Title: Resistant measures in assessing the adequacy of split-plot design models

Authors: Ikwuoche J. David; Osebekwin E. Asiribo; Hussaini G. Dikko

Addresses: Department of Mathematics, Ahmadu Bello University, Zaria 800001, Nigeria ' Department of Mathematics, Ahmadu Bello University, Zaria 800001, Nigeria ' Department of Mathematics, Ahmadu Bello University, Zaria 800001, Nigeria

Abstract: This paper assesses the adequacy of model fit of the split-plot design models, that is the whole plot (WP) sub-design model with WP error and the split-plot (SP) sub-design model with SP error for comparing the effectiveness of resistant measures that use medians instead of means, resulting in a coefficient that is more resistant to outliers or extreme data points. This paper presents empirical application of four measures of model adequacy check and they are coefficient of determination (R²), modelling efficiency (MEF) statistic, prediction coefficient of determination (R²_prod), and mean square error prediction (MSEP). These four measures were explored using their mean and median form. A 2⁽¹⁺³⁾ replicated two-level SP design and a 3¹ × 4² replicated mixed level SP design were used for computing the measures of model adequacy of fit for each WP and SP sub-design models. These measures in their median form described the predictive performance of each WP and SP sub-design models adequately.

Keywords: modelling efficiency; mean square error; MSE prediction; whole plot errors; split-plot errors; model adequacy; split-plot design; model fit; resistant measures; medians.

DOI: 10.1504/IJDS.2016.081360

International Journal of Data Science, 2016 Vol.1 No.4, pp.382 - 396

Received: 30 Aug 2013
Accepted: 02 Aug 2014
Published online: 06 Jan 2017 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article