Blocked, Split-Plot, and Strip-Plot Complete Factorial Designs

2016 ◽  
pp. 107-130
Keyword(s):  
Factorial Designs ◽  
Split Plot

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.

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

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