How does the Ministry of Education calculate tertiary qualification completion rates?

Publication Details

This factsheet describes the method used by the New Zealand Ministry of Education to calculate tertiary qualification completion, attrition and direct progression rates. It covers terminology and definitions, and provides worked examples of the calculations, as well as example data tables with guides to their interpretation.

Author(s): Tertiary Sector Performance Analysis, Ministry of Education

Date Published: December 2018


The proportion of students who complete a tertiary qualification is one of a number of statistics produced by the Ministry of Education to measure the New Zealand tertiary education system’s performance. Other statistics include the proportion of students who go on to further study without completing a qualification (called direct progression) and the proportion who start but don’t complete a qualification (attrition). These all relate to formal study that leads towards gaining a qualification.

While students study towards specific qualifications, these statistics are produced for levels and types of qualification, rather than individual qualifications. For example, statistics are produced for bachelors-level study, or certificates at Levels 1 to 3, or all non-degree qualifications.

These statistics are usually reported as ‘rates’, and answer questions such as, “After eight years of study, what proportion of students have completed a bachelors degree?”. Also of interest is the timing of these events. Timing is reported as the probability that an event will occur in a particular year, or as the annual change in the rate. These statistics can answer questions such as, “When are diploma students most likely to discontinue their studies?” or “When do most diploma students complete?”.

The method to produce these statistics uses cohorts of students. For completion, attrition and direct progression rates, the cohorts are made up of students who begin studying with some common characteristic(s).

Students in a cohort can and do change their study characteristics from year to year. For instance, students can start studying toward a qualification at a particular tertiary education provider, and then transfer to another provider to complete it. A student may study part-time in one year, and full-time in another. Other characteristics, like the age a student starts studying at, are constant for the duration of a study spell. These time-varying characteristics result in the cohort changing size from year to year, and mean that conventional cohort-based calculations, which use a fixed starting cohort, cannot be used. Instead, the Ministry uses event history analysis (also known as survival analysis) as the method to calculate completion statistics, as it is able to analyse time-series data with both time-constant and time-varying characteristics.

This factsheet outlines some of the considerations involved in using event history analysis, including some specific problems that need to be solved in analysing time-series data. It then describes the three events; completion, attrition and direct progression. A detailed worked example is provided, showing the calculations involved in producing the statistics. Finally, sample results are presented, with guidance on their interpretation, and some advice on how to ensure conclusions based on this data are sound.


  1. The full name of the method used is discrete-time, competing-risks event history analysis.

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