An illustrative study of examination marks by the methods of factor analysis and the analysis of variance

Abstract

The essence of an examination is stated to be measurement and the thesis analyses the measurements given by some examinations. The methods of scoring examination marks and the application of them are outlined. (i) Factor Analysis of Marks with different Types of Scoring. The marks of two university examinations for eight consecutive years are analysed. In the case of one examination, the instructions given to the examiners demand that the marks should approximately fit a normal distribution curve. The other examination papers are marked without restrictions. In this section an endeavour has been made to determine whether the instructions to fit the marks to a normal distribution curve affect the factors obtained by analysis. (ii) Analysis of Variance of Two Sets of Scores for Some. Examination Candidates The college assessment and the examiner's mark for one subject in a university examination are analysed to test the significance of the difference between the variances of the two sets of scores. The revising examiner has marked independently some of the border-line cases together with some of the poorest and best papers picked at random. The significance of the difference between the variances of these re-markings and the original marks is also tested.(iii) Correlations between Persons. The marks of an examination for entrance to secondary schools are analysed. In this case the same candidates are examined in both 1937 and 1938. One purpose of this analysis is to determine the change if any, in the factor saturations for the set of persons after the lapse of a year, using Burt's method. The second aim is to try out another method which has recently been evolved and to test the agreement of the results obtained by this method with those obtained by using Burt's method. Results and Conclusions The main conclusions are:- (i) According to the data used in this research, fitting the score-scatter to a normal distribution curve does not influence the resulting factors. Some interesting facts concerning the individual examinations are revealed. (ii) In many cases the difference between the college assessment and the examiner's marks is significant. There is evidence that there is no difference in the average mark assigned by the first and revising examiners, and that the marks do bear some relation to the ability of the individual concerned.( iii) There is reasonable agreement in the first factor saturation of the marks of both years but there are differences in value and sign in the second and third factor saturations. The other method used gives results which agree to the degree of accuracy used.