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TL;DR: The margin of error gets smaller with the proportion: the given margin of error is most relevant the closer to 50% the support.

Warning: I am taking the polls to be of the form

Will you vote for party X: yes or no?

There is more than a little confusion about the margin of error in political polling amongst the Irish political commentators.

Polls frequently come with margins of error such as “3%” and if a small party polls less than this some people comment that the real support could be zero.

In this piece, I will present a new way of interpreting low poll numbers, show how it is derived, further explain where the approximate 3% figure comes from and show what the calculation should be for mid-ranking proportions.

The main point is that none of these margins of error are accurate for small proportions.

For those who don’t like the mathematics of it all I will explain in a softer way why polling at 1-2% is very unlikely when your true support is 0.5%.

The reality of the situation is that a far greater proportion than 5.2% of Leaving Cert students sitting Higher Level maths are presenting work that should confer less than 40% on their exam and those in the system know that the marking scheme receives a thorough massaging in order to get 94.8% of this cohort through.

A number of students are simply not allowed fail because failing 8-20+% of those sitting would be a political and logistical nightmare.

The final result of this fear of failing students, is the dumbing down of Higher Level maths and this is good for nobody.

I feel a solution to this is to do away with the pass/fail regime for maths: keep LC points for grades above 40% but mark the papers properly. This would effectively do away with the requirement for a pass in maths for third level courses, save for those such as engineering and science who want students with certain grades.

This will allow students take on Higher Level maths in good faith with the knowledge that if they do get less than 40%, it will not be a total disaster and they will still be able to attend a third level institution.

There is still a cut off in that 35% would confer 0 points and 40% would confer 70 points but this cut-off already exists (in theory!) but it is the failing not the lack of points that is somehow forcing the Department of Education to pass these students who really should be failing.

We should keep the bonus points for higher level maths because we should want our pupils to have good maths skills for the smart economy. However, at the moment, the stick of failing is proving to have more impact than the carrot of the 25 extra points.