Experiments with complex treatment structures are not uncommon in horticultural research. For example, in augmented factorial designs, one control treatment is added to a full factorial arrangement, or an experiment might be arranged as a two-factorial design with some groups omitted because they are practically not of interest. Several statistical procedures have been proposed to analyze such designs. Suitable linear models followed by F-tests provide only global inference for main effects and their interactions. Orthogonal contrasts are demanding to formulate and cannot always reflect all experimental questions underlying the design. Finally, simple mean comparisons following global F-tests do not control the overall error rate of the experiment in the strong sense. In this article, we show how multiple contrast tests can be used as a tool to address the experimental questions underlying complex designs while preserving the overall error rate of the conclusions. Using simultaneous confidence intervals allows for displaying the direction, magnitude, and relevance of the mean comparisons of interest. Along with application in statistical software, shown by two examples, we discuss the possibilities and limitations of the proposed approach. In agricultural and horticultural research, controlled experiments are set up to evaluate the effect of several treatments and their interactions on physiological or developmen- tal variables. If the levels of a first factor of potential influence are combined with all levels of a second factor, the resulting exper- iment has a two-factorial, completely cross- classified treatment structure. However, often the experimental questions are manifold and, together with the background knowledge on the practical problem, lead to complex treat- ment structures. Augmented factorial designs
[1]
P. McCullagh,et al.
Generalized Linear Models
,
1972,
Predictive Analytics.
[2]
S Braat,et al.
Joint One-Sided and Two-Sided Simultaneous Confidence Intervals
,
2008,
Journal of biopharmaceutical statistics.
[3]
V. Guiard,et al.
Simultaneous confidence sets and confidence intervals for multiple ratios
,
2006
.
[4]
R. Marini.
Approaches to Analyzing Experiments with Factorial Arrangements of Treatments Plus Other Treatments
,
2003
.
[5]
A. Tamhane,et al.
Multiple Comparison Procedures
,
2009
.
[6]
Hans-Peter Piepho,et al.
A Hitchhiker's guide to mixed models for randomized experiments
,
2003
.
[7]
A. Tamhane,et al.
Multiple Comparison Procedures
,
1989
.
[8]
Piepho.
Analysing disease incidence data from designed experiments by generalized linear mixed models
,
1999
.
[9]
P. R. Nelson.
Multiple Comparisons of Means Using Simultaneous Confidence Intervals
,
1989
.
[10]
R. G. Petersen,et al.
Agricultural Field Experiments: Design and Analysis
,
1994
.
[11]
C. Dunnett.
A Multiple Comparison Procedure for Comparing Several Treatments with a Control
,
1955
.
[12]
Hans-Peter Piepho,et al.
A Note on the Analysis of Designed Experiments with Complex Treatment Structure
,
2006
.
[13]
T. Hothorn,et al.
Simultaneous Inference in General Parametric Models
,
2008,
Biometrical journal. Biometrische Zeitschrift.
[14]
Peter H. Westfall,et al.
Multiple Testing of General Contrasts Using Logical Constraints and Correlations
,
1997
.
[15]
A. Genz,et al.
On the Numerical Availability of Multiple Comparison Procedures
,
2001
.