1. Spearman’s Rank correlation coefficient
used with ordinal data . . .

2. Inferential statistics
We move from descriptive to inferential statistics. Nor longer are we simply comparing data sets ; we are now seeking ‘cause and effect’ relationships.
Note that a ‘statistical relationship’ can occur where no ‘meaningful relationship’ is possible. Such a relationship is spurious.
So any positive statistical result must always be backed up by sound reasoning.

3. Scatter graphs
It is usually wise to draw a scatter graph, if undertaking any correlation. It is an easy way to highlight any relationship that may exist and its type, whether direct or inverse.

4. GNP and adult literacy
Let us test whether there is a relationship between GNP per capita and educational provision.
GNP per capita
% adult literacy
Nepal
210
39.7
Sudan
290
55.5
Gambia
340
34.5
Peru
2460 89
Turkey
3160
81.4
Brazil
4570 84
Argentina
8970 97
Israel
15940 96
U.A.E.
18220
74.3
Netherlands
24760
100

5. GNP and adult literacy
First, construct a null hypothesis (Ho) – that there is no relationship between GNP per capita and % adult literacy.
GNP per capita
% adult literacy
Nepal
210
39.7
Sudan
290
55.5
Gambia
340
34.5
Peru
2460 89
Turkey
3160
81.4
Brazil
4570 84
Argentina
8970 97
Israel
15940 96
U.A.E.
18220
74.3
Netherlands
24760
100

6. GNP and adult literacy
Spearman’s Rank correlation coefficient (Rs) is the best method to use, as the GNP data is skewed.
GNP per capita
% adult literacy
Nepal
210
39.7
Sudan
290
55.5
Gambia
340
34.5
Peru
2460 89
Turkey
3160
81.4
Brazil
4570 84
Argentina
8970 97
Israel
15940 96
U.A.E.
18220
74.3
Netherlands
24760
100
Remember, Spearman’s Rank can only be used with ordinal data.
It is necessary, therefore, to rank-order the data first.

7. Setting out Spearman’s Rank . . .
Set the data out as shown with columns for ‘ranking’ the variables and ‘n =’ and ‘Σd2’ at base :

8. Ranking the X data . . .
The GNP (X) is already rank-ordered ; all it needs is to enter the ranking, in this case from lowest to highest.

9. Ranking the Y data . . .
Ranking is now complete for GNP. Do the same for % adult literacy (again start with the lowest value. . .)

10. Rank ordering completed . . .
Both variables X and Y are now ranked. It is time to find the difference of (Rank X - Rank Y) or ‘d’.

11. Squaring ‘d’ . . .
To get rid of the minuses, square (d) . . .

12. Summing ‘d^2’ . . .
Now sum ‘d^2’ which gives the answer 44.

13. Getting ‘n’ . . .
There are ten countries – so ‘n’ = 10

14. Calculating Spearman’s Rank . . .
Insert the figures into the equation . . .
( 6 x 44 )
(1000 – 100)
Rs = 1 -

15. The answer to Spearman’s . . .
. . . and, he presto, the answer to Rs is
264
990
Rs = 1 -
Rs = 1 – 0.267
Rs = 0.733

16. Your (Rs) findings . . .
Null hypothesis (Ho) was that there was no relationship between GNP per capita and % adult literacy.
The degrees of freedom are (n – 1). So ‘df’ = 9.
Spearman’s Rank correlation coefficient (Rs) result of exceeds the 95% probability value of 0.60 at 9 degrees of freedom.
Therefore the Ho must be rejected and replaced by the alternative hypothesis (H1) – that there is a relationship between GNP per capita and % adult literacy.