If N=10 and rank order correlation (P, rho)= 0.80, then, which is the value of

Correct option is B

The rank order correlation is given by Spearman's Rank Correlation Coefficient formula:
ρ=1−6∑d2N(N2−1)\rho = 1 - \frac{6 \sum d^2}{N(N^2 - 1)}ρ=1−N(N2−1)6∑d2​
Where:
· ρ\rhoρ is the rank correlation coefficient
· ddd is the difference between the ranks of corresponding values
· NNN is the number of pairs of values
Given:
· N=10N = 10N=10
· ρ=0.80\rho = 0.80ρ=0.80
Now, we substitute these values into the formula and solve for ∑d2\sum d^2∑d2:
0.80=1−6∑d210(102−1)0.80 = 1 - \frac{6 \sum d^2}{10(10^2 - 1)}0.80=1−10(102−1)6∑d2​ 0.80=1−6∑d210(99)0.80 = 1 - \frac{6 \sum d^2}{10(99)}0.80=1−10(99)6∑d2​ 0.80=1−6∑d29900.80 = 1 - \frac{6 \sum d^2}{990}0.80=1−9906∑d2​ 0.80−1=−6∑d29900.80 - 1 = - \frac{6 \sum d^2}{990}0.80−1=−9906∑d2​ −0.20=−6∑d2990-0.20 = - \frac{6 \sum d^2}{990}−0.20=−9906∑d2​ 0.20=6∑d29900.20 = \frac{6 \sum d^2}{990}0.20=9906∑d2​ ∑d2=0.20×9906\sum d^2 = \frac{0.20 \times 990}{6}∑d2=60.20×990​ ∑d2=1986\sum d^2 = \frac{198}{6}∑d2=6198​ ∑d2=33\sum d^2 = 33∑d2=33
Thus, the value of ∑d2\sum d^2∑d2 is 33.
Information Booster:
1. Spearman's Rank Correlation: This non-parametric test measures the strength and direction of association between two ranked variables.
2. The formula involves computing the difference between ranks ddd, squaring those differences, and then plugging them into the equation.
3. The value ∑d2\sum d^2∑d2 represents the sum of the squared rank differences, a key factor in calculating the correlation coefficient.
Additional Information:
· Rank Order Correlation is used when the data are ordinal, and it is especially useful in situations where the data do not meet the assumptions required for Pearson’s correlation.
· The sum of squared rank differences (∑d2\sum d^2∑d2) directly impacts the magnitude of the correlation: the smaller ∑d2\sum d^2∑d2 is, the higher the rank correlation.