Estimating parameter in two-way analysis of variance when variance between cells is heterogeneous

Abstract

Analysis of Variance (ANOVA) is a technique in statistics to test the mean differences of more than two groups in the presence of factors that may affect the mean difference. There are three types of analysis of variance, namely one-way analysis of variance, two-way analysis of variance, and multi-way analysis of variance. In this paper, we will discuss two-way analysis of variance which can be seen also the interaction of two factors. In the two-way analysis of variance, there are assumption that must be met, is observed in the cell or group must be normally distributed, the observations between cells or groups are mutually independent, and the variance between cells or groups is homogeneous. A common problem with two-way analysis of variance is unfulfilled assumptions, one of which variance between cells or groups is heterogeneous. Before determining test statistics for two-way analysis of variance, there are parameters to be estimated. This paper discusses the estimation of parameters for testing the effects of main factors and interaction factors on a two-way analysis of variance when the variance between cells or groups is heterogeneous.