Two-Way ANOVA

Two-way analysis of variance (two-way ANOVA) is the test used to analyze the DATA from a study in which the investigator wishes to examine both the separate and the combined effects of two VARIABLES on some measure of behavior. The data come from a factorial experiment or study in which separate levels of each of two variables or factors (e.g., Factor A and Factor B) are identified and all combinations are formed. Factors A and B may be manipulated INDEPENDENT VARIABLES, such as incentive level or performing alone versus in groups, or measured levels of subject variables, such as age and sex. Among the more interesting applications in the social sciences are ones in which Factor A is a manipulated independent variable and Factor B is a subject variable. The primary interest is then whether the effect of Factor A on the response measure differs for individuals defined by different levels of Factor B.

Consider, for example, a study of the effects of exposure to violent video games on subsequent aggressive behavior exhibited by young boys and girls. Let's say that the behavior being recorded—the DEPENDENT VARIABLE—is the number of times a child hits, kicks, or pushes another child during a 15-minute play session. Using a population of children of a certain age (say, 6 to 7 years old), children are randomly [Page 1150]assigned to a condition where they play a 30-minute violent video game or a 30-minute nonviolent video game before the play session with other children. This constitutes the independent variable manipulation. This RANDOM ASSIGNMENT is done separately for boys and girls, resulting in a 2 × 2 design with two levels of type of video game crossed with two levels of gender.

Table 1 Case of Significant Main Effects and No Significant Interaction
Source	DF	SS	MS	F	p
Gender	1	122.51	122.51	33.56	<.0001
Game	1	103.51	103.51	28.35	<.0001
Gender × Game	1	1.01	1.01	0.28	.600

The resulting data and two-way ANOVA then can be used to address the following research questions: (a) Are boys more aggressive than girls? (b) Are children more aggressive following experience with a violent video game? and (c) Do boys and girls differ in the effect of exposure to violent video games? In ANOVA parlance, the first two questions are addressed by MAIN EFFECT tests—that is, averaged over experimental conditions, are the mean aggression scores significantly higher for boys than for girls, and, averaged over gender, are the mean aggression scores significantly higher in the Violent Video Game condition than in the Nonviolent Video Game condition? The third question, which is probably the one of greatest interest, is addressed by a test of INTERACTION—does the effect of exposure to violent video games differ significantly between boys and girls?

Table 2 Case of Significant Main Effects and Significant Interaction
Source	DF	SS	MS	F	p
Gender	1	137.81	137.81	50.76	<.0001
Game	1	103.51	103.51	38.12	<.0001
Gender × Game	1	37.81	37.81	13.93	<.0004

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