Incomplete Block Designs

INCOMPLETE BLOCK DESIGNS INCOMPLETE BLOCK DESIGNS Aloke Dey Indian Statistical Institute, New Delhi, India [[email protected] HINDUSTAN U L1!J UBOOK AGENCY W. World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI Published by World Scientific Publishing Co. Pie. Ltd. S Tob Tuck Link, Singapore 596224 USA ojfice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 51 Shelton Street. Covent Garden, London WC2H 9HE Brlllsb Library Cataloguiag·iD·Publlcatioa Data A catalogue record for this book is available from the British Library. INCOMPLETE BLOCK DESIGNS Copyright 0 2010 Hindustan Book Agency (HBA) Authorized edition by World Scientific Publishing Co. Pte. Ltd. for exclusive distribution worldwide except India. The dislribution rights for print copies ofthe book for India remain with HindustanBook Agency (HBA). All rights reserved. This book, or parts thereof. may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any irifomaation storage and retrieval system now known or to be invented, without written permission from the Publisher. ISBN-13 978-981-4322-68-3 ISBN-10 981-4322-68-7 Printed in India, bookbinding made in Singapore. Contents ix Preface 1 Introduction 1.1 Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Outline of the Book . . . . . . . . . . . . . . . . . . . . 2 Analysis and Properties of Block Designs 2.1 Introduction. . . . . . . . . . . . . . . . . 2.2 Intrerblock Analysis . . . . . . . . . . . . 2.3 Balancing in Block Designs . . . . . . . . 2.4 Recovery of Inter-block Information . . . 2.5 Efficiency Factor . . . . . . . . . . . . . . 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Balanced Designs 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Some Properties of Bm Designs . . . . . . . . . . . . . . . 3.3 Analysis of Bm Designs . . . . . . . . . . . . . . . . . . . 3.4 Construction and Existence of BIB Designs . . . . . . . . 3.4.1 BIB Designs Through Finite Geometries . . . . . . 3.4.2 Method of Differences . . . . . . . . . . . . . . . . 3.4.3 Some Other Constructions . . . . . . . . . . . . . . 3.4.4 Existence of BIB Designs . . . . . . . . . . . . . . 3.5 Some Generalizations of BIB designs . . . . . . . . . . . . 3.6 Construction of Variance- and Efficiency-balanced Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Nested BIB Designs . . . . . . . . . . . . . . . .