Let us look at the correlation between mathematics and verbal reasoning. Suppose we took a range of children from Years 4, 5 and 6. We could develop suitable tests to cover the gap in ages. Some of the Year 4 questions would need to be easier than those offered for the more able Year 5 and Year 6 children. We would hope, if it was an eleven plus test, that the older children would be able to answer many of the more difficult questions.
To achieve a pass mark the scores of the two tests would be added together – and a pass mark would be established. Some children would, therefore, pass while other would not achieve the pass mark.
There are, however, differences in the ages of the children taking the tests. One way to try to eliminate the age difference would be to express each score as a deviation from the mean score of each Year Group. We could then see if there is a correlation between the scores on the two tests – but the correlation would be on the deviations from the mean – rather than the raw scores.
We could then use this evidence to say that the mathematics test was harder than the verbal reasoning test – or vice versa. Without this evidence we have to rely on anecdotal evidence rather than cold facts.
If, and this would be a big if, all the children could be given an I.Q. test then it would be possible to try to find a correlation between intelligence and verbal reasoning and the intelligence and mathematics. Adding a third party may help!
Correlation, however, does not imply a direct casual relationship- the connection between the correlated measures may be indirect and rely on other factors.
“All my friends found the mathematics hard. We all found the reasoning easy.”
We would all need to be rather cautions about accepting that `all my friends’ implies a strong correlation. The eleven plus board, however, do not offer any information on the tests other than to offer a pass mark or a fail. Should we be offered the opportunity to apply for more and different information?