EXAMPLE 14.4 ANOVA Model for the Moral Reasoning Study
CASE 14.1 In Case 14.1, there are three groups that we want to compare, so . The population means , and are the mean values for the control group, moral decoupling group, and moral rationalization group, respectively. The sample sizes are 41, 43, and 37, respectively. It is common to use numerical subscripts to distinguish the different means, and some software requires that levels of factors in ANOVA be specified as numerical values. An alternative is to use subscripts that suggest the actual groups. In our example, we could replace , and by , and , respectively.
The observation , for example, is the likelihood score for the first participant in the control group. Accordingly, the data for the other control group participants are denoted by , and so on. Similarly, the data for the other two groups have a first subscript indicating the group and a second subscript indicating the participant in that group.
According to our model, the score for the first participant in the control group is , where is the average for the population of all consumers and is the chance variation due to this particular participant. Similarly, the score for the last participant assigned to the moral rationalization group is , where is the average score for all consumers primed with moral rationalization and is the chance variation due to this participant.