Anova - genstat

Anova and Design

A Guide to Anova and Design in GenStat® (15th Edition) by Roger Payne.

GenStat is developed by VSN International Ltd, in collaboration with practising statisticians at Rothamsted and other organisations in Britain, Australia, New Zealand and The Netherlands.

Published by: E-mail: Website:

VSN International, 5 The Waterhouse, Waterhouse Street, Hemel Hempstead, Hertfordshire HP1 1ES, UK [e-mail] http://www.genstat.co.uk/

First published 2007, for GenStat for Windows 10th Edition This edition published 2012, for GenStat for Windows 15th Edition

GenStat is a registered trade of VSN International. All rights reserved.

© 2012 VSN International

Contents
Introduction 1 1 From t-test to one-way anova 2 1.1 Comparing two treatments: the twosample t-test 3 1.2 Practical 8 1.3 One-way analysis of variance 8 1.4 Practical 14 1.5 One-way analysis of variance with several treatments 15 1.6 Polynomial contrasts 16 1.7 Practical 18 1.8 Multiple comparisons 19 1.9 Practical 20 1.10 Completely randomized designs 20 2 Blocking structures 22 2.1 Completely randomized designs 23 2.2 Randomized block designs 23 2.3 Practical 28 2.4 Blocking in two directions: Latin square designs 28 2.5 Practical 31 3 Treatment structure 32 3.1 Factorial designs with two treatment factors 33 3.2 Fitting contrasts 36 3.3 Practical 43 3.4 Syntax of model formulae 43 3.5 Factorial plus added control 45 3.6 Covariates 48 3.7 Practical 51 4 Checking the assumptions 52 4.1 Homogeneity of variance 53 4.2 Normality and independence of the residuals 54 4.3 Additivity of the model 55 4.4 Outliers 55 4.5 Transformations 56 4.6 Automatic testing of the assumptions 60 4.7 Practical 63 4.8 Permutation and exact tests 63 4.9 Practical 64 5 Designs with several error terms 65 5.1 Split-plot design 66 5.2 Practical 68 5.3 Other stratified designs 69 5.4 Practical 72 6 Design and sample size 73 6.1 Designing an experiment 74 6.2 Practical 78 6.3 Control treatments