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Statistical approach on grading: mixture modeling

The purpose of this study is to compare results obtained from three methods of assigning letter grades to students’ achievement. The conventional and the most popular method to assign grades is the Straight Scale method. Statistical approaches which use the Standard Deviation and conditional Bayes...

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Main Author: Md. Desa, Zairul Nor Deana
Format: Thesis
Language:English
Published: 2006
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/3017/1/ZairulNorDeanaMdDesaMFS2006.pdf
http://eprints.utm.my/id/eprint/3017/
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spelling my.utm.30172018-06-25T00:46:08Z http://eprints.utm.my/id/eprint/3017/ Statistical approach on grading: mixture modeling Md. Desa, Zairul Nor Deana QA Mathematics The purpose of this study is to compare results obtained from three methods of assigning letter grades to students’ achievement. The conventional and the most popular method to assign grades is the Straight Scale method. Statistical approaches which use the Standard Deviation and conditional Bayesian methods are considered to assign the grades. In the conditional Bayesian model, we assume the data to follow the Normal Mixture distribution where the grades are distinctively separated by the parameters: means and proportions of the Normal Mixture distribution. The problem lies in estimating the posterior density of the parameters which is analytically intractable. A solution to this problem is using the Markov Chain Monte Carlo method namely Gibbs sampler algorithm. The Gibbs sampler algorithm is applied using the WinBUGS programming package. The Straight Scale, Standard Deviation and Conditional Bayesian methods are applied to the examination raw scores of 560 students. The performance of these methods are compared using the Neutral Class Loss, Lenient Class Loss and Coefficient of Determination. The results showed that Conditional Bayesian performed out the Conventional Method of assigning grades 2006-04 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/3017/1/ZairulNorDeanaMdDesaMFS2006.pdf Md. Desa, Zairul Nor Deana (2006) Statistical approach on grading: mixture modeling. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Md. Desa, Zairul Nor Deana
Statistical approach on grading: mixture modeling
description The purpose of this study is to compare results obtained from three methods of assigning letter grades to students’ achievement. The conventional and the most popular method to assign grades is the Straight Scale method. Statistical approaches which use the Standard Deviation and conditional Bayesian methods are considered to assign the grades. In the conditional Bayesian model, we assume the data to follow the Normal Mixture distribution where the grades are distinctively separated by the parameters: means and proportions of the Normal Mixture distribution. The problem lies in estimating the posterior density of the parameters which is analytically intractable. A solution to this problem is using the Markov Chain Monte Carlo method namely Gibbs sampler algorithm. The Gibbs sampler algorithm is applied using the WinBUGS programming package. The Straight Scale, Standard Deviation and Conditional Bayesian methods are applied to the examination raw scores of 560 students. The performance of these methods are compared using the Neutral Class Loss, Lenient Class Loss and Coefficient of Determination. The results showed that Conditional Bayesian performed out the Conventional Method of assigning grades
format Thesis
author Md. Desa, Zairul Nor Deana
author_facet Md. Desa, Zairul Nor Deana
author_sort Md. Desa, Zairul Nor Deana
title Statistical approach on grading: mixture modeling
title_short Statistical approach on grading: mixture modeling
title_full Statistical approach on grading: mixture modeling
title_fullStr Statistical approach on grading: mixture modeling
title_full_unstemmed Statistical approach on grading: mixture modeling
title_sort statistical approach on grading: mixture modeling
publishDate 2006
url http://eprints.utm.my/id/eprint/3017/1/ZairulNorDeanaMdDesaMFS2006.pdf
http://eprints.utm.my/id/eprint/3017/
_version_ 1643643716940857344
score 13.211869

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