Title: Monitoring the disparity of teaching and learning process variability: a statistical approach

Authors: Maman A. Djauhari; Revathi Sagadavan; Siaw Li Lee

Addresses: Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia ' Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia ' Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia

Abstract: In social sciences, such as education management, scientists frequently encounter the problem to understand and handle the disparity of process variability from a target group to another group. Unfortunately, the methods of statistical process control can only help to solve this problem if the sample size is the same for all groups but this is not generally the case in social sciences. To solve this problem, in this paper, we generalise the existing methods of control charting to cover the case of unequal sample size. Under this sampling design, to conduct a root-causes analysis when a group differs significantly from the others, a statistic called Q-statistic is introduced. This statistic is to explain to what extent the groups differ to each other. The results of this generalisation together with Q-statistic are then used in a case study at a high school to help the school management in understanding and handling the disparity in process variability of teaching and learning among different classes. Some recommendations for the management of this school will be delivered.

Keywords: conditional variance; generalised variance; multivariate process control; process variability; scree plot; vector variance.

DOI: 10.1504/IJPQM.2017.085259

International Journal of Productivity and Quality Management, 2017 Vol.21 No.4, pp.532 - 547

Received: 01 Apr 2016
Accepted: 13 May 2016

Published online: 22 Jun 2017 *

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