Explain the steps involved in the calculation of Spearman's Rank Correlation Coefficient.
Answers
Answer: sample Question:
The scores for nine students in physics and math are as follows:
Physics: 35, 23, 47, 17, 10, 43, 9, 6, 28
Mathematics: 30, 33, 45, 23, 8, 49, 12, 4, 31
Compute the student’s ranks in the two subjects and compute the Spearman rank correlation.
Step 1: Find the ranks for each individual subject. I used the Excel rank function to find the ranks. If you want to rank by hand, order the scores from greatest to smallest; assign the rank 1 to the highest score, 2 to the next highest and so on:
spearman rank correlation 1
Step 2: Add a third column, d, to your data. The d is the difference between ranks. For example, the first student’s physics rank is 3 and math rank is 5, so the difference is 3 points. In a fourth column, square your d values.
spreaman 2
Step 4: Sum (add up) all of your d-squared values.
4 + 4 + 1 + 0 + 1 + 1 + 1 + 0 + 0 = 12. You’ll need this for the formula (the Σ d2 is just “the sum of d-squared values”).
Step 5: Insert the values into the formula. These ranks are not tied, so use the first formula:
rank correlation coefficient formula
= 1 – (6*12)/(9(81-1))
= 1 – 72/720
= 1-0.1
= 0.9
The Spearman Rank Correlation for this set of data is 0.9.
Steps with example may help you in better understanding