Statistical properties of indicators of first-year performance at university

Abstract

Appraisal of admission procedures is a matter of urgency for South African universities, as well as for schools producing the prospective students. In this article the focus is on how various statistical procedures can be used to assess admission measures. Properties of the statistical distributions related to school results, access test results and first-year university performance are vital for decision-makers in schools preparing the prospective students and for those who wish to refine university admission procedures. These properties are scrutinised for the 1999, 2000 and 2001 intake groups required to write access tests before being admitted to Stellenbosch University. Using kernel density estimates the univariate distributions of all variables concerned are described in detail. Bagplots are proposed for visual displays of important features like location, spread, correlation, skewness, outliers and tails of bivariate distributions composed of university average performance and a school result or access test variable. Evidence is provided that certain access tests (Mathematics, Science and Numeracy Skills) have statistical distributions similar to that of average first-year university performance, but that average school marks could not be trusted to discriminate between potentially successful and unsuccessful university students.

Keywords: access tests, admission procedures, average first-year university performance, bagplots, bivariate distribution, depth median, kernel density estimates, school marks

ORiON: The Journal of ORSSA Vol. 20(2) 2005: 161–178