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A factorial design contains two or more independent variables and one dependent variable. The independent variables, often called factors, must be categorical. Groups for these variables are often called levels. The dependent variable must be continuous, measured on either an interval or a ratio scale.
Suppose a researcher is interested in determining if two categorical variables (treatment condition and gender) affect a continuous variable (achievement). The researcher decides to use a factorial design because he or she wants to examine population group means. A factorial analysis of variance will allow him or her to answer three questions. One question concerns the main effect of treatment: Do average achievement scores differ significantly across treatment conditions? Another question concerns the main effect of gender: Does the average achievement ...
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Factor Loadings
Variations on Experimental Designs
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Single-Case
Experimental Designs
Single-case
experimental design uses experimental methodology to focus on only one subject.
This design is distinct from case study methodology, which also focuses on one
individual, because single-case experimental designs use the same systematic
procedures as other experimental designs. The researcher sets up the study to
manipulate an independent variable (or variables) and to measure how a
dependent variable responds to changes in the independent variable. This design
has the experimental benefit of a controlled comparison, because the individual
subject serves as his or her own control by participating in all of the
conditions.
In a reversal design, the individual’s behavior of interest is measured at baseline, then the intervention is implemented and the behavior is measured again. Finally, the intervention is withdrawn and the behavior of interest is measured again. This sort of reversal design is sometimes referred to as an ABA design.
The ABAB design offers the same benefits as a reversal design, but involves one additional iteration of the intervention. A multiple baseline design uses a varying time schedule that helps determine if the treatment itself (as opposed to just the passage of time) is actually leading to the change.
Advantages
of Single-Case Experimental Designs
Single-case
design requires studying only one individual, which is obviously easier and
more convenient than assembling a large group of participants. This type
of design also retains the powerful advantage of experimental control,
allowing you to collect evidence to determine causal relationships.
Disadvantages
of Single-Case Experimental Designs
Because
single-case designs focus on a single subject, it is difficult (if not impossible)
to draw any conclusions about a larger population. Multiple observations
and exposures to the intervention itself may also affect the responses
of your participant. There are also ethical concerns regarding the withdrawal
of treatment in single-case designs.
Quasi-Experimental
Designs
A
quasi-experimental design is partially experimental; it manipulates an
independent variable but perhaps does not have a full set of other experimental
controls, such as random assignment. Conversely, a study can be
quasi-experimental if it has some experimental controls but does not fully
manipulate an independent variable.
Advantages
of Quasi-Experimental Designs
Because
quasi-experimental methodology does not have as many requirements as a full
experimental design, researchers have greater freedom, both in how they set up
their methods and in the topics they choose to study. Quasi-experimental
research designs offer good options for studying a number of topics that pose
practical or ethical constraints preventing full-fledged experimental studies.
Disadvantages
of Quasi-Experimental Designs
Quasi-experimental
designs will not provide as much clarity about cause-and-effect relations as
full experimental designs. In some cases, a quasi-experimental design can be
indistinguishable from a correlational design.
Factorial
Designs
A
factorial design refers to any experimental design that has more than one
independent variable. Because a factorial design looks at multiple independent
variables simultaneously, it gives you the ability to look not only at the
effects of single variables in isolation, but also at the effects of
combinations of variables. Therefore, factorial designs allow us to examine the
complexity of the real world in an experimental paradigm.
Basic
Factorial Designs: The 2 x 2
A
2 x 2 design has four possible conditions. Each condition (often referred to as
a cell) represents a unique combination of the levels of the independent variables.
Experimental
Independent Variables vs. Participant Variables
Each
factor can either be a traditional independent variable that is manipulated
by the experimenter, or a participant variable that is not manipulated
by the experimenter.
Main
Effects and Interactions
A
main effect refers to the effect of a single independent variable on a dependent
variable. An interaction refers to the joint effect of multiple independent
variables considered in combination. Testing for an interaction
allows a researcher to examine whether the effects of one variable
on another variable (the dependent variable) are conditional on
the other remaining variables. Main effects and interactions can occur
in a number of combinations. You can have multiple main effects
and an interaction; you can have only main effects (or a single main
effect) and no interaction; or you can have no main effects but still
have an interaction. When significant interactions are present, they
substantially modify how one might frame (or think about) the importance
of the main effect.
An
Example of a Between-Subjects Factorial Design
Michelene
Chi’s work, introduced in Chapter 4, is an example of a 2 x 2 between-subjects
factorial design. Chi was interested in determining whether
age or knowledge (expertise) was the central driving force for
cognitive development in the area of memory recall. To determine which
was more important, she pitted child chess experts against college-age
novices in a task to recall either pieces on a chessboard or a
list of numbers. The first factor, memory task, had two levels— either
chess pieces or the number list. The second factor, maturation/expertise,
also had two levels—either child expert or adult
novice. Chi’s findings indicated that child experts performed at a superior
level to adult novices when completing the chessboard task, but
adult novices outperformed child experts on the number list task. The
findings serve as an elegant example of an interaction.
An
Example of a Within-Subjects Factorial Design
In
contrast to the between-subjects factorial design, within-subjects factorial
designs involve conditions where the groups for each level of a
factor are not independent of each other, but rather each group is exposed
to each level of the factor. Imagine that you are interested in the
effects of caffeine dosage (high or low) on two different memory tasks—a
visual recall task and an auditory recall task. This could be set
up as a 2 (high vs. low caffeine dosage) x 2 (visual vs. auditory memory
task) within-subjects design, so that your research subjects participate
in both the auditory and visual recall tasks, probably on different
days, and are given both high and low dosages of caffeine in combination
with the recall tasks.
An
Example of a Mixed Factorial Design
In
the most basic version of a mixed design, one independent variable is
set up as between-subjects, and another is set up as within-subjects. Participants
would be randomly assigned to one of the two conditions of
the first independent variable (the between-subjects independent variable),
and each participant would then be exposed to both conditions
of the second independent variable (the within-subjects independent
variable). As a researcher you get the benefits of a “within”
comparison, and the benefits of a “between” comparison.
Higher-order factorial designs have three or more factors that are considered simultaneously. A higher-level factorial design is best suited to capture the complexity of the world that we live in, increasing the external validity of your study. The downside of such complexity is the difficulty in interpreting multi-factor interactions.