fixed effects designs is important because it influences the choice of denominator error
term in the F test (see for example Chapter 8).
The term subjects usually refers to individuals taking part in an experiment. All
subjects who are allocated to a particular level of treatment within a factor are referred to
as being in a cell in the experimental design. In the fixed-effects teaching methods
example all subjects allocated to the storytelling experimental condition would belong to
one cell. This would be a one-factor experimental design. Experimental designs are more
efficient (more powerful for the same number of subjects) if the designs are balanced
which means having equal numbers of subjects in each cell of the design. A one-factor
fixed ANOVA design could be extended if pupils were classified by sex, thus introducing
a second factor. If every level of every factor is crossed with every level of every other
factor, this is called a completely crossed factorial design and is an example of what is
called a two-factor design. In the methods by sex experiment this would be a 3×2
factorial design with six cells (see Figure 1.3).
Factor 1:^ Factor 2: Method^
Sex Level 1 (Silent
reading)
Level 2
(Storytelling)Level 3 (Storytelling enhanced
by pictures)
Level 1
(female)Cell 1 Cell 2 Cell 3Level 2
(male)Cell 4 Cell 5 Cell 6Figure 1.3: Two-way (unrelated)
completely crossed factorial design
(one-factor ‘sex’ with 2 levels and one-
factor ‘method’ with 3 levels)
The term two-way ANOVA may be used to refer to analysis of the two factors. It is
possible to have an experimental design with both fixed and random effects. This is
known as a mixed-model design.
In the example of a two-factor experimental design, methods by sex, if the researcher
examines only differences among the three teaching methods, ignoring the other factor,
sex, this is looking at the main effects of teaching method. The researcher may then
decide to look at the other main effect in this design, sex, ignoring any effects of teaching
method. If the researcher were to look at the effect of a factor at one level of another
factor, for example, to compare differences among three teaching methods (teaching
methods factor) for females only (at one level of factor, sex), this is looking at the simple
effects for females. If the effects of one factor are different at different levels of the other
factor then an interaction between the two factors is said to exist. For example, if the
differences in vocabulary score due to teaching method were much greater for males than
females then an interaction exists between the factors teaching method and sex
(interaction effects are explained in Chapter 8).
All the examples referred to thus far are examples of between subject designs
because different subjects appear in each cell of the experimental design, which is the
same as different subjects being allocated to each combination of experimental
conditions. When the experimental design requires the same subjects to be included
Statistics and research design 13