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

To find the Spearman Rank Correlation Coefficient (rs), we use the formula:
rs = 1 - (6 Σd^2)/(n(n^2 -1))
where Σd^2 is the sum of squared differences in ranks, and n is the sample size (in this case, n= 10 for both men and women).

Given Σd^2 = 8 and n=10, we can calculate rs as follows:
rs = 1 - (6 * 8)/(10* (10^2 -1))
rs = 1 - (48/990)
rs = 0.952

Therefore, the answer is B.

A Researcher Wished to Compare the Automobile Colour Preferences of Men