Anova in Fixed-Effects Experimental Design Models

Sir R. A. Fisher developed the technique of analysis of variance (ANOVA) during the turn of the twentieth century to test hypotheses for various experimental design models by partitioning the total variation in the sample into various components and assigning these components to various sources to test various hypotheses of the linear models. But it was not clear why the F tests were used except for some compelling intuitive reason. We found the answer with the advent of the introduction of the Neyman-Pearson Lemma followed by the development of the likelihood ratio test. In this book, we consider the most common fixed-effects experimental design linear models. We described how the ANOVA tests of hypotheses are derived using the likelihood ratio test for few linear fixed-effects experimental design models and indicated that the ANOVA tests for the rest of the fixed-effects models can be obtained in the same way.In addition to these, we considered many other topics related to these models. We considered numerical examples for each model and prepared the ANOVA tables manually. We also used the statistical library of the software R to compare the ANOVA tables created manually. The R codes used for the models are also included.