Adaptive Scheme for ANOVA Models
Gilbert Biney *
Department of Statistics, Faculty of Mathematical Sciences, University for Development Studies, Tamale, Navrongo Campus, Ghana.
Gabriel Asare Okyere
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Abukari Alhassan
Department of Statistics, Faculty of Mathematical Sciences, University for Development Studies, Tamale, Navrongo Campus, Ghana.
*Author to whom correspondence should be addressed.
Abstract
This paper deals with the concept of adaptive scheme and with an application to the Oneway ANOVA model under uncorrelated errors. Oneway ANOVA model is sensitive to nonnormality as well as variance heterogeneity. To overcome these problems, an adaptive scheme is proposed. The adaptive test is a two step procedure. The given data is first examined and classified based on measures of skewness and tailweight. Secondly, a selector statistic is used for selecting a test to be conducted. A 10,000 simulations were conducted to compare the performance of the two models from different continuous distributions. Analysis of real data sets on equal and unequal sample sizes were performed to evaluate the efficiency of the two models. The findings showed that our adaptive scheme outperformed the parametric F-test in symmetric or skewed distributions with varying tailweights except for symmetric and medium-tailed distributions.
Keywords: Uncorrelated errors, adaptive test, selector statistic, skewness, tailweight, simulation, asymptotic relative efficiency (ARE).