Ch. 11: Factorial Designs

Question 1

factor

Answer 1

an independent variable in an experiment, especially those that include two or more independent variables

Question 2

factorial design

Answer 2

a research design that includes two or more factors

Question 3

single-factor design

Answer 3

a research study with only one independent variable

Question 4

annotation of factorial designs

Answer 4

• 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

Question 5

what does a 2 x 3 x 2 design represent?

Answer 5

a three-factor design with two, three, and two levels of each of the factors respectively, for a total of 12 conditions

Question 6

advantage of factorial designs

Answer 6

Factorial designs create a more realistic situation where multiple factors influence behaviour

Question 7

main effect

Answer 7

the mean differences among the levels of one factor

Question 8

interpreting factorial design matrixes

Answer 8

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

Question 9

how many main effects does a two-factor design have?

Answer 9

two main effects: one for each factor

Question 10

interaction

Answer 10

occurs whenever two factors, acting together produce mean differences that are not explained by the main effects of the two factors

Question 11

when is there no interaction effect?

Answer 11

If the main effect for either factor applies equally across all levels of the second factor

Question 12

alternative views of the interaction between factors

Answer 12

• 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

Question 13

identifying interactions

Answer 13

• 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

Question 14

statistical analyses of factorial designs

Answer 14

• 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

Question 15

are main effects and interactions independent?

Answer 15

yes

Question 16

advantages of between-subjects factorial designs

Answer 16

• Avoids problems from order effects
• Well-suited for situations in which a lot of participants are available

Question 17

limitations of between-subjects factorial designs

Answer 17

• Require a large number of participants
• Individual differences can become confounding variables

Question 18

advantages of within-subjects factorial designs

Answer 18

• Require only one group of participants
• Reduce the problems associated with individual differences

Question 19

limitations of within-subjects factorial designs

Answer 19

• 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

Question 20

mixed design

Answer 20

a factorial study that combines two different research designs

Question 21

example of a mixed design

Answer 21

one between-subjects and one within-subjects factor

Question 22

combined strategy

Answer 22

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)

Question 23

2 main categories of combined strategies

Answer 23

• The second factor is a preexisting participant characteristic, which creates nonequivalent or quasi-independent variables
• The second factor is time

Question 24

person-by-environment or person-by-sitation designs

Answer 24

designs that add participant characteristics as a second factor

Question 25

two groups of participants in pretest-posttest control group designs

Answer 25

• The treatment group is measured before and after receiving a treatment
• The control group is also measured twice but does not receive any treatment

Question 26

what type of design are pretest-posttest control group designs?

Answer 26

two-factor mixed designs; one factor (treatment/control) is a between-subjects factor
The other (pretest/ posttest) is a within-subjects factor

Question 27

higher-order factorial designs

Answer 27

a more complex design that involves three or more factors

Question 28

three-way interaction

Answer 28

indicates that the two-way interaction between A and B depends on the levels of factor C

Question 29

statistical analysis of factorial designs

Answer 29

• 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

Question 30

applications of factorial designs

Answer 30

• Expanding and replicating a previous study
• Reducing variance in between-subjects designs
• Evaluating order effects in within-subjects designs

Question 31

how can you reduce variance in between-subject designs?

Answer 31

by using the specific variable as a second factor, thereby creating a two-factor design

Question 32

how should you measure and evaluate order effects in a factorial design?

Answer 32

you must use counterbalancing and a factorial design with the order of treatments as the second factor

Question 33

structure of a counterbalanced design

Answer 33

can be presented as a matrix with the two treatment conditions defining the columns and the order of treatments defining the rows

Question 34

Three possible outcomes can occur by using the order of treatments as a second factor

Answer 34

• no order effects
• symmetrical order effects
• nonsymmetrical order effects

Question 35

no order effects

Answer 35

it doesn’t matter if a treatment is presented first or second

Question 36

symmetrical order effects

Answer 36

when order effects exist, the scores in the second treatment are influenced by participation in the first treatment

Question 37

nonsymmetrical order effects

Answer 37

there is a lopsided or nonsymmetrical interaction between the treatments and orders

Question 38

can you construct a factorial study for which all factors are true independent variables?

Answer 38

yes

Question 39

can you construct a factorial study for which all the factors are nonmanipulated, quasi-independent variables?

Answer 39

yes