Analysis of Factorial Experiments Using Generalized Matrix Operations-Reference-Cited by-同舟云学术

Analysis of Factorial Experiments Using Generalized Matrix Operations

Published:1967-07 Issue:3 Volume:14 Page:508-519
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Oliver I.¹

Affiliation:

1. Computer Center, Ohio State University, Columbus, Ohio and Computer Centre, University of Queensland, Queensland, Australia

Abstract

The computer analysis of factorial experiments is discussed in terms of a new generalized matrix notation which highlights the special properties of factorial designs. A method of calculating an analysis of a variance suitable for programming as a library subroutine is described. An orthogonal transformation is used to obtain components of variance based on single degrees of freedom. The transformation is done sequentially so that no additional storage for intermediate results is required. The analysis of variance table is obtained by summation of the components according to a simple indexing procedure. An algorithm for the calculation of sums and means over all combinations of factor levels is proposed.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/321406.321413

Reference6 articles.

1. Tabular Analysis of Factorial Experiments and the Use of Punch Cards

2. A General Analysis of Variance Scheme Applicable to a Computer With a Very Large Memory

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1. COMPUTERS AS AN INSTRUMENT FOR DATA ANALYSIS;TECHNOMETRICS;1970

2. COMPUTERS AND PROCESS CONTROL;Industrial & Engineering Chemistry;1969-01-01

3. Algorithms: Algorithm 330: Factorial analysis of variance;Communications of the ACM;1968-06