A researcher wished to compare the automobile colour preferences of men and women.An experiment was performed recording the preferences of 10 men and 10 women.If the sum of squares of the ranking
Differences is equal to 8, what is the Spearman Rank Correlation Coefficient ?
A)0.975
B)0.952
C)0.476
D)0.905

Question

A researcher wished to compare the automobile colour preferences of men and women.An experiment was performed recording the preferences of 10 men and 10 women.If the sum of squares of the ranking
Differences is equal to 8, what is the Spearman Rank Correlation Coefficient  ?
A)0.975 
B)0.952 
C)0.476 
D)0.905

Quizplus · Accepted Answer

The Spearman Rank Correlation Coefficient formula is:
r = 1- (6Σd²)/(n(n²-1))

where 
Σd² = sum of squares of ranking differences
n = number of pairs

Substituting the given values, we get:
r = 1- (6(8))/(20(20²-1))
r = 0.952
Therefore, the best choice is B. The Spearman Rank Correlation Coefficient can be calculated using the formula 1- (6Σd^2)/(n(n^2-1)), where d is the difference in ranks and n is the sample size. Plugging in the values given in the question, we get 1-(6*8)/(20*19) = 0.952. Therefore, the best choice is B.

A Researcher Wished to Compare the Automobile Colour Preferences of Men