Two-Way ANOVA. Two-way Analysis of Variance. Two-way ANOVA is applied to a situation in which you have two independent nominal-level variables and one interval or better dependent variable
What is the impact of gender and ethnicity on annual salary, and how do they interact? In this example, there may not be much of a main effect either for gender or ethicnity, but there may be an interaction effect: for example, are females who are Hispanic paid more than males who are Hispanic, while females who are African-American are paid less than males who are African-American?
Factors (main effects and interaction effect)
According to the Levene test the group variances are significantly different so we will use the Tamhane post hoc test instead of Sheffe to see which group means are significantly different. We will only do a test on the factors for which the main effect was significant
According to the Tamhane test the means for blacks and whites in Socioeconomic status were significantly different, but neither group was significantly different from “other”
Plot of interaction effect: Note that the lines for males (red) and females (green) are very similar although there is a tiny bit of an interaction effect in the Other category where women are actually higher than men
Generally, although the results are not significant, it would appear that unmarried or non-partnered people spend more time on the net, and net use peaks with the post-high school group and declines for college grads
Education Level is plotted along the horizontal axis and hours spent on the net is plotted along the vertical axis. The red and green lines show how marital status interacts with education level. If marital status had the same effect on time spent on the net across all levels of education, the lines would be more or less parallel. In an interaction effect, they cross or diverge from parallel in some way. Here we note that the general trend for single people to spend more time on the net is very strong for the post-high school group but is reversed for high school grads and college grads, where married people spend more time What do you think might explain this?
1. Sex of respondent has a significant main effect on hours per day spent watching TV
2. Home ownership has a significant main effect on hours per day spent watching TV
3. Sex of respondent and home ownership have a significant interaction effect on hours per day spent watching TV
Now write a paragraph in which you report the results of the significance tests! Remember that the interpretation of the main effects in a straightforward way is complicated by the significant interaction We also need to be a bit skeptical since the partial eta squares are very low and as you will see on the next slide there is a very large SD in one of the conditions
Although the interaction effect is not extremely strong, there is a trend for the relationship between homeownership and hours spent watching TV to be different for men than women; women who don’t own homes are much more likely to spend more time watching tv than owners, compared to men, for whom homeownership makes less of a difference