Simulation Studies of Three-Way Unbalanced Design on Fixed, Random, and Mixed Model

Abstract

Analysis of Variance (ANOVA) is a statistical technique used to compare means from various samples. Generally, a balanced design is used in ANOVA, but in some conditions, an unbalanced design can happen when the sample size is different in each treatment. This design will have the calculation of the F-test is different from usual for fixed, random, and mixed models. In this research, a simulation study will be carried out to see the differences in the results of the F-test decision in a three-way ANOVA with an unbalanced design based on a fixed, random, and mixed model. Simulation data is generated based on several scenarios, small sample size and large sample size, e~Normal (0,1) and e~Gamma (2,3), and applied to 8 models, that combine fixed effects and random effects in a 3-factor design. The simulation shows that sample size, error distribution, and the used model can affect F-test decisions. Designs with large sample sizes and e~Normal (0,1) produce more significant F-test decisions than small sample sizes and e~Gamma (2,3), and model 1 or the fixed model has more significant F-test decisions than other models in each scenario.