The ratings of 6 laptops in two websites A and B are given below- Find the rank coefficient for the ratings of the two websites- beginarray - WhineLaptops - A - B WhlineL1- 7 - 8 Whline L2 - 8-5 - 9-5 illhline L3 - 9-5 - 8 whline L4 - 8 - 8 lilhline L5 - 8-5 - 6-5 illhlineL6 - 7-5 - 7-5 11 hline e n d a r r a y A- 0-095B- 0-114- 0-174D- 0-235

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Spearman's Rank Coefficient for Repeating Ranks

The ratings o...

Question

The ratings of 6 laptops in two websites A and B are given below. Find the rank coefficient for the ratings of the two websites.

$\begin{matrix} L a p t o p s & A & B L_{1} & 7 & 8 L_{2} & 8.5 & 9.5 L_{3} & 9.5 & 8 L_{4} & 8 & 8 L_{5} & 8.5 & 6.5 L_{6} & 7.5 & 7.5 \end{matrix}$

0.095

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0.114

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0.174

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0.235

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Solution

The correct option is B
0.114

Convert the ratings to the corresponding ranks and calculate the deviations.

$\begin{matrix} L a p t o p s & A & B & D_{i} = A - B & D_{i}^{2} L_{1} & 6 & 3 & 3 & 9 L_{2} & 2.5 & 1 & 1.5 & 2.25 L_{3} & 1 & 3 & - 2 & 4 L_{4} & 4 & 3 & 1 & 1 L_{5} & 2.5 & 6 & - 3.5 & 12.25 L_{6} & 5 & 5 & 0 & 0 \sum = 28.5 \end{matrix}$

The rank 2.5 is repeating 2 times for A and the rank 3 is repeating 3 times for B
$∴ m_{1} = 2 m_{2} = 3$
$r_{k} = 1 - \frac{6 [\sum D_{i}^{2} + \frac{m_{1}^{3} - m_{1}}{12} + \frac{m_{2}^{3} - m_{2}}{12} + \dots]}{n^{3} - n}$
$= 1 - \frac{6 \times (28.5 + 0.5 + 2)}{216 - 6} = 1 - \frac{186}{210} = 0.114$

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