Tools for constructing optimal two-level factorial designs for a linear model containing main effects and one two-factor interaction

2007 ◽  
Vol 137 (4) ◽  
pp. 1452-1463 ◽  
Author(s):  
A.S. Hedayat ◽  
H. Pesotan
Keyword(s):  
Linear Model ◽  
Factorial Designs ◽  
Main Effects ◽  
Factor Interaction

Factorial Designs

2021 ◽  
pp. 139-160
Author(s):  
Andy Hector
Keyword(s):  
Linear Model ◽  
Plant Diversity ◽  
Fertilizer Treatment ◽  
Factorial Designs ◽  
Data Set ◽  
Simple Linear Model ◽  
Main Effects

This chapter moves on from simple ‘one-way’ designs to more complex factorial designs. It extends the simple linear model to include interactions as well as average main effects. Interactions are assessed relative to a null additive expectation where the treatments have no effect on each other. Interactions can be positive, when effects are more than additive, or negative, when they are less than expected. The chapter considers in detail the analysis of an example data set concerning the mechanisms of loss of plant diversity following fertilizer treatment.

scholarly journals On 4³ factorial designs with confounding.

1953 ◽  
Vol 1 (1) ◽  
pp. 11-14
Author(s):  
N.H. Kuiper
Keyword(s):  
Factorial Designs ◽  
Four Levels ◽  
Main Effects

A design is given for three factors each at four levels in three blocks of 8 x 8 plots. In each block in the field, fertility in the direction of columns and of rows is not neglected. The main effects are not confounded. The interactions are partially confounded. The part is

scholarly journals Experimental Investigation of Emulsion AGET ATRP of MMA in a Stirred Tank Reactor

2021 ◽  
Author(s):  
Kishor Regmi
Keyword(s):  
Monomer Conversion ◽  
Single Step ◽  
Reducing Agent ◽  
Influential Factor ◽  
Aget Atrp ◽  
Molecular Weights ◽  
Step Procedure ◽  
Catalyst Complex ◽  
Main Effects ◽  
Factor Interaction

This study investigates the emulsion AGET ATRP of MMA in a 2-L reactor using the reactants: surfactant (Brij 98), catalyst complex (CuBr2/dNbpy), initiator (EBiB) and reducing agent (ascorbic acid). Preliminary trials demonstrate that the two-step procedure preserves the ATRP living features much better than the single-step procedure. An experimental design and statistical analysis were performed to investigate the main effects and two-factor interaction effects of temperature, surfactant, catalyst complex, initiator and reducing agent on the monomer conversion, average molecular weights and polydispersity index of the polymer. The input-output model predictions agree with experimental data. The results revealed that the temperature was the most influential factor for all three-process responses with 71.34%, 32.78% and 27.76 % contribution. However, the initiator was the least influential factor for both conversion and PDI with 0.035% and 0.13% contribution, whereas the surfactant was the least influential factor for molecular weight with 0.068% contribution

Recent developments in the design of field experiments. IV. Lattice squares with split plots

1947 ◽  
Vol 37 (2) ◽  
pp. 156-162 ◽  
Author(s):  
O. Kempthorne
Keyword(s):  
Field Experiments ◽  
Factorial Designs ◽  
Split Plot ◽  
Trial Testing ◽  
Recent Developments ◽  
Factor Interaction ◽  
Three Factor

The testing of a large number of varieties or treatments can generally be most conveniently made by the use of the quasi-factorial designs devised by Yates. The value of such designs is enhanced by the possibility of introducing further treatments on parts of the plots. The present paper describes a lattice square trial testing 25 organic treatments (actually 22 different treatments with a control represented three times) in which all combinations of nitrogen, phosphate and potash were also tested by splitting the plots and confounding the three-factor interaction with whole plots, the total number of split-plots being 300. Both the design and analysis are comparatively simple and straight-forward, and will serve as an example of the use of split-plot confounding in most types of quasi-factorial designs.

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