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Introduction to Experimental Design Read chapter Read first chapter

2018 | OriginalPaper | Chapter

6. Two-Factor Cross-Classification Designs

Authors : Paul D. Berger, Robert E. Maurer, Giovana B. Celli

Published in: Experimental Design

Publisher: Springer International Publishing

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Abstract

Chapter 2 introduced one-factor designs – experiments designed to determine whether the level of a factor, the (one) independent variable, affects the value of some quantity of interest, the dependent variable. By way of example, we considered whether device/usage influences battery life. We expanded on this initial analysis by introducing multiple-comparison testing and orthogonal breakdowns of sums of squares.

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previous chapter Orthogonality, Orthogonal Decomposition, and Their Role in Modern Experimental Design
next chapter Nested, or Hierarchical, Designs
Appendix
Available only for authorised users
Footnotes
1
In fact, this is definitely the case. In general, a battery can be manufactured to cater to one type of usage, often at the expense of another kind of usage.
 
2
In this chapter, we discuss experiments with and without replication, with all combinations of levels of the two factors. Later in the text, we consider experiments in which we could, but choose not to, for good reasons, run all combinations of levels of the two factors. The two factors are, however, still considered to be cross-classified. In addition, the definition of cross-classified extends to more than two factors.
 
3
Having an equal number of replicates in each cell is a sufficient, but not necessary, condition for the design to be orthogonal.
 
4
A balanced design is one in which all levels of all factors are together with all levels of all other factors an equal number of times.
 
5
There isn’t a direct command in JMP for this type of analysis. In order to run a two-way ANOVA, we have to select Fit Model under Analyze, then select the appropriate Y and construct model effects (in this case, course, weeks, and course*weeks).
 
6
We saw a brief definition of fixed and random models in Chap. 3.
 
7
This type of experiment, in which “people” is one of the factors, is often called a “repeated-measures” design, or a “within-subjects” design, to denote that the same person (say, as the row) is utilized for more than one level of the other factor(s).
 
8
H. H. Friedman and W. S. Dipple Jr. (1978), “The Effect of Masculine and Feminine Brand Names on the Perceived Taste of a Cigarette.” Decision Sciences, vol. 9, pp. 467–471.
 
9
M. Friedman (1937), “The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance.” Journal of the American Statistical Association, vol. 32, pp. 675–701.
 
10
Even though there are several nonparametric tests, we are limited to the Friedman test as an equivalent to two-way ANOVA. Unfortunately, there is no direct command for this test in JMP and Excel. However, it is available in SPSS as we shall demonstrate in the Appendix.
 
11
This is true for sufficiently high values of R and C. For R = 4, it is considered true for C > 4 (our example has R = 9). Tables of exact values for lower values of R for different C’s appear in various texts on nonparametric statistics and in Friedman’s original article (Journal of the American Statistical Association, 1937, vol. 32, pp. 688–689 for the tables).
 
12
There has been an increased concern with the design of certain clinical trials for new drugs as they often focus on one gender (most often, male), even though the results will be extrapolated to the whole population.
 
13
An “add-in” is an additional piece of software that works seamlessly with the original piece of software (here, Excel) and enhances its capabilities, or at least makes the program more user-friendly. Many add-ins with experimental design capabilities are available for Excel, depending on the type of PC or Macintosh used.
 
14
Each factor’s effect, by itself, is called a “main effect.” If we pooled the main effects, we would add, for each factor, the sums of squares and the degrees of freedom, which yields a mean square and an F calc value. If we wondered whether the main effects taken as a whole are significant (although this is often not a useful question), we would use the pooled F calc and p-value.
 
15
It is important to check to see if the independent variables are recognized as factors (or categorical variables) by R; otherwise the analysis will not work properly. This is because we used integers to name the different levels, which could be misinterpreted as numeric vectors by the software. The variables can be converted to factors, if necessary. Alternatively, one can use the factor() function to indicate that “brand” and “device” are indeed factors.
 
Metadata
Title
Two-Factor Cross-Classification Designs
Authors
Paul D. Berger
Robert E. Maurer
Giovana B. Celli
Copyright Year
2018
Book
Experimental Design

Print ISBN: 978-3-319-64582-7

Electronic ISBN: 978-3-319-64583-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-64583-4_6

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