Permutation Covariate Analyses of Residuals Based on Euclidean Distance

1997 ◽  
Vol 81 (3) ◽  
pp. 795-802 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry
Keyword(s):  
Euclidean Distance ◽  
Latin Square ◽  
Experimental Designs ◽  
Permutation Procedure ◽  
Split Plot ◽  
Compound Symmetry ◽  
Homogeneity Of Variance

A new procedure to analyze the results of experimental designs is introduced. A permutation procedure based on Euclidean distance is used to evaluate residuals obtained from least sum of absolute deviations regression. Applications include completely randomized and randomized block configurations including one-way, factorial, split-plot, and Latin square designs, with or without covariates. Parametric assumptions of homogeneity of variance, compound symmetry, and normality are eliminated with this procedure.

A Fortran Program for Permutation Covariate Analyses of Residuals Based on Euclidean Distance

1998 ◽  
Vol 82 (2) ◽  
pp. 371-375 ◽  
Author(s):  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Euclidean Distance ◽  
Latin Square ◽  
Fortran Program ◽  
Experimental Designs ◽  
Permutation Procedure ◽  
Split Plot

A FORTRAN program is presented to analyze the results of experimental designs. A Euclidean distance permutation procedure is used to evaluate residuals obtained from least sum of absolute deviations regression. Applications include completely randomized and randomized block configurations including one-way, factorial, split plot, and Latin square designs, with or without covariates.

Multivariate Multiple Regression Analyses: A Permutation Method for Linear Models

2002 ◽  
Vol 91 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry
Keyword(s):  
Multiple Regression ◽  
Euclidean Distance ◽  
Linear Models ◽  
Latin Square ◽  
Experimental Designs ◽  
Regression Analyses ◽  
Permutation Procedure ◽  
Multivariate Extension ◽  
Multivariate Multiple Regression ◽  
Euclidean Distances

A multivariate extension of a univariate procedure for the analysis of experimental designs is presented. A Euclidean-distance permutation procedure is used to evaluate multivariate residuals obtained from a regression algorithm, also based on Euclidean distances. Applications include various completely randomized and randomized block experimental designs such as one-way, Latin square, factorial, nested, and split-plot designs, with and without covariates. Unlike parametric procedures, the only required assumption is the randomization of subjects to treatments.

The split-plot and split-split-plot designs.

2021 ◽  
pp. 204-243
Author(s):  
Edward F. Durner
Keyword(s):  
Agricultural Research ◽  
Experimental Designs ◽  
Split Plot

Abstract This chapter focuses on one of the most flexible and useful experimental designs for agricultural research, the split-plot and its variations. An experiment with strawberry production was used as an example.

Least Absolute Regression Residuals: Analyses of Split-Plot Designs

1999 ◽  
Vol 85 (2) ◽  
pp. 445-453 ◽  
Author(s):  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Least Squares ◽  
Euclidean Geometry ◽  
Ordinary Least Squares ◽  
Regression Residuals ◽  
Split Plot ◽  
Homogeneity Of Variance ◽  
Plot Design

Residuals obtained from least sum of absolute deviations regression are analyzed by a procedure consistent with Euclidean geometry. Applications to a split-plot design are illustrated and evaluated. The procedure is applicable to balanced and unbalanced split-plot designs and avoids the customary assumptions of ordinary least squares analyses including normality, homogeneity of variance and covariance, and sphericity.

Split-Plot Experimental Designs for Combinatorial and High-Throughput Experimentation

2005 ◽  
Vol 24 (1) ◽  
pp. 38-44 ◽  
Author(s):  
Flor A. Castillo ◽  
Jeff Sweeney ◽  
Peter Margl ◽  
Wayne Zirk
Keyword(s):  
High Throughput ◽  
Experimental Designs ◽  
High Throughput Experimentation ◽  
Split Plot

F-test bias for experimental designs of the Latin square type

Psychometrika ◽  
1955 ◽  
Vol 20 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Neil Gourlay
Keyword(s):  
Latin Square ◽  
Test Bias ◽  
Experimental Designs ◽  
F Test

scholarly journals Mixed two- and four-level experimental designs for interchangeable parts with different degrees of assembly difficulty

2017 ◽  
Vol 34 (8) ◽  
pp. 1152-1166
Author(s):  
Carla A. Vivacqua ◽  
Linda Lee Ho ◽  
André L.S. Pinho
Keyword(s):  
General Framework ◽  
Design Methodology ◽  
Experimental Designs ◽  
Content Type ◽  
Number Of Generators ◽  
Split Plot ◽  
Exclusive Sets ◽  
Direct Use ◽  
Plot Type ◽  
Selection Of

Purpose The purpose of this paper is to show how to properly use the method of replacement to construct mixed two- and four-level minimum setup split-plot type designs to accommodate the presence of hard-to-assemble parts. Design/methodology/approach Split-plot type designs are economical approaches in industrial experimentation. These types of designs are particularly useful for situations involving interchangeable parts with different degrees of assembly difficulties. Methodologies for designing and analyzing such experiments have advanced lately, especially for two-level designs. Practical needs may require the inclusion of factors with more than two levels. Here, the authors consider an experiment to improve the performance of a Baja car including two- and four-level factors. Findings The authors find that the direct use of the existing minimum setup maximum aberration (MSMA) catalogs for two-level split-plot type designs may lead to inappropriate designs (e.g. low resolution). The existing method of replacement for searching exclusive sets of the form (α, β, αβ) available in the literature is suitable for completely randomized designs, but it may not provide efficient plans for designs with restricted randomization. Originality/value The authors provide a general framework for the practitioners and have extended the algorithm to find out the number of generators and the number of base factor at each stratum, which guide the selection of mixed two-level and four-level MSMA split-plot type designs.

The efficiency of some experimental designs used in dairy husbandry experiments

1953 ◽  
Vol 43 (4) ◽  
pp. 407-412 ◽  
Author(s):  
W. B. Taylor ◽  
P. J. Armstrong
Keyword(s):  
Milk Fat ◽  
Latin Square ◽  
Experimental Designs ◽  
Analysis Of Covariance ◽  
Fat Percentage

Records for milk, fat, solids-not-fat and fat percentage over forty-eight complete lactations were used as uniformity data to determine the relative efficiencies of a variety of experimental designs used in dairy husbandry experiments.In general, it was found that:1. Experiments conducted during the earlier part of the lactation are more efficient than those conducted during the later part.2. Three-weekly periods are generally more efficient than 5-weekly periods.3. If 3-weekly periods are used, then extending the time of the experiment over four such periods instead of three reduces the error. The converse is the case with 5-weekly periods since the experiment is carried over into the highly variable later part of the lactation.4. Grouping the animals according to the yields recorded during the first 40 days of lactation does not appear to reduce the error.An analysis of covariance using the pro-experimental records of the performance of the animals has been carried out on ordinary group trials and it is hoped to publish the results at a later date, but investigations on the data have shown that both reversal and Latin square designs are more efficient than ordinary group trials even when such an analysis is performed.

Homogeneity of variance and the Latin square design.

1950 ◽  
Vol 47 (2) ◽  
pp. 118-129 ◽  
Author(s):  
Allen L. Edwards
Keyword(s):  
Latin Square ◽  
Homogeneity Of Variance
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