## Tuesday, August 10, 2010

### The Eleven Plus and Probability

What would happen to eleven plus teaching if the tests were scored with a formula score where wrong answers incurred a negative mark and the right answers helped to build a positive score? We see this on `A Question of Sport’, in the final battery of questions, where a team can lose the lead through one or two wrong answers.

Multiple choice eleven plus tests give children a choice of answers. We offer the advice – eliminate the answers that can not be correct – and then take a guess. (But only when you are pushed for time.)

If the tests became true-false tests then the assumption would be that the eleven plus child would guess at the answer and had a chance of getting the answer right. The odds are 0.5 that the right answer will be selected.

If the multiple choice test has four choices then there is a 0.25 chance of success, with three answers we get a probability of 0.33 – and back to two answers where the probability is 0.5.

The whole formula becomes more of a problem if items are left out from the test. If a child lost marks for a wrong answer it may be better to leave out answers if the child was not absolutely certain of the answer.

The more difficult the test the more there is a need to have a policy that favours the eleven plus children. There could, for example, be a penalty for leaving an answer out. (“If you omit an answer, you lose half a mark!”)

W could then come up with a formula:

+ 1 mark for a correct answer.
- 0.5 marks for leaving out an answer.
- 0.25 marks for a wrong answer.

Would this focus the mind of some eleven plus children?