Question

What are various steps for the calculation of rank order correlation?

Answer 1

Step 1: Rank both sets of data. Give the largest value rank 1, the second largest value rank 2, etc.
Step 2: Calculate the differences in the ranks, d.
Step 3: Work out the squares of the differences (d²).
Step 4: Calculate the sum of these squared differences, ∑d²
Step 5: Spearman’s Rank Correlation Coefficient is found by substituting this sum into the following formula.

`1 - (6 xx sumfx^2)/("n"("n"^2 - 1))`

where n is how many pairs of data you have.
Example: Find rank correlation from data given below:

Team	Goals in 1992	Goals in 1993
1	125	109
2	80	76
3	96	101
4	65	77
5	30	27
6	134	142
7	54	76
8	16	12
9	64	80
10	72	93
11	49	82

 

Team	Goals In 1992	Goals In 1993	R,	R2	R1-R2	(R, R2²
1	125	109	2	2	0	0
2	80	76	4	8.5	-4.5	20.25
3	96	101	3	3	0	0
4	65	77	6	7	-1	1
5	30	27	10	10	0	0
6	134	142	1	1	0	0
7	54	76	8	8.5	-0.5	0.25
8	16	12	11	11	0	0
9	64	80	7	6	1	1
10	72	93	5	4	1	1
11	49	82	9	5	4	16
						39.5

So, for this set of data, the finished equation looks like this:

rank = `1 - (6sum"d"^2)/("n"("n"^2 - 1))`

`1 - (6 xx 39.5)/(11 xx (11^2 - 1))`

`1 - (237)/(1320)= -0.17954`

= 0.82046

High Positive Correlation.