Interpreting Two-way ANOVA Results: Guyer Prisoner's Dilemma & Barley Germination - Prof. , Assignments of Statistics

Download Interpreting Two-way ANOVA Results: Guyer Prisoner's Dilemma & Barley Germination - Prof. and more Assignments Statistics in PDF only on Docsity! 22s:152 Homework 6 solutions Two-way ANOVA with balanced designs 1. The Guyer data set in the car library has data collected on a game called ‘prisoner’s dilemma. The variables in the data set include three variables: cooperation, condition, and sex. (a) Depending on which variable you plotted on the x-axis, your plot should look like one of the following: Sex C on di tio n male female 30 40 50 60 70 80 ● ● ● ● ● ● ● ● ● ● Public Anonymous Condition S ex Anonymous Public Choice 30 40 50 60 70 80 ● ● ● ● ● ● ● ● ● ● ● Sex=F Sex=M Both plots tell the same story... that there appears to be a substantial ‘condition’ effect, but not much of a ‘sex’ effect. (b) > means F M A 40.2 41.6 P 57.4 54.0 (c) No output needed. (d) State your conclusions in full sentences and in terms of the research at hand, not just whether an effect is ’significant’ or not. > lm.out=lm(cooperation~condition + sex + condition:sex) > Anova(lm.out,type="III") 1 Anova Table (Type III tests) Response: cooperation Sum Sq Df F value Pr(>F) (Intercept) 46658 1 271.5426 1.851e-11 *** condition 1095 1 6.3739 0.02253 * sex 5 1 0.0291 0.86669 condition:sex 29 1 0.1676 0.68767 Residuals 2749 16 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 There is no significant interaction, so we can therefore consider the tests for main effects (sex and condition). You could now fit the simpler additive model, but some people leave the interaction term in (you use a df for the interaction term, but it shouldn’t make much difference in the error estimate because it was not significant). I’ll use the above table to state that sex was not a significant factor, but condition was. IN TERMS OF THE RESEARCH: The fact that there was a significant ‘condition’ effect on cooperation is not unex- pected. People tended to be more cooperative when their choice was made public. There is pressure from the community to share and to cooperate. The lack of a sex effect is of interest to the researcher. The expected cooperation for men is about the same as the expected cooperation for women. Both men and women are more cooperative when their choices are made public, and the increase in cooperation (when the decision is made public) is the same for the sexes (no interaction). 2