Chapter 8: Experimental Design II - Factorial Designs
A factorial design involves any study with more than one independent variable (the
terms “independent variable” and “factor” mean the same thing) – factorial designs could
have many independent variables but in practice these designs involve two or three
factors, sometimes four.
Identifying Factorial Designs
A factorial is described with a numbering system that identifies the number of
independent variables and the number of levels of each variable, for example, 2 X 3
factorial design has two independent variables – the first has two levels and the second
has three OR a 3 X 4 X 5 factorial design has three independent variables, with three,
four and five levels.
The total number of conditions to be tested in a factorial study can be identified by
looking at all possible combinations of the different levels of each independent variable
which produces a factorial matrix – the term “levels” refers to the number of levels of
the independent variable whereas the term “conditions” equals the number of cells in a
matric, for example, the 2 X 2 memory study has two independent variables, each with
two levels and it has four different conditions because of the four cells in the matrix – the
number of conditions can be determined by calculating the product of the numbers in the
notation system, for example, 3 X 3 design has nine conditions and 2 X 2 X 2 design has
eight conditions. Outcomes – Main Effects and Interactions
In factorial studies/designs, two kinds of results occur – main effects and interactions.
Main effects refer to the overall influence of the independent variables, and interactions
examine whether the variables combine to form a more complex result.
In the memory study, the researcher is interested in the effects of two independent
variables: type of training and presentation rate – the term main effect is used to describe
the overall effect of a single independent variable therefore, in a study with two
independent variables, 2 X 2 factorial, there can be at most two significant main effects.
Determining the main effect of one variable or factor involves combining all of the data
for each of the levels of that factor – in the memory study, the main effect of type of
training is determined by combining the data for those trained to use imagery (for both
presentation rates) and comparing it to all of the data for those using rote repetition.
The way to find out if there is a main effect of type of training is to compare all of the
“imagery” data with all of the “rote” data – this involves calculating what are called row
means and you would calculate column means in order to see if there is a main effect of
presentation rate – you would have to conduct ANOVA to see if the differences are
statistically significant or simply due to chance. Interactions
In a factorial design, an interaction is said to occur when the effect of one independent
variable depends on the level of another independent variable – interactions provide the
most interesting results and can sometimes render main effects irrelevant.
For example, comparing course type for general psychology (lecture or lab) and if its true
for certain types of students (student’s major – science or humanities) – 2 X 2 factorial
design – the dependent variable would be some measure of learning so use a score from 1
to 100 on a standardized test of knowledge of general psychology given during final
There are no main effects because the row and column means are the same: 75. However,
something still happened in the study – the science students did better I the lab course but
the humanities student