Analysis of variance for dummies with the Automatic Anova package Seminar

Abstract
The analysis of variance (Anova) is one of the most popular statistical methods for analysing data. It is most powerful when applied to data from designed experiments. Statistics courses for biologists and other scientists usually explain the underlying theory for simple designs such as the completely randomized design, the randomized complete block design or two-factor factorial designs. However, in applications usually much more advanced designs are used which involve complicated crossing and nesting structures as well as random and fixed effects. Although when designing an experiment scientists can often rely on their intuition, analysing the collected data frequently represents a major challenge to the non-expert.

This talk presents the AutomaticAnova package which has been designed as a user-friendly Mathematica package that enables researchers to analyse complicated Anova models without requiring much statistical background. It is based on RA Bailey's theory of orthogonal designs which covers a wide range of models and in particular all designs that can be obtained by iterative crossing and nesting of factors. The theory distinguishes between block factors, which have random effects, and treatment factors whose effects are fixed and so in general the models are mixed effects models. For these designs the Anova table can be derived in an elegant way by using Hasse diagrams.

The AutomaticAnova package provides a graphical user interface which has been implemented by using Mathematica's GUIKit. Input data are submitted in the form of a Microsoft Excel spreadsheet and essentially the user only has to specify which columns in the spreadsheet represent block and treatment factors respectively, and whether only main effects or main effects and interactions should be included in the analysis. Dynamic enabling/disabling of dialogs and controls minimizes the risk of providing incorrect input information. The most important feature of the AutomaticAnova package is then, however, that the model for the analysis of variance is automatically inferred from the structure of the design in the Excel file. In particular, no model formula needs to be specified for the analysis. It is believed that this aspect of the package's functionality will be highly attractive to practitioners. The output includes the Anova table, estimated variance components and Hasse diagrams and can be saved as a PDF file.

Another feature of the package is that it can be used at the planning stage of an experiment when no response data are yet available to see what the analysis would like. That is, having only specified the design in the form of a spreadsheet the packages provides the so-called skeleton analysis of variance which shows the breakdown of the sum of squares and corresponding degrees of freedom. Also, when no response data are available the package uses Mathematica's symbolic capabilities to derive analytical formulae for the estimators of the variance components.

The presentation will demonstrate the use of the package and describe the principles underlying its implementation. Several examples will be used to illustrate how the AutomaticAnova package can help the non-statistician to analyse complicated Anova designs without having to worry too much about statistics.