Practical analysis of factorial experiments in forestry

1995 ◽  
Vol 25 (3) ◽  
pp. 446-461 ◽  
Author(s):  
S.V. Stehman ◽  
M.P. Meredith
Keyword(s):  
Full Advantage ◽  
Practical Approach ◽  
Standard Errors ◽  
Factorial Designs ◽  
Factorial Experiments ◽  
Default Options ◽  
Practical Analysis ◽  
Treatment Structure ◽  
Main Effects ◽  
Multiple Comparison Procedures

Factorial designs are among the most frequently employed for arranging treatments in forestry experiments. Yet researchers often fail either to recognize the factorial treatment structure or to take full advantage of the structure for interpreting treatment effects. The analysis of factorial experiments should focus on comparisons of means of research interest specified by the investigator. Reliance on default options of computing packages or routine application of multiple comparison procedures often fails to address research hypotheses directly. A two-step strategy for the analysis of factorial experiments entails a check for interaction followed by estimation of either main effects or simple effects. This strategy emphasizes sensible mean comparisons through estimation of contrasts and their standard errors. The strategy also applies to the analysis of factorial experiments in which unequal replication or empty cells complicate the analysis. We summarize a practical approach for use by forest scientists and applied statisticians consulting with such scientists so that they may analyze and interpret their experiments more effectively.

Factorials.

2021 ◽  
pp. 56-66
Author(s):  
Edward F. Durner
Keyword(s):  
Application Rate ◽  
Interactive Effects ◽  
Nitrogen Application ◽  
Factorial Experiments ◽  
Main Effect ◽  
Significance Levels ◽  
Four Levels ◽  
Treatment Structure ◽  
Main Effects ◽  
Single Factor Experiment

Abstract This chapter focuses on factorials. Experiments involving two or more factors, each at two or more levels, are called 'factorial experiments'. There is no such thing as a factorial design. Factorial refers to treatment structure. Factorial treatment structures are combined in an efficient experimental design. When considering two or more factors, it introduces the concepts of 'main effects' and 'interactive effects' (interactions). The 'main effect' of a factor is a measure of the change in the response variable to changes in the level of the factor, averaged over all levels of all other factors in an experiment. An 'interaction' occurs when the response to various levels of one factor changes as the levels of another factor change. A single-factor experiment, with the factor 'nitrogen application rate' at four levels to evaluate strawberry yield, and modify it to now include the concept of a factorial treatment structure in a completely random design were conducted. The significance levels for time (0.0926) and rate (0.4287) were neither significant. Thus it doesn't seem to matter when nitrogen is applied or not; there is no effect of nitrogen application on strawberry yield.

Inter­Effect­Orthogonality in Factorial Experiments

1979 ◽  
Vol 28 (1-4) ◽  
pp. 83-108 ◽  
Author(s):  
Rahul Mukerjbe
Keyword(s):  
Sufficient Conditions ◽  
Orthogonality Condition ◽  
Necessary And Sufficient Conditions ◽  
Factorial Designs ◽  
Factorial Experiments ◽  
Necessary And Sufficient

A set of necessary and sufficient conditions has been established for best linear estimates of estimable treatment contrasts belonging to different facotrial effects to be mutually orthogonal. The cases of both connected and disconnected designs have been considered. The analysis of connected designs satisfying the orthogonality condition has been derived. The orthogonality condition obtained is seen to throw new light on some of the existing methods of construction of symmetric and asymmetric factorial designs. Extension of the conditions to designs eliminating heterogeneity in several directions is immediate

s-Level Multiple-Response Main-Effects Factorial Plans

1992 ◽  
Vol 42 (3-4) ◽  
pp. 237-246
Author(s):  
U. Batra ◽  
M.L. Aggarwal
Keyword(s):  
Dispersion Matrix ◽  
Multiple Response ◽  
Relative Importance ◽  
Factorial Experiments ◽  
Response Variable ◽  
Main Effects ◽  
Observation Vector ◽  
Response Variables

This paper deals with construction of plans for s-level factorial experiments in which there are p response variables and each respose is affected by one or more factors. The plans are orthogonal for each response variable. Estimates of the parameters in the models for such plans are obtained when Σ, the dispersion matrix of an observation vector is known. The properties of these estimates can be of help in designing the experiment so that the variances of estimates of the parameters can be influenced by their relative importance.

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.

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