Question

The table lists 7 schools and provides data about the percentage of pupils who have free school meals and their GCSE results. Calculate Spearman’* rank correlation coefficient and explain what this means in the context of this question.

| School | % of pupils claiming free school meals, x | % of pupils gaining 5 or more GCSE at grades A+C,Y |
| Appledore | 14.4 | 54 |
| Butterscotch | 7.2 | 64 |
| Copperdale | 27.5 | 44 |
| Damson View | 33.8 | 32 |
| Eagle High | 38.0 | 37 |
| Forrest Green | 15.9 | 68 |
| Greengage | 4.9 | 62 |

Answer 1

| School | Rank x | Rank y | d | d2 |
| Appledore | 3 | 4 | -1 | 1 |
| Butterscotch | 2 | 6 | -4 | 1 |
| Copperdale | 5 | 3 | 2 | 4 |
| Damson View | 6 | 1 | 5 | 25 |
| Eagle High | 7 | 2 | 5 | 25 |
| Forrest Green | 4 | 7 | -3 | 9 |
| Greengage | 1 | 5 | -4 | 16 |
| Total | | | | 96 |

Using the formula

This value represents negative rank correlation, so the schools with the highest proportion of pupils receiving free school meals tend to have the least successful GCSE results (and vice versa).

Note: When an item is repeated m times in a series , then common rank is the average of the ranks which these items would have assumed if they are slightly different from each other and the next item will get the rank next to the ranks already assumed. As a result of this ,correction factor

= m(m2 -1)/12 to be added to ∑ d2

Where m is the no. of item is repeated. This c.f should be added for each repeated value.