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Forecasting the demand for national qualifications of the Scottish Qualifications Authority

Boyle, Gillian Louise (2010) Forecasting the demand for national qualifications of the Scottish Qualifications Authority. MSc(R) thesis, University of Glasgow.

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Abstract

The Scottish Qualifications Authority (SQA) currently uses an ad hoc method to predict the number of entries for each of its examinations for the coming year, based on a weighted average of the numbers of entries in the previous three years. Data for the years 2004-9 were analysed with the aim of providing a more accurate method of prediction or, failing that, statistical justification for the prediction method currently used. The best method of prediction identified by this work would then be used by the SQA for planning purposes such as future resourcing and funding. Standard multiple regression models are explored for predicting the number of entries from explanatory variables such as year (a simple linear trend) and total school roll. If the numbers of entries for the same subject in successive years are autocorrelated, then this information might be used to improve the model predictions. So the Durbin-Watson test is applied to determine whether first-order autocorrelation is present and, where there is evidence that it is, an autoregressive term is added to the models. The mean square error of prediction is used to compare the performance of different models, including the simple weighted average model currently favoured by the SQA. The modelling has to be carried out with just 5 data points, for the years 2004 - 2008. Data from before 2004 can not be used because it was noticed that the entry profile for the intermediate courses had changed and is no longer useful when trying to model the courses in their current structure. In an attempt to overcome the deficiencies of standard parametric analysis when there are so few data points, bootstrapping is applied. Bias-corrected and accelerated bias-corrected percentile confidence limits are calculated for the Durbin-Watson statistic. Data for seven school subjects are explored in detail: Accounting and Finance, Art, English, Mathematics, Physics, Psychology and Spanish. It is concluded that the current SQA method produces a prediction value that is always close to the actual number of entries but which can sometimes underestimate it. The prediction which produces a value close to the actual number of entries, but which never underestimates it, is the number of subjects enrolled by the schools and colleges.

Item Type: Thesis (MSc(R))
Qualification Level: Masters
Keywords: SQA, education, prediction, regression, bias-corrected, bootstrapping, Durbin-Watson
Subjects: L Education > LF Individual institutions (Europe)
H Social Sciences > HA Statistics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Statistics
Supervisor's Name: McColl, Prof. John H.
Date of Award: 2010
Depositing User: Miss Gillian Boyle
Unique ID: glathesis:2010-3266
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 16 Mar 2012
Last Modified: 10 Dec 2012 14:05
URI: http://theses.gla.ac.uk/id/eprint/3266

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