotted by rs = 1-6∑d2/n(n² - 1)