Question

Compare the various types of ANOVA by discussing when each is most appropriate for use and which types of research questions each best answer. Include specific examples to illustrate the appropriate use of each test and how interaction is assessed using ANOVA.

Answer 1

Various types of ANOVA are:

1) One way ANOVA - used to compare means from 2 independent groups. It uses the F-distribution in the process, the null hypothesis being that the 2 means are equal. Hence, is the F-statistic is significant, we reject the null hypothesis concluding that the means are unequal. One way ANOVA is used when we have a group of individuals performing different tasks.

For example, we can divide a group into 3 sub-groups to study the effects of diet/exercise on weight loss. First group might be undertaking only dieting, the second undertaking dieting with exercise, and the third undertaking only exercise.

2) Two way ANOVA - used as an extension to the One Way ANOVA.where instead of one independent variables, there are 2 independent variables whose effect on the dependent variable is being studied. It is appropriate to use when the experiment has one quantitative outcome and two categorical predictor variables, and these two categorical variables are called the two factors in the Two Way ANOVA.

For example, while cooking a dish, the taste of the dish can be affected by the time of cooking and the amount of spices used in the dish. Here, taste of the dish is the dependent variable and the time of cooking and spices used are the explanatory variables (factors).

Here, ANOVA output tells us the main effect, i.e. the individual effect of each explanatory variables, as well as the interaction effect, i.e. the simultaneous effect of the 2 factors on the dependent variable. The interaction effect is output as a separate column in the ANOVA output and looking at the F-statistic value for the interaction term, we can judge the strength of the interaction effect.