## Characterizations and analysis of block designs |

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### Contents

INTRODUCTION | 1 |

ANALYSIS OF BLOCK DESIGNS | 9 |

BALANCED AND PARTIALLY BALANCED DESIGNS | 23 |

7 other sections not shown

### Common terms and phrases

Annals of Mathematical associate PBIB designs association scheme balanced incomplete block binary block sizes Bradley Chapter circulant matrix class of designs class PBIB designs concurrence matrix Consider Corollary cyclic designs denotes design D(v design with parameters diagonal elements diagonal matrix dose dual design EB design efficiency balanced designs efficiency classes efficiency factor eigen vectors estimated existence experimental factorial experiment factorial structure factorially balanced following theorem GD design group divisible Gupta Hedayat i-th incidence matrix incomplete block designs initial block interaction Kageyama Kronecker product design latin square Lemma linear linked block main effect multiplicities mutually orthogonal non-zero eigen values number of treatments optimal partial geometry Proof Puri and Nigam reduced normal equations regular graph replications resulting design robust Royal Statistical Society Sankhya Snedecor's F distribution SPEB sum of squares supplemented block designs TFB design treatment combinations values of NN variance balanced design Wolock