Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.

Download the file ANOVA1.sas from my SAS programs page and run it. The contrived data (I created them with SAS' normal random number generator) are within the program. We shall imagine that we are evaluating the effectiveness of a new drug (Athenopram HBr) for the treatment of persons with depressive and anxiety disorders. Our independent variable is the daily dose of the drug given to such per...

We carry out an ANOVA analysis to compare multiple treatment effects for longitudinal studies with missing values. The treatment effects are modeled semiparametrically via a partially linear regression which is flexible in quantifying the time effects of treatments. The empirical likelihood is employed to formulate nonparametric ANOVA tests for treatment effects with respect to covariates and t...

This appendix contains the results obtained from the analysis of variance described in chapter three using " set " as the second factor.

We propose a procedure to test complicated ANOVA designs for functional data. The procedure is effective, flexible, easy to compute and does not require a heavy computational effort. It is based on the analysis of randomly chosen onedimensional projections. The paper contains some theoretical results as well as some simulations and the analysis of some real data sets. Functional data include mu...

The purpose of this study was to examine the Practice Difficulty on exam performance for each of the four exam given during the semester. Practice Difficulty was a 3-condition variable practice problems were either about the same difficulty as the exam problems (=1), they were easier than the exam problems (=2), or they were more difficult than the exam problems (=3). Different sections of the ...

Given k independent samples of functional data the problem of testing the null hypothesis of equality of their respective mean functions is considered. So the setting is quite similar to that of the classical one-way anova model but the k samples under study consist of functional data. A simple natural test for this problem is proposed. It can be seen as an asymptotic version of the well-known ...

ANOVA provides a general approach to the analysis of single and multiple factor experiments on both one- and two-color microarray platforms. Mixed model ANOVA is important because in many microarray experiments there are multiple sources of variation that must be taken into consideration when constructing tests for differential expression of a gene. The genome is large, and the signals of expre...