Research Methods for the Behavioral Sciences (MindTap Course List)
5th Edition
ISBN: 9781305104136
Author: Frederick J Gravetter, Lori-Ann B. Forzano
Publisher: Wadsworth Publishing
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Chapter 11, Problem 8E
In Figure 11.5, we show three combinations of main effects and interactions for a 2 × 2 factorial design. Using the same 2 × 2 structure, with factor A defining the rows and factor B defining the columns, create a set of means that produce each of the following patterns:
a. A main effect for factors A and B, but no interaction.
b. A main effect for factor A and an interaction, but no main effect for factor B.
c. A main effect for both factors and an interaction.
FIGURE 11.5
Three Possible Combinations of Main Effects and Interactions in a Two-Factor Experiment.
(a) Data showing a main effect for factor A but no main effect for factor B and no interaction.
(b) Data showing main effects for both factor A and factor B but no interaction.
(c) Data showing no main effect for either factor, but an interaction.
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In Figure 11.5, we show three combinations of main effects and interactions for a 2 X 2 factorial design. Using the same 2 X 2 structure, with factor A defining the rows and factor B defining the columns, create a set of means that produce each of the following patterns:
The main effect for factors A and B, but no interaction.
The main effect for factor A and interaction, but no main effect for factor B.
The main effect for both factors and interaction
In a two-factor experiment with two levels of factor A and two levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means?
a. a main effect for factor A
b. a main effect for factor B
c. an interaction between A and B
d. main effects for both A and B, and an interaction
In a 25−1 design (such as the one in Exercise 12) what does the estimate of the main effectof factor A actually represent?a) The main effect of A.b) The sum of the main effect of A and the BCDE interaction.c) The difference between the main effect of A and the BCDE interaction.d) The interaction between A and BCDE.
Chapter 11 Solutions
Research Methods for the Behavioral Sciences (MindTap Course List)
Ch. 11.1 - Define a factorial research design, including the...Ch. 11.2 - Define a main effect for one factor and an...Ch. 11.2 - Explain how the existence of an interaction can...Ch. 11.2 - Describe and explain the independent relationship...Ch. 11.3 - Explain how a factorial study can combine...Ch. 11.3 - Identify the statistical analyses that are...Ch. 11.4 - Describe three specific applications of the...Ch. 11 - In addition to the key words, you should also be...Ch. 11 - In a classic study, Shrauger (1972) examined the...Ch. 11 - Suppose a researcher conducts a two-factor study...
Ch. 11 - The following matrix represents the results (the...Ch. 11 - The following data show the pattern of results...Ch. 11 - Under what circumstances will the main effects in...Ch. 11 - Prob. 7ECh. 11 - In Figure 11.5, we show three combinations of main...Ch. 11 - For a two-factor research study with two levels...Ch. 11 - A researcher would like to use a factorial study...Ch. 11 - A two-factor analysis of variance is used to...Ch. 11 - Prob. 1EACh. 11 - In Figure 11.5, we show three combinations of main...
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