Are particular school subjects associated with better performance at university?

6. Data and definitions

We used two sources of data in our study. School achievement data was provided by the New Zealand Qualifications Authority. This data was linked, via the national student number,³⁰ to tertiary enrolment data supplied by tertiary education providers to the Ministry of Education. The study population was confined to first year intramural domestic students studying for a bachelors degree at a university. In addition, students were selected if they had gained NCEA level 3 and university entrance. Students varied between 17 and 20 years of age, and were studying in the years 2006 to 2008. When considering a particular subject, we excluded students who had gained less than 14 credits in that subject.

Sample sizes varied between the different models used in the analysis. For the bar graphs (figures 4 to 7) there were at least 50 students in each subject category. Sample sizes for the other figures are given in table 5. The sample sizes varied because we excluded students who had gained less than 14 credits in the particular subjects in a model. Table 6 gives the sample sizes and model fit statistics for the analyses in section 4 (figures 22 to 25).

The requirement for students in the study population to have university entrance derives from the fact that the university entrance requirement is not required for entrance to university for older students. Those 20 years and over can be granted special admission to a university, without the usual prerequisites. Since previous academic success is such an important determinant of performance at tertiary level, it was important to ensure that all students could have gained entry to university based on their school qualifications, rather than by special admission.

Scott and Smart (2005) found that extramural students had significantly lower rates of qualification completion, even when controlling for other variables. This is confirmed for students in the present study, where 54 per cent of extramural students passed most of their courses, compared to 76 per cent for intramural students. Extramural students also make up less than 1 percent of students in the data available for this study. For these reasons extramural students are excluded from the study population.

By limiting the study to first-time first-year students, vagaries arising from external factors that influence success at university study are reduced, and a stronger link is maintained between success at school and performance at university. It does not however, provide an indication of the overall success in gaining a qualification, which is arguably the ultimate success factor for this group. In spite of this, first year course pass rates are an important guide to later results (Birch and Miller 2006). At least for younger students, passing most or all of the courses in first year is correlated with continuing with study, and a pre-requisite to gaining the overall qualification. Older students are more likely to be studying part-time, which decreases qualification completion rates.

A note on the use of logistic regression

The relationship between university performance and achievement in secondary school subjects can be investigated in a number of ways. University performance can be measured as a percent of courses passed, instead of the measure we adopted, the proportion of students that passed most—more than 75 per cent—of their courses. It can be argued that using the probability measure is less efficient, since the data contains the number of courses passed or failed, which is a nearly continuous variable. We chose to use the probabilistic measure because the logistic regression models are simpler, and are less constrained by assumptions, than those regression models that use a continuous variable as the outcome measure. We also believe that predicting the proportion of courses a student passes still leaves open the question as to what constitutes good performance at university. We have used passing more than 75 per cent of first-year courses in a particular field of study (either broadly or narrowly defined), in line with other reports (Earle 2008), although when we explored the data, the results were almost no different had we used a value of 100 per cent. Of course, the best measure of university performance is whether a student eventually gains a qualification or not. It is not possible to use this latter measure with our current data, but it is an area that will be considered in the future, as more years of data become available.

A note on the use of confidence limits

The data is in this report is mostly presented in graphical form, with means and 90 per cent confidence intervals. 90 per cent confidence intervals are used so that readers, when comparing the intervals between two means, can be at least 95 per cent certain that the means are significantly different. The reasons why this apparently counter-intuitive approach is used can be found in Schenker and Gentleman (2001).

Statistical package used

The logistic regression analysis was performed using the SAS® statistical package, version 9.1.3.

Footnote

30. More information on the national student number can be found at http://www.minedu.govt.nz/NZEducation/EducationPolicies/Schools/SchoolOperations/NationalStudentNumber/InformationForParentsAndStudents/FrequentlyAskedQuestions.aspx.