Iterative scaling of marks using APL-a case study

ABSTRACT

This paper presents a case study where APL was used successfully to tackle a problem that appeared to be quite complex. The work was carried out for the NSW Department of Technical and Further Education in 1985 and 1986, and is the subject of ongoing research at present. A common problem in educational measurement is the comparison of scores obtained on different tests when the candidature for each test is not identical. Such a situation exists in NSW at the Higher School Certificate secondary school matriculation examinations. Different subjects attract candidatures of differing ability, yet it is important to calculate an aggregate mark as fairly as possible since it is used as a basis for selection into tertiary institutions. The iterative scaling procedure which has been used has been the subject of some controversy, caused in part by the fact that most people find it hard to understand exactly what is going on. The Tertiary Preparation Certificate is a matriculation course offered by the NSW Department of TAFE and is designed to prepare mature-age students for tertiary study. The aggregate mark obtained in this course was required to be comparable to HSC aggregate marks, so the iterative scaling procedure was implemented using APL to process these marks. The APL program has been used successfully during the previous two years on groups of up to 100 students. The algorithm is documented here for the first time in a form that is ready to be used by anyone with access to APL. There is discussion on the rationale and assumptions used in the calculations, and comments are made on the role that APL played in the whole process.

REFERENCES

• 1: Seneta E. "A Technical Note on the Proposed University of Sydney Scaling System" Dept. of Malhematical Statistics, University of Sydney 1984.
• 2: The University of Sydney "Report on the Scaling of the 1986 New South Wales Higher School Certi Jicate" May 1987.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms

  K. Computing Milieux
  K.3 COMPUTERS AND EDUCATION

General Terms:
Algorithms, Human Factors, Languages, Theory