Biostatistics

352 CHAPTER 8 ANALYSIS OF VARIANCE
in knowing if there were differences between the two treatments on subjects that were
measured multiple times.
Assumptions The assumptions of the two-factor repeated measures design are the same
as the single-factor repeated measures design. However, it is not uncommon for there to be
interactions among the treatments in this design, a potential violation of Assumption 5,
above. Interaction effects can be interesting to examine, but are complex to calculate. For
this reason, and at the level of the intended audience using this text, we will assume that
interaction effects, when present, are mathematically handled using a statistical software
package that provides correct calculations for this issue.
The Model The model for the two-factor repeated measures design must represent the
fact that there are two factors, A and B, and they have a potential interaction. These
features, along with the block effect and error, must be accounted for in the model, which is
given by
x ijk ¼ m þ r ij þ a i þ b j þðabÞ ij
þ e ijk
i ¼ 1; 2; ...; a; j ¼ 1; 2; ...; b; k ¼ 1; 2; ...; n
(8.4.2)
In this model
x ijk is a typical individual from the overall population
m an unknown constant
r ij represents a block effect
a j represents the main effect of factor A
b k represents the main effect of factor B
ðabÞ jk
represents the interaction effect of factor A and factor B
e ijk is a residual component representing all sources of variation other than treatments
and blocks.
This model is very similar to the two-factor ANOVA model presented in Section 8.5.
EXAMPLE 8.4.2
The Mid-Michigan Medical Center (A-16) examined 25 subjects with neck cancer and
measured as one of the outcome variables an oral health condition score. Patients were
randomly divided into two treatment groups. These were a placebo treatment (treatment 1)
and an aloe juice group (treatment 2). Cancer health was measured at baseline and at the
end of 2, 4, and 6 weeks of treatment. The goal was to discern if there was any change in
oral health condition over the course of the experiment and to see if there were any
differences between the two treatment conditions.
Solution:
1. Data. See Table 8.4.2.
2. Assumptions. We assume that the assumptions for the two-factor
repeated measures experiment are met.