Statistics for the Behavioral Sciences (5th ed.) Gravetter & Wallnau

Chapter 15

Two-Factor ANOVA:Independent Measures, Equal ns

University of GuelphPsychology 3320 — Dr. K. Hennig

Fall 2003 Term

Chapter 15 in outline1) Overview2) Main Effects and Interactions3) An example4) Assumptions

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)

Fig. 15.1Effect of an audience on errors for low and high self-esteem individuals How many separate samples? How many independent variables?

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Table 15-1 (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°).

Table 15-2 (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

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.

Figure 15-4 (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.)

Figure 15-2 (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

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

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

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

Figure 15-3 (p. 487) (a) A line graph and (b) a bar graph showing the results from a two-factor experiment.

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

the extra

Fig.15-5 (p. 490): Arousal-Performance StudyTwo levels of task difficulty (easy and hard) and three levels of arousal (low, medium, and high),i.e., six different treatment conditions (n = 5)

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 interactionH1: There is an interaction

Main effect

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Effect size for 2-way ANOVA As with repeated measures ANOVA, remove

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η2 = .004 (or 0.4%) Reporting: F(1,76) = 4.51, p < .05, η2 = 0.056

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Table 15-6 (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.

Table 1 (p. 500)

Figure 15-5 (p. 501) A table and a graph showing the mean number of crackers eaten for each of the four groups in Example 15.2.