@ 2012 wadsworth, cengage learning chapter 9 applying the logic of experimentation: between-subjects...
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@ 2012 Wadsworth, Cengage Learning
Chapter 9Chapter 9
Applying the Logic Applying the Logic of Experimentation: of Experimentation: Between-Subjects Between-Subjects
DesignsDesigns
@ 2012 Wadsworth, Cengage Learning
@ 2012 Wadsworth, Cengage Learning
Topics
1. Between-Subjects Design Terminology2. Completely Randomized Design3. Multilevel Completely Randomized Designs4. Factorial Design
@ 2012 Wadsworth, Cengage Learning
Topics (cont’d.)
5. Factorial Designs: The Logic of Experimentation and the Interaction Effect
6. Eight Possible Outcomes of 2 X 2 Factorial Experiments
7. Interpretation of Subject Variables With Factorial Designs
8. Advantages of Factorial Designs
@ 2012 Wadsworth, Cengage Learning
Between-Subjects Design Terminology
@ 2012 Wadsworth, Cengage Learning
Between-Subjects Design Terminology
• Between-subjects designs– General class of designs in which different
research participants are used in each group– Involve comparisons between different groups of
participants
@ 2012 Wadsworth, Cengage Learning
Between-Subjects Design Terminology (cont’d.)
• Characteristics– Any given participant receives only one level of
the independent variable– Only one score for each participant is used in the
analysis of the results
• Alternative: within-subjects designs– Present different levels of the independent
variable to the same group of participants
@ 2012 Wadsworth, Cengage Learning
Completely Randomized Design
@ 2012 Wadsworth, Cengage Learning
Completely Randomized Design
• One of the simplest between-subjects designs • Also called the simple randomized design or
the simple random subject design• The assignment of participants is completely
randomized between groups• Simplest form: composed of two levels of the
independent variable
@ 2012 Wadsworth, Cengage Learning
Multilevel Completely Randomized Designs
@ 2012 Wadsworth, Cengage Learning
Multilevel Completely Randomized Designs
• Completely randomized design that contains more than two levels of the independent variable
• Diagrammed as:
@ 2012 Wadsworth, Cengage Learning
Multilevel Completely Randomized Designs (cont’d.)
• Use a post hoc test– To determine whether there is a statistically
significant difference between any combinations of groups
• If you perform a large number of post hoc tests:– Expect more of them to be significant by chance
than if you performed only a few tests• Familywise error rates: possibility of a Type I error
@ 2012 Wadsworth, Cengage Learning
Multilevel Completely Randomized Designs (cont’d.)
• Single-factor analysis of variance (ANOVA)– Most common way to analyze a completely
randomized design– Null hypothesis: each research participant group
was drawn from the same population– If we reject the null hypothesis, we apply post hoc
tests– If we rule out confounds, then we conclude that
the independent variable influenced our results
@ 2012 Wadsworth, Cengage Learning
Factorial Design
@ 2012 Wadsworth, Cengage Learning
Factorial Design
• Allows us to examine scientifically the effects of more than one independent variable, both individually and collectively, on the dependent variable
• Composite of several simple completely randomized designs
• 2 X 2: two levels of one independent variable and two levels of another
@ 2012 Wadsworth, Cengage Learning
Factorial Design (cont’d.)
• Independent variables: also called factors• Treatment differences: called main effects• Interaction effect
– Result of two independent variables combining to produce a result different from that produced by either variable alone
– Occurs when the effect of one independent variable depends on the level of another independent variable
@ 2012 Wadsworth, Cengage Learning
Figure 9.2 Schematic representation of 2 X 2, 3 X 3, and 2 X 3 X 2 factorial designs. Note that the total number of treatment conditions in each design can be obtained by multiplying the number of levels of each factor
@ 2012 Wadsworth, Cengage Learning
Figure 9.2 Schematic representation of 2 X 2, 3 X 3, and 2 X 3 X 2 factorial designs. Note that the total number of treatment conditions in each design can be obtained by multiplying the number of levels of each factor (cont’d.)
@ 2012 Wadsworth, Cengage Learning
Factorial Designs: The Logic of Experimentation
and the Interaction Effect
@ 2012 Wadsworth, Cengage Learning
Factorial Design:The Logic of Experimentation
Figure 9.3 Matrix showing the four possible combinations of each of the two levels of a 2 X 2 factorial random-subject design. Notice that each cell contains one of the four possible combinations of our two independent variables (housing condition and feeding schedule)
@ 2012 Wadsworth, Cengage Learning
Figure 9.4 Schematic representation of the five steps involvedin a factorial random-subjectdesign involving two levels of each of two independent variables. (1) The entire group of 40 mice is obtainedfrom a commercial animal supplier. (2) These 40 mice are randomly assigned tofour groups of 10 each. (3) Each group is exposed to the appropriate level of each factor. (4) All subjects are measured on our dependent variable. (5) We determine whether the interaction effect and themain effects are statistically significant
@ 2012 Wadsworth, Cengage Learning
Factorial Design:The Logic (cont’d.)
• Two major questions in analyzing the outcome of any factorial design:– Does either of our independent variables produce
a statistically significant treatment effect?– As our two independent variables occur together,
do they influence each other or do they remain independent of one another in their influence on the dependent variable?
@ 2012 Wadsworth, Cengage Learning
Factorial Design:The Logic (cont’d.)
• When interpreting the results of a factorial experiment– Always interpret the interaction effects first
Table 9.2 Analysis of Variance F Table for the Mouse Study
@ 2012 Wadsworth, Cengage Learning
Eight Possible Outcomes of 2 X 2 Factorial Experiments
@ 2012 Wadsworth, Cengage Learning
Figure 9.5 The main effects and interaction effect of treatments Aand B are all nonsignificant
Figure 9.6 Treatment A is significant; treatment B and the interaction are nonsignificant
@ 2012 Wadsworth, Cengage Learning
Figure 9.7 B is significant; A and the interaction are nonsignificant
Figure 9.8The interaction is significant; A and B are nonsignificant
@ 2012 Wadsworth, Cengage Learning
Figure 9.9 A and theinteraction are significant; B is nonsignificant
Figure 9.10B and the interaction are significant; A is nonsignificant
@ 2012 Wadsworth, Cengage Learning
Figure 9.11 A and B are significant; the interaction isnonsignificant
Figure 9.12A, B, and the interaction are all significant
@ 2012 Wadsworth, Cengage Learning
Interpretation of Subject Variables With Factorial Designs
@ 2012 Wadsworth, Cengage Learning
Interpretation of Subject Variables With Factorial Designs
• Subject variable– A characteristic or condition that a participant is
seen to possess in a relatively permanent manner– Examples: sex of the participant, eye color, being
shy or outgoing, having cancer
• Logic of experimentation is weakened • Additional control measures are required
@ 2012 Wadsworth, Cengage Learning
Advantages of Factorial Designs
@ 2012 Wadsworth, Cengage Learning
Advantages of Factorial Designs
• Examine simultaneously more than one hypothesis or factor
• Much more economical in the number of participants and the total experimenter effort than studying each factor separately
• See how the various causal factors influence performance
@ 2012 Wadsworth, Cengage Learning
Figure 9.13 Participant requirements for (a) two completely randomized experiments and (b) a single 2 3 2 factorial design experiment. Note that the factorial design experiment requires half as many participants
Advantages of Factorial Designs (cont’d.)
@ 2012 Wadsworth, Cengage Learning
Advantages of Factorial Designs (cont’d.)
Figure 9.13 Participant requirements for (a) two completely randomized experiments and (b) a single 2 3 2 factorial design experiment. Note that the factorial design experiment requires half as many participants (cont’d.)
@ 2012 Wadsworth, Cengage Learning
Summary
• Between-subjects designs: involve comparisons between different groups of participants
• Interaction effect: reflects the extent to which one independent variable varies as a function of the level of the other independent variable
• In a factorial design with two independent variables, there are three null hypotheses
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