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Question
Arjun has calculated the Spearman's rank coefficient for 6 students based on their scores in economics and mathematics to be 0.69. Three students had the same score in economics and 2 students had the same score in Mathematics. Arjun forgot to add the correction factor in his calculations. What will be the corrected Rank coefficient?
Arjun has calculated the Spearman's rank coefficient for 6 students based on their scores in economics and mathematics to be 0.69. Three students had the same score in economics and 2 students had the same score in Mathematics. Arjun forgot to add the correction factor in his calculations. What will be the corrected Rank coefficient?
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Solution
The correct option is A 0.58
Without correction, the rank coefficient is given by
rk=1−6∑D2in3−n=0.69
With correction, the rank coefficient is
rk=1−6∑[D2i+m31−m112+m32−m212+…]n3−n=0.69−6×m31−m112+m32−m212n3−nGiven, m1=2 & m2=3
∴corrected rk=0.69−6×6+2412×(63−6)=0.69−0.07=0.62
0.58
Without correction, the rank coefficient is given by
rk=1−6∑D2in3−n=0.69
With correction, the rank coefficient is
rk=1−6∑[D2i+m31−m112+m32−m212+…]n3−n=0.69−6×m31−m112+m32−m212n3−nGiven, m1=2 & m2=3
∴corrected rk=0.69−6×6+2412×(63−6)=0.69−0.07=0.62
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