Ch. 11: Factorial Designs Flashcards
factor
an independent variable in an experiment, especially those that include two or more independent variables
factorial design
a research design that includes two or more factors
single-factor design
a research study with only one independent variable
annotation of factorial designs
- Each factor is denoted by a letter (A, B, C, and so on)
- Factorial design notation species the number of levels or conditions that exist for each factor
what does a 2 x 3 x 2 design represent?
a three-factor design with two, three, and two levels of each of the factors respectively, for a total of 12 conditions
advantage of factorial designs
Factorial designs create a more realistic situation where multiple factors influence behaviour
main effect
the mean differences among the levels of one factor
interpreting factorial design matrixes
When the research study is represented as a matrix with one factor defining the rows and the second factor defining the columns, the mean differences among the rows define the main effect for one factor and the mean differences for the columns define the main effect for the other
how many main effects does a two-factor design have?
two main effects: one for each factor
interaction
occurs whenever two factors, acting together produce mean differences that are not explained by the main effects of the two factors
when is there no interaction effect?
If the main effect for either factor applies equally across all levels of the second factor
alternative views of the interaction between factors
- The notion of independence: if the effect of one factor depends on the influence of the other factor, then there is an interaction
- Focuses on the pattern that is produced when the means from a two-factor study are presented in a graph: the existence of nonparallel lines (lines that cross or converge) is an indication of an interaction between the two factors
identifying interactions
- You can identify an interaction by comparing the mean differences in any individual row or column with the mean differences in other rows or columns
- If the size and direction of the difference in one row or column are the same as the corresponding differences in other rows and columns, then there is no interaction
- If the differences change from one row or column to another, then there is evidence of an interaction
statistical analyses of factorial designs
- Data must be evaluated by a hypothesis test to determine if the effects are statistically significant
- Even if statistical analyses indicate significant effects, you still need to be careful about interpreting the outcome
- If the analysis results in a significant interaction, the main effects may present a distorted view of the actual outcome
are main effects and interactions independent?
yes
advantages of between-subjects factorial designs
- Avoids problems from order effects
- Well-suited for situations in which a lot of participants are available
limitations of between-subjects factorial designs
- Require a large number of participants
- Individual differences can become confounding variables
advantages of within-subjects factorial designs
- Require only one group of participants
- Reduce the problems associated with individual differences
limitations of within-subjects factorial designs
- Participants must be measured in many different conditions, which can increase participant attrition (walking away before the study is done)
- Increases the potential for testing effects
- Makes it more difficult to counterbalance the design
mixed design
a factorial study that combines two different research designs
example of a mixed design
one between-subjects and one within-subjects factor
combined strategy
uses different research strategies in the same factorial design. One factor is a true independent variable (experimental strategy) and the other is a quasi-independent variable (nonexperimental or quasi-experimental strategy)
2 main categories of combined strategies
- The second factor is a preexisting participant characteristic, which creates nonequivalent or quasi-independent variables
- The second factor is time
person-by-environment or person-by-sitation designs
designs that add participant characteristics as a second factor
two groups of participants in pretest-posttest control group designs
- The treatment group is measured before and after receiving a treatment
- The control group is also measured twice but does not receive any treatment
what type of design are pretest-posttest control group designs?
two-factor mixed designs; one factor (treatment/control) is a between-subjects factor
The other (pretest/ posttest) is a within-subjects factor
higher-order factorial designs
a more complex design that involves three or more factors
three-way interaction
indicates that the two-way interaction between A and B depends on the levels of factor C
statistical analysis of factorial designs
- The standard procedure is to compute the mean for each treatment condition and use an analysis of variance (ANOVA) to evaluate the statistical significance of the mean differences
- The two-factor ANOVA conducts three separate hypothesis tests: one to evaluate the two main effects and one to evaluate the interaction. The test then uses an F-ratio to determine whether the actual mean differences in the data are significantly larger than reasonably would be expected by chance
applications of factorial designs
- Expanding and replicating a previous study
- Reducing variance in between-subjects designs
- Evaluating order effects in within-subjects designs
how can you reduce variance in between-subject designs?
by using the specific variable as a second factor, thereby creating a two-factor design
how should you measure and evaluate order effects in a factorial design?
you must use counterbalancing and a factorial design with the order of treatments as the second factor
structure of a counterbalanced design
can be presented as a matrix with the two treatment conditions defining the columns and the order of treatments defining the rows
Three possible outcomes can occur by using the order of treatments as a second factor
- no order effects
- symmetrical order effects
- nonsymmetrical order effects
no order effects
it doesn’t matter if a treatment is presented first or second
symmetrical order effects
when order effects exist, the scores in the second treatment are influenced by participation in the first treatment
nonsymmetrical order effects
there is a lopsided or nonsymmetrical interaction between the treatments and orders
can you construct a factorial study for which all factors are true independent variables?
yes
can you construct a factorial study for which all the factors are nonmanipulated, quasi-independent variables?
yes
