Balance in Designed Experiments with Orthogonal Block Structure

Ela Commutative Orthogonal Block Structure and Error Orthogonal Models

A model has orthogonal block structure, OBS, if it has variance-covariance matrix that is a linear combination of known pairwise orthogonal orthogonal projection matrices that sum to the identity matrix. These models were introduced by Nelder is 1965, and continue to play an important part in randomized block designs. Two important types of OBS are related, and necessary and sufficient conditio...

Commutative orthogonal block structure and error orthogonal models

A model has orthogonal block structure, OBS, if it has variance-covariance matrix that is a linear combination of known pairwise orthogonal orthogonal projection matrices that sum to the identity matrix. These models were introduced by Nelder is 1965, and continue to play an important part in randomized block designs. Two important types of OBS are related, and necessary and sufficient conditio...

Analyzing Statistically Designed Experiments

A white paper on analyzing data from statistically designed experiments in industry, business and research using the IMSL™ C Numerical Library.

On Orthogonal Block Elimination

We consider the block elimination problem Q A 1 A 2 = ?C 0 , where, given a matrix A 2 R mk , A 11 2 R kk , we try to nd a matrix C with C T C = A T A and an orthogonal matrix Q that eliminates A 2. Sun and Bischof recently showed that any orthogonal matrix can be represented in the so-called basis-kernel representation Q = Q(Y; S) = I ? Y ST T. Applying this framework to the block elimination ...

On Computer‐Designed Quantum Experiments