Have you ever heard stories about parents moving their child to a new school where they think that it is likely that their child will be properly prepared for the eleven plus examinations? We actually know of one set of parents who moved their child from a small class of about 24 children to a school that claimed a 100% eleven plus pass rate. The new school, however, had only entered two out of 23 children for the eleven plus. We just hope that the new school allows the new boy to enter the examination!
Suppose that the numbers to crunch are a little bigger. Parents do not always leave everything to chance. They could collect the data over a few years until they had a reasonable number of eleven plus candidates to analyse and dig into.
Boys: Pass 75 Fail 125 = Total 200
Girls: Pass 24 Fail 76 = 100
Totals: Pass 99 Fail 201 = 300
These are called obtained frequencies. If there was to be no difference in the proportion of passes between boys and girls we would expect two thirds of boys to pass and one third of girls. This is called `expected frequencies’.
Boys: Pass 66 Fail 134 = Total 200
Girls: Pass 33 Fail 67 = 100
Total 99 Pass and 201 Fail = 300 children.
We now have Boys: Pass + 9 Fail -9
Girls: Pass – 9 and Fail + 9
The totals all add up to 0.
Some parents may wonder why there were more boys than girls sitting the eleven plus examinations in the school. There are some who may firmly believe in the water. It could be argued, for example, that lots of limestone may cause more boys to be born in a particular neighbourhood.
If of course you believe the limestone fallacy you will probably not believe that changing your child to a school with 100% eleven plus passes will be advantageous.