Anova - genstat

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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 info@genstat.co.uk 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: thetwosample 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 twodirections: 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 4.3Additivity 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 treatments78 6.4 Practical 80 7 Balance and non-orthogonality 81 7.1 Confounding and efficiency factors 82 7.2 Balance 87 7.3 Practical 88 7.4 Unbalanced designs with two treatment factors 89 7.5 Practical 91 7.6 Unbalanced designs with several treatment factors 92 7.7 Practical 97 8 REML analysis of unbalanced designs 98 8.1 Linear mixed models: split-plot design 99 8.2 Practical 104 8.3 Linear mixedmodels: a nonorthogonal design 104 8.4 Practical 111 8.5 Analysis of variance by ANOVA, regression or REML 112 8.6 Practical 113 9 Commands for analysis of variance 114 Index 120

Introduction
Analysis of variance is one of the most widely used statistical techniques, with application areas that include biology, medicine, industry and finance. GenStat has a very powerful set of ANOVA techniques,that are nevertheless very straightforward and easy to use. This book is designed to introduce you to these techniques, and give you the underlying knowledge and confidence to use them correctly and effectively. It also covers the basic principles of experimental design to help you plan effective experiments and investigations. It was written to provide the notes for VSN’s course on anova and designin GenStat, but it can be used equally well as a self-learning tool. Starting with the simplest situation, where two different treatments are compared by the standard t-test, straightforward examples will be used to introduce the following concepts. • Analysis ! covering simple to sophisticated situations, explaining ideas such as balance, and introducing advanced features like the use of REML forunbalanced designs • Interpretation ! explaining the results, producing relevant tables, graphs and figures for publication in reports and papers. • Design ! a range of experimental designs will be described, to cover the situations encountered by most GenStat users. • Blocking ! how to increase the accuracy of an experiment by forming the basic units (e.g. plots or subjects) into groups with...
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