IJPAM: Volume 41, No. 6 (2007)

ONE-WAY ANALYSIS OF VARIANCE UNDER
HETEROSCEDASTICITY FOR TESTING
THE EQUIVALENCY OF MEANS AGAINST
AN ORDERED ALTERNATIVE
WITH VARYING INITIAL SAMPLE SIZES

Meltem Ekiz$^{1}$, Ufuk Ekiz$^{2}$
$^{1,2}$Department of Statistics
Faculty of Arts and Science
Gazi University
Besevler, Ankara, 06500, TURKEY
$^1$e-mail: ozmeltem@gazi.edu.tr
$^2$e-mail: ufukekiz@gazi.edu.tr


Abstract.The conventional F test of ANOVA, is only applicable when the assumption of the equal variances holds. The departures from the equal variances mislead authors to wrong conclusions, especially if the sample sizes are not equal. There appear many modifications of the statistic F in literature. These modifications mostly cover the employability of it in case of unequal variances. There after approximate distributions are derived. In this study we use a general one-stage method described by Chen et al [6] for testing the equality of normal means against an ordered alternative in one-way layout, when variances are unknown and unequal. By simulation, this method is applied to randomly chosen $n_{0}=n_{i}-1$ and $n_{0}$ $\left( 2\leq n_{0}<n_{i}\right) $ of $n_{i}$ observations. Then the calculated powers and the approximations of the reject ratios of a true null hypothesis to the given level $\alpha $ are compared, with each other.

Received: May 17, 2007

AMS Subject Classification: 62J10, 62J15

Key Words and Phrases: general one-stage method, one-way layout, power, unequal variances

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 6