# Irish Leaving Certificate indicators

Results were collected from 870 students who completed CAT4 and the Leaving Certificate. Subject grades were obtained as either Ordinary (O) or Higher (H) level. The equivalence between the Ordinary and Higher grades as set out in https://www.cao.ie/index.php?page=scoring&s=lcepointsgrid was used to combine results from the two levels to a common scale. For example, Higher 6 grade is equivalent to Ordinary 2 grade and both of these have 46 points.

The strength of the relationship between two variables can be measured by a statistic called the correlation coefficient. A value of zero indicates no relationship between the two measures, whereas a value of one indicates a perfect positive relationship. The correlations between CAT4 scores and Leaving Certificate subjects grades are shown below. These show that the overall mean CAT4 SAS has a moderate to strong association with the subject grades. The Leaving Certificate indicators for each subject are derived from the statistical relationship between CAT4 scores and Leaving Certificate subject grades or points scores. Indicators are calculated from the mean CAT4 Standard Age Score (SAS) for Maths, Physics, Chemistry, Art and Construction Studies and are based on verbal SAS for the other subjects.

## Likelihood of Leaving Certificate grades

The example below shows the grades most likely to be achieved by one student. The most likely grade for Construction Studies is H3 but this student has an 18% chance of obtaining a grade higher than H3, a 26% chance of obtaining grade H4 and a 23% chance of obtaining a grade below H4. The indicators are not precise: they indicate the outcomes expected for students with a particular CAT4 score making average progress in a typical school. They come with a margin of error which reflects the differences in progress that may be made by different students. This is reflected in the probabilities of obtaining each grade. ## CAT4 and Leaving Certificate 'Best 6' score

A summary ‘Best 6’ indicator based on the total points score for Maths and the best of five other subjects was calculated for each student. The correlation between the 'Best 6' points score and the mean CAT4 score was 0.61 and the relationship is displayed graphically below. ## Leaving Certificate indicators for groups of students

The table below shows how the group/class indicators have been calculated for a fictitious class with five students and shows the most likely grade achieved and the probabilities associated with getting different Mathematics grades. The group indicator is an average of the individual student outcomes and probabilities.

Calculating group indicators for Mathematics for a fictitious class of five students 