Approximate test for testing a null variance ratio in the Unbalanced One-Way Random Model

Sevgi Demircioğlu ,Bilgehan Güven

doi:10.31801/cfsuasmas.467319

Abstract

The approximate test for testing the signicance of the random effect is presented in the unbalanced one-way random model in which both random effects and errors are from non-normal universes. The test is based on the asymptotic distribution of the F-statistic. Under the condition that the number of groups tends to infinity while the average of powers of the group sizes is bounded, the asymptotic dis tribution of the F-statistic is obtained. Robustness of the proposed test is given.

Highlights

We derive the approximate test for testing the signi...cance of the random e¤ect in the unbalanced one-way random e¤ects model where both random e¤ects and errors are from nonnormal universes
In the present paper we establish the approximate test for the hypothesis of zero variance ratio in the unbalanced one way random e¤ects model from non normal universes
The di¤erences between the calculated and generated sizes and power values are closer to a small design and lower variance ratios than a large design and higher variance ratios

Summary

Introduction

We derive the approximate test for testing the signi...cance of the random e¤ect in the unbalanced one-way random e¤ects model where both random e¤ects and errors are from nonnormal universes. To derive the approximate test, we ...rst obtain the asymptotic distribution of the F -ratio. To get the asymptotic distribution of the F -ratio, we use the method of Westfall and establish the following asymptotic condition. The number of groups is large while the average of powers of the group sizes is bounded This asymptotic condition may be viewed as modi...cation of the asymptotic condition established by Wesfall (1987, 1988). He assumed that the number of groups is large while the group sizes are from a ...nite set of positive integers. Asymptotic normality; F -test; robustness of the approximate F -test; random e¤ects.

The Model and Asymptotic

Asymptotic Distribution of FN

The Proposed Test

Robustness of the Test

Numerical and Simulation Study

Conclusion