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

Topics 1.Between-Subjects Design Terminology 2.Completely Randomized Design 3.Multilevel Completely Randomized Designs 4.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 involved in a factorial random-subject design involving two levels of each of two independent variables. (1) The entire group of 40 mice is obtained from a commercial animal supplier. (2) These 40 mice are randomly assigned to four 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 the main 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 A and 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 9.8 The interaction is significant; A and B are nonsignificant

@ 2012 Wadsworth, Cengage Learning Figure 9.9 A and the interaction are significant; B is nonsignificant Figure 9.10 B and the interaction are significant; A is nonsignificant

@ 2012 Wadsworth, Cengage Learning Figure 9.11 A and B are significant; the interaction is nonsignificant Figure 9.12 A, 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 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 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