1. Statistics for the Behavioral Sciences (5th ed.) Gravetter & Wallnau
Chapter 15 Two-Factor ANOVA:
Independent Measures, Equal ns
University of Guelph Psychology 3320 — Dr. K. Hennig Fall 2003 Term

2. Chapter 15 in outline Overview Main Effects and Interactions
An example
Assumptions

3. Overview
Goal of research: isolate two variables and examine their relation, eliminating or reducing the influence of extraneous/outside variables
Single factor analyses thus far
More typically behavior is more complex and is influenced by a variety of variables acting and interacting simultaneously
manipulate 2 (or more variables) => one DV (univariate analysis)

4. How many separate samples? How many independent variables?
Fig Effect of an audience on errors for low and high self-esteem individuals
How many separate samples?
How many independent variables?
no aud audience
number of errors
no aud audience
High SE Low SE

6. Table 15-1 (p. 479) Structure of a two-factor experiment
Table (p. 479) Structure of a two-factor experiment. Two levels for the humidity factor (low and high), and three levels for the temperature factor (70°, 80°, and 90°).

7. Table (p. 481) Hypothetical data from an experiment examining two different levels of humidity (factor A) and three different levels of temperature (factor B).
Main effects for Factors A and B
Consistent 10-pt difference - no interaction

8. Definition
When the effect of one factor depends on the different levels of a second factor, then there is an interaction between the factors
e.g., The effect of changing humidity depends on the temperature, and there is an interaction.

9. Figure (p. 482) Two different levels of humidity (factor A) and three different temperature conditions (factor B). What is the effect of temperature on performance? Depends…
(These data show the same main effects as the data in Table 15.2, but the individual treatment means have been modified to produce an interaction.)

10. Figure 15-2 (p. 484) (a) Graph showing the data from Table 15
Figure (p. 484) (a) Graph showing the data from Table 15.2, where there is no interaction. (b) Graph showing the data from Table 15.3, where there is an interaction. • Look for the existence of non-parallel lines

11. Figure 15-4a (p. 486) Different combinations of main effects and interaction for a two-factor study.

12. Figure 15-4b (p. 486) Different combinations of main and interaction effects for a two-factor study.

13. Figure 15-4c (p. 486) Three sets of data showing different combinations of main effects and interaction for a two-factor study.

14. Figure (p. 487) (a) A line graph and (b) a bar graph showing the results from a two-factor experiment.

15. Figure 15-4 (p. 489) Structure of the analysis for a two-factor analysis of variance.
the extra

16. Fig (p. 490): Arousal-Performance Study Two levels of task difficulty (easy and hard) and three levels of arousal (low, medium, and high), i.e., six different treatment conditions (n = 5)

17. Steps Factor A (humidity has no effect on performance):
Ho: A1 = A2
H1: A1 <> A2
Factor B (overall there are no differences in mean performance among the three temperatures):
Ho: B1 = B2 = B3
H1: At least one mean is different from another
General formular: variance (differences between rows(colmns)/ variance (differences) by chance
Interaction: Ho: There is no interaction H1: There is an interaction

18. Main effect

19. Interaction effect (the extra)

20. Effect size for 2-way ANOVA
As with repeated measures ANOVA, remove any variability than arises from other sources
η2 = .004 (or 0.4%)
Reporting: F(1,76) = 4.51, p < .05, η2 = 0.056

21. Table (p. 496) Results from an experiment examining the eating behavior of non-obese and obese individuals who have either a full or an empty stomach.

22. Table 1 (p. 500)

23. Figure (p. 501) A table and a graph showing the mean number of crackers eaten for each of the four groups in Example 15.2.