Spearman's following data
Answers
We then complete the following table:
English (mark) Maths (mark) Rank (English) Rank (maths) d d2
56 66 9 4 5 25
75 70 3 2 1 1
45 40 10 10 0 0
71 60 4 7 3 9
62 65 6 5 1 1
64 56 5 9 4 16
58 59 8 8 0 0
80 77 1 1 0 0
76 67 2 3 1 1
61 63 7 6 1 1
Where d = difference between ranks and d2 = difference squared.
We then calculate the following:
Spearman Formula
We then substitute this into the main equation with the other information as follows:
Spearman Formula
as n = 10. Hence, we have a ρ (or rs) of 0.67. This indicates a strong positive relationship between the ranks individuals obtained in the maths and English exam. That is, the higher you ranked in maths, the higher you ranked in English also, and vice versa.
How do you report a Spearman's correlation?
How you report a Spearman's correlation coefficient depends on whether or not you have determined the statistical significance of the coefficient. If you have simply run the Spearman correlation without any statistical significance tests, you are able to simple state the value of the coefficient as shown below:
Spearman Formula
However, if you have also run statistical significance tests, you need to include some more information as shown below:
Spearman Formula
where df = N – 2, where N = number of pairwise cases.