26. Earlier in this chapter we described a study byBartholow and Anderson (2002) examining how theexperience of violence in video games influenced ag-gressive behavior for males and females. Their resultssuggest that increased violence increase aggressivebehavior for males but has little or no effect for fe-males. The following data are measures of aggressivebehavior similar to the results obtained in the study.Nonviolent Game Violent GameFemaleMale3622479948108945846121613171313a. Use an ANOVA with a = .05 to evaluate the data.Describe the effect of the violent game comparedwith a nonviolent game on the aggressive behaviorfor males and for females.b. Calculate the effect size (n²) for each main effectand for the interaction.

Introduction: It is required to perform three tests- to assess the effect of the type of video game (nonviolent/violent), gender (female/male), and the interaction between these two factors.a. The response variable is the score of aggressive behavior. The two factors are type of game with two levels- nonviolent and violent, and gender also with two levels- female and male. Suppose the gender is represented by A, and the type of game is represented by B. The two-way analysis of variance or ANOVA procedure with replications is suitable to test the hypothesis to ensure the interaction effect is also studied, which is possible because each factor combination has multiple observations. Note that, for each type of game, there are 12 rows containing values, wherein 6 rows values correspond to the females, and the other 6 rows correspond to the males. The null and alternative hypotheses to test for the main effect of gender (A or rows) are: H0A: There is no significant main effect of gender on aggressiveness score, that is, the mean aggressiveness scores for the two gender groups are the same. H1A: There is significant main effect of gender on aggressiveness score, that is, the mean aggressiveness score is not the same for the two gender groups. The null and alternative hypotheses to test for the main effect of type of game (B or columns) are: H0B: There is no significant main effect of the type of game on aggressiveness score, that is, the mean aggressiveness scores for the two types of games are the same. H1B: There is significant main effect of the type of game on aggressiveness score, that is, the mean aggressiveness score is not the same for the two types of games. The null and alternative hypotheses to test for the interaction effect between gender and type of game (A × B) are: H0AB: There is no significant interaction effect between gender and type of game. H1AB: There is significant interaction effect between gender and type of game. The level of significance is, α = 0.05. We have used Excel. The dataset is as follows: Go to Data > Data Analysis > Anova: Two-Factor With Replication > OK. Enter Input Range as $A$1:$C$13, enter Rows per sample as 6, enter Alpha as 0.05 and click OK. The output obtained is: Decision rule: Reject the null hypothesis if P-value ≤ α, the level of significance. Otherwise, fail to reject the null hypothesis. In the “ANOVA” table of the output, the p-values are given under the “P-value” column. The values for gender are given corresponding to the “Source of Variation” labelled as “Sample”, the values for the type of game are given corresponding to the source “Columns”, the values for the interaction between these two factors are given corresponding to the source “Interaction”, and the values for error are given corresponding to the row “Within”. For gender (A), P-value (= 0.000000718008) < α (= 0.05). Thus, reject H0A. Hence, the conclusion regarding the main effect for gender (A) is that, there appears to be an effect due to the gender of an individual on their aggressiveness score. For type of game (B), P-value (= 0.000129683) < α (= 0.05). Thus, reject H0B. Hence, the conclusion regarding the main effect for type of game (B) is that, there appears to be an effect of the type of game on the aggressiveness score of an individual. For interaction (A × B), P-value (= 0.028398874) < α (= 0.05). Thus, reject H0AB. Hence, the conclusion regarding the interaction effect between gender and type of game (A × B) is that, there appears to be an interaction between gender and type of game. In the presence of a significant interaction effect, it is not possible to practically interpret the significance of the main effects. The significant interaction effect leads to the conclusion that the different types of games- violent or nonviolent- have different effects on individuals of different genders- males and females- with respect to their aggressiveness scores.b. The effect sizes η2 calculated for each main effect and the interaction effect for a two-way ANOVA are the partial η2 values. For each effect (main or interaction), the numerator of the effect size will be the sum of squares due to that factor, and the denominator will be the sum of squares due to that factor added to the error or within groups sum of squares. In the “ANOVA” table of the output, the sums of squares are given under the “SS” column. The analyses for gender are given corresponding to the “Source of Variation” labelled as “Sample”, the analyses for the type of game are given corresponding to the source “Columns”, the analyses for the interaction between these two factors are given corresponding to the source “Interaction”, and the analyses for error are given corresponding to the row “Within”. For main effect of gender (A or rows): Partial η2 for Sample (A) = SS A / [SS A + SS Within] = 216 / (216 + 86) = 216 / 302 ≈ 0.7152. For main effect of type of game (B or columns): Partial η2 for Columns (B) = SS B / [SS B + SS Within] = 96 / (96 + 86) = 96 / 182 ≈ 0.5275. For interaction effect between gender and type of game (A × B): Partial η2 for Interaction (A × B) = SS (A × B) / [SS (A × B) + SS Within] = 24 / (24 + 86) = 24 / 110 ≈ 0.2182. Thus, The effect size due to the main effect of gender is 0.7152. The effect size due to the main effect of type of game is 0.5275. The effect size due to the interaction effect between gender and type of game is 0.2182. The interaction has a moderately large effect size, the type of game has a very large effect size, while the gender of an individual has the maximum effect size.