@ 2012 Wadsworth, Cengage Learning Chapter 9 Applying the Logic of Experimentation: Between-Subjects Designs @ 2012 Wadsworth, Cengage Learning

@ 2012 Wadsworth, Cengage Learning

Chapter 9Chapter 9

Applying the Logic Applying the Logic of Experimentation: of Experimentation: Between-Subjects Between-Subjects

DesignsDesigns



Topics

1. Between-Subjects Design Terminology2. Completely Randomized Design3. Multilevel Completely Randomized Designs4. Factorial Design


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


Between-Subjects Design Terminology


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


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


Completely Randomized Design


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


Multilevel Completely Randomized Designs


Multilevel Completely Randomized Designs

• Completely randomized design that contains more than two levels of the independent variable

• Diagrammed as:


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


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


Factorial Design


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


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


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


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.)


Factorial Designs: The Logic of Experimentation

and the Interaction Effect


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)


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


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?


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


Eight Possible Outcomes of 2 X 2 Factorial Experiments


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


Figure 9.7 B is significant; A and the interaction are nonsignificant

Figure 9.8The interaction is significant; A and B are nonsignificant


Figure 9.9 A and theinteraction are significant; B is nonsignificant

Figure 9.10B and the interaction are significant; A is nonsignificant


Figure 9.11 A and B are significant; the interaction isnonsignificant

Figure 9.12A, B, and the interaction are all significant


Interpretation of Subject Variables With Factorial Designs


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


Advantages of Factorial Designs


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


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.)


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.)


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

Documents

@ 2012 Wadsworth, Cengage Learning Chapter 9 Applying the Logic of Experimentation: Between-Subjects Designs @ 2012 Wadsworth, Cengage Learning