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Statistical approach on grading the student achievement via normal mixture modelling

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 (SS). Statistical approaches which used the Standard Deviation (GC) and conditio...

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Main Authors: Md. Desa, Zairul Nor Deana, Mohamad, Ismail
Format: Conference or Workshop Item
Published: 2007
Subjects:
L Education (General)
Online Access:http://eprints.utm.my/id/eprint/14482/
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spelling my.utm.144822017-08-07T04:14:53Z http://eprints.utm.my/id/eprint/14482/ Statistical approach on grading the student achievement via normal mixture modelling Md. Desa, Zairul Nor Deana Mohamad, Ismail L Education (General) 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 (SS). Statistical approaches which used the Standard Deviation (GC) 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 approach namely Gibbs sampler algorithm. The Straight Scale, Standard Deviation and Conditional Bayesian methods are applied to the examination raw scores of two sets of students. The performances of these methods are measured using the Neutral Class Loss, Lenient Class Loss and Coefficient of Determination. The results showed that Conditional Bayesian outperformed the Conventional Methods of assigning grades. 2007 Conference or Workshop Item PeerReviewed Md. Desa, Zairul Nor Deana and Mohamad, Ismail (2007) Statistical approach on grading the student achievement via normal mixture modelling. In: 3rd International Conference on Research and Education in Mathematics, 2007, Legend Hotel, Kuala Lumpur.
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/
topic L Education (General)
spellingShingle L Education (General)
Md. Desa, Zairul Nor Deana
Mohamad, Ismail
Statistical approach on grading the student achievement via normal mixture modelling
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 (SS). Statistical approaches which used the Standard Deviation (GC) 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 approach namely Gibbs sampler algorithm. The Straight Scale, Standard Deviation and Conditional Bayesian methods are applied to the examination raw scores of two sets of students. The performances of these methods are measured using the Neutral Class Loss, Lenient Class Loss and Coefficient of Determination. The results showed that Conditional Bayesian outperformed the Conventional Methods of assigning grades.
format Conference or Workshop Item
author Md. Desa, Zairul Nor Deana
Mohamad, Ismail
author_facet Md. Desa, Zairul Nor Deana
Mohamad, Ismail
author_sort Md. Desa, Zairul Nor Deana
title Statistical approach on grading the student achievement via normal mixture modelling
title_short Statistical approach on grading the student achievement via normal mixture modelling
title_full Statistical approach on grading the student achievement via normal mixture modelling
title_fullStr Statistical approach on grading the student achievement via normal mixture modelling
title_full_unstemmed Statistical approach on grading the student achievement via normal mixture modelling
title_sort statistical approach on grading the student achievement via normal mixture modelling
publishDate 2007
url http://eprints.utm.my/id/eprint/14482/
_version_ 1643646407277543424
score 13.211869

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