# Accounting for statistical anomalies in collated data

## Schools with significantly falling numbers can have grossly inflated progression rates

Falling numbers of students taking the Leaving Cert in specific schools affect perceived progression rates to college in an unexpected way. There are 566 schools in Ireland where the number of students who took the Leaving Cert in 2017 is 85 per cent, or less, of the number who took the exam in 2016.

In these schools, and many others with a significant reduction in Leaving Cert numbers since last year, the fact the progression rate of former students to third level is measured in these progression charts as a percentage of the 2017 class, results in a false and inflated percentage figure.

Measured as a percentage of the class of 2017, Castlerea Community School appears to send 149 per cent of its students (including past pupils) to college, and the percentage progression for Rathdown School, Glenageary, appears to be 142 per cent. But, in both cases the numbers of students sitting the Leaving Cert in 2017 is down dramatically by 51 and 42 per cent respectively on 2016 numbers.

Who goes to college each year?

Up to 22 per cent of those identified by colleges as originally coming from a named school, who start an undergraduate course each year, come from Leaving Cert classes prior to 2017.

These students have taken post-Leaving Cert (PLC) programmes, or delayed going to college for a year or more, or dropped out of a previous CAO course, and are starting into a new college programme again in 2017.

Therefore, The Irish Times estimates that for a school where the numbers taking the Leaving Cert remains relatively constant, we can deduct 22 per cent from their published progression rate in today's charts to calculate the true progression rate of the 2017 class.

When this normal flow of previous pupils, averaging 22 per cent of overall incoming 1st year undergraduate students, is added to those from the class of 2017, and that number is expressed as a percentage of a significantly lower number of 2017 final year students than in previous years, it given a highly distorted positive progression picture.

How do we give a true picture of improving progression rates?

To calculate an accurate picture of school progression rates, we must find a way to counteract this phenomenon, and avoid creating the impression that a school that is experiencing a significant reduction in numbers of Leaving Cert students in 2017 is in fact experiencing a surge in the percentage of their students securing third-level places.

We must do so because the reduction in the class size of this year’s Leaving Cert group creates a statistical aberration – they have what seem to be high progression percentage rates precisely because their Leaving Cert student numbers are declining.

To include such schools when we tabulate the “most improved schools” would create a false impression and distort the figures. For that reason, we have excluded from all the smaller tables schools where the number of students who sat the Leaving Cert in 2017 was 85 per cent or less than the number that sat it in 2016.

There are a range of other schools that seem to show an improvement in progression rates, but have reductions of less than 15 per cent in Leaving Cert students in 2017, which may be leading to a perceived improvement because of that, but we have left them in our most improved progression charts.

How is it mathematically possible for some schools to continuously record more than 100 per cent attendance of their former students at third level?

The explanation for this apparent mathematical impossibility is that where a student registers with a college in the CAO system they are credited to their former school. If every past pupil of that school eventually undertook a third-level course through the CAO, the total number of students so registered would equal the number of former pupils for that period of years.

College dropouts

The only explanation for schools which consistently seem to perform at above the 100 per cent participation rate in CAO college courses is that some of their students are counted twice. If a student drops out of one course having been counted and is credited back to his/her school and starts a new programme in another course in that college or another college altogether, they are again credited back to their original school.

The higher the level of college drop-outs experienced by former pupils of any given school, the higher the school’s progression rate will appear as recorded by colleges in the CAO system.

The reality of this phenomenon will remain hidden within the progression numbers if the total number of students progressing to college from any school over a period of years remains significantly below the total number who took the Leaving Cert during that time.