A Zero Sampling Plan for the Moderation of Examination Papers

Abstract

Quality assurance within local educational institutions has been under the spotlight in recent years. In particular these institutions are increasingly subjected to minimum standards specified by controlling bodies such as the Higher Education Quality Committee and others. The moderation of examination papers is an important quality assurance activity to ensure that an examination paper's standard, content, span and marking are fair and reasonable. This paper describes a sampling plan to determine the number of answer books to be checked to confirm that individual marks were awarded correctly. The sampling procedure relates the confidence that marks awarded in a set of examination books meets a specified minimum standard to the number of books moderated. OPSOMMINGGehalteversekering binne plaaslike opvoedkundige instellings word toenemend onderwerp aan minimum standaarde soos neergelê deur die Kwaliteitskomitee vir Hoër Onderwys en ander. Die moderering van eksamenantwoordstelle is 'n belangrike gehalteversekeringsaktiwiteit wat verseker dat 'n eksamen se standaard, inhoud, bestek en nasien regverdig en redelik is. Die artikel beskryf 'n steekproefplan vir die proses om individueel toegekende punte vir korrektheid na te gaan. Die voorgestelde prosedure gee die verband tussen die sekerheid dat die punte toegeken deur die eksaminator voldoen aan 'n gespesifieerde minimum standaard en die aantal boeke wat gemodereer moet word (steekproefgrootte).

A Non-Zero Sampling Plan for the Moderation of Examination Papers

“…the standard). If C is forced not to exceed zero (C=0) the sampling plan defaults to the zero sampling plan discussed in [7], and it can be shown that the above inequality reduces to equation (10) in [7]. The reader will also notice that if the entire set of books is moderated (k=s), then the acquired confidence is 100% (which of course must be the case).…”

“…2 The uniform distribution was used for no other reason than its simplicity. During the analysis of the zero sampling plan [7] it was found that the form and parameters of this prior distribution have a relatively small effect on the results. It appeared that the knowledge obtained about the specific examiner during the moderation of the sample and captured by the process of Bayesian statistics contained much more information than the prior assumption about the population to which the examiner belongs.…”

“…This article is the final report on research that was done to find a mathematical approach to improve the process of moderation, and represents an extension and enhancement of previous research that was published in this journal [7].…”

“…A scientific procedure is given for finding the minimum number of answer books to moderate (sample size) so that the statement -that no answer book in a set will contain more than a prespecified proportion of errors -can be made with a pre-specified confidence. The procedure is an extension and enhancement of previous research [7], and guarantees a statistical statement in all cases. …”

“…'n Wetenskaplike prosedure word voorgestel waarvolgens die minimum getal antwoordstelle (steekproefgrootte) vir moderering bepaal kan word sodat die stelling dat geen antwoordstel in 'n groep meer as 'n vooraf-gespesifiseerde aantal foute sal bevat nie met 'n voorafgespesifiseerde vlak van vertroue gemaak kan word. Die prosedure is 'n uitbreiding en verfyning van vorige navorsing [7], en waarborg in alle gevalle 'n statistiese uitspraak. …”