A COMPARATIVE STATISTICAL ANALYSIS OF 22 FACTORIAL EXPERIMENT AND TWO-WAY ANALYSIS OF VARIANCE INTERACTIVE MODEL

Abstract

statistical comparative analysis of 22 factorial experiments were compared with Two-Way analysis of variance (ANOVA) interactive model. The three models for Two-Way ANOVA were considered with respect to when to test for the main effects. The three models are; fixed effect, random and mixed effect models. When the two factors namely; factor A and factor B are fixed, the common denominator for testing for the main effects is mean square error (MSe). Conversely, when the two factors are random, the common denominator for testing for the main effects is mean square interaction (MSλ). However, when factor A is fixed and factor B is random, the denominator for testing for factor A is MSλ while that of factor B is MSe. Conversely, when factor A is random and factor B is fixed, the denominator for testing for factor A is MSe while that of factor B is MSλ. The 22 factorial experiments have no model specifications. After the statistical analysis, the results from the fixed effect model for the Two-Way ANOVA gave the same result with that of 22 factorial experiments using the Yates’ technique or any other technique. The researcher therefore recommends that when both factors are fixed, either 22 factorial design or Two-Way analysis of variance (ANOVA) interactive model could be used. But when both factors are random or mixed, the Two-Way analysis of variance (ANOVA) interactive model is highly recommended.