Randomized Block Design
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Block Designs: A Randomization Approach
Author: Tadeusz Calinski
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
In most of the literature on block designs, when considering the analysis of experimental results, it is assumed that the expected value of the response of an experimental unit is the sum of three separate components, a general mean parameter, a parameter measuring the effect of the treatment applied and a parameter measuring the effect of the block in which the experimental unit is located. In addition, it is usually assumed that the responses are uncorrelated, with the same variance. Adding to this the assumption of normal distribution of the responses, one obtains the so-called "normal-theory model" on which the usual analysis of variance is based. Referring to it, Scheffe (1959, p. 105) writes that "there is nothing in the 'normal-theory model' of the two-way layout . . . that reflects the increased accuracy possible by good blocking. " Moreover, according to him, such a model "is inappropriate to those randomized-blocks experiments where the 'errors' are caused mainly by differences among the experimental units rather than measurement errors. " In view of this opinion, he has devoted one of the chapters of his book (Chapter 9) to randomization models, being convinced that "an understanding of the nature of the error distribution generated by the physical act of randomization should be part of our knowledge of the basic theory of the analysis of variance.
Experimental Design and Data Analysis for Biologists
Author: Gerald Peter Quinn
language: en
Publisher: Cambridge University Press
Release Date: 2002-03-21
An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data. The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models. Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models. Multivariate techniques, including classification and ordination, are then introduced. Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results. The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature. The book is supported by a website that provides all data sets, questions for each chapter and links to software.
Design and Analysis of Ecological Experiments
Author: Samuel M. Scheiner
language: en
Publisher: Oxford University Press
Release Date: 2001-04-26
Ecological research and the way that ecologists use statistics continues to change rapidly. This second edition of the best-selling Design and Analysis of Ecological Experiments leads these trends with an update of this now-standard reference book, with a discussion of the latest developments in experimental ecology and statistical practice. The goal of this volume is to encourage the correct use of some of the more well known statistical techniques and to make some of the less well known but potentially very useful techniques available. Chapters from the first edition have been substantially revised and new chapters have been added. Readers are introduced to statistical techniques that may be unfamiliar to many ecologists, including power analysis, logistic regression, randomization tests and empirical Bayesian analysis. In addition, a strong foundation is laid in more established statistical techniques in ecology including exploratory data analysis, spatial statistics, path analysis and meta-analysis. Each technique is presented in the context of resolving an ecological issue. Anyone from graduate students to established research ecologists will find a great deal of new practical and useful information in this current edition.