## Tuesday, January 01, 2013

### Eleven Plus Passes

In one year, in one school, thirteen children passed the eleven plus. So the head teacher, the teachers, the governors and the parents all voted for the teacher to be offered promotion. The next year, with a different teacher, only five children passed. Assuming that an equal number of children in the school sat the examination, do the new figures suggest that the head, the teachers, the governors and the parents were all wrong? Is the reduction in the number of eleven plus passes down to chance?

One of the parents, in Year One, is a statistician and is co-opted to look into the potential problem. After all no one wants the same thing to happen.

X, the smaller number of children who passed = 5
Y, the number who passed in the previous year = 13

N = x + y
= 5 + 13
= 18

Because the number does not exceed forty the statistician looks at what is called the 50% Probability Test. This shows that if x = 5 and y = 13 – with a total of 18 then there is a probability of 10%.

The difference between the two eleven plus pass rates is not statistically proven.