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

Authors

  • Amalia Nailul Husna  Department of Statistics, IPB University, Bogor, West Java, Indonesia
  • Muhammad Nur Aidi  Department of Statistics, IPB University, Bogor, West Java, Indonesia
  • Indahwati  Department of Statistics, IPB University, Bogor, West Java, Indonesia
  • Fitrah Ernawati  Department of Statistics, IPB University, Bogor, West Java, Indonesia

DOI:

https://doi.org/10.32628/IJSRSET2310548

Keywords:

ANOVA, F-Test, Simulation, Unbalanced Design

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.

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International Journal of Scientific Research in Science, Engineering and Technology

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Published

2023-10-30

Issue

Volume 10, Issue 5, September-October-2023

Section

Research Articles

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How to Cite

[1]
Amalia Nailul Husna, Muhammad Nur Aidi, Indahwati, Fitrah Ernawati "Simulation Studies of Three-Way Unbalanced Design on Fixed, Random, and Mixed Model" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 10, Issue 5, pp.270-278, September-October-2023. Available at doi : https://doi.org/10.32628/IJSRSET2310548