Interaction

Example 1: Categorical Factors and Data—The Number of Cases in Each Category

For a simple example, consider the fictional data in Table 1, reporting the number of children who complete their homework versus those who do not. In the entire sample of 200 boys and 200 girls, children were equally likely to complete their homework regardless of gender. But when another factor—year of schooling—is considered alongside gender, as in Table 2, an interesting, underlying pattern emerges. In Year 3, girls were far more likely than boys to complete their homework; but in Year 8, the pattern was reversed. This difference in the pattern for gender, depending upon which year group is studied, is an interaction.

An interaction is usually described in terms of the simple main effects that make it up. A simple main effect is the effect of one factor when just one category of the other factor is considered. Because there are 2 year groups, there will be two simple main effects for gender, one for each year group. For Year 3 students, the simple main effect of gender is that more girls than boys complete their homework, as shown in the left side of Table 2. For Year 8 students, the simple main effect of gender is that more boys than girls complete their homework, as shown in the right side of Table 2. It is equally valid to describe the interaction using the simple main effects of year; there are two simple main effects for year because there are two genders. For boys, the simple main effect of year is that most of them complete homework in Year 8 than in Year 3 (70 vs. 30). For girls, the simple main effect of year is that fewer of them complete homework in Year 8 than in Year 3 (30 vs. 70).

Table 2 shows an interaction between gender and year—homework was completed by 30 boys versus 70 girls in Year 3 and 70 boys versus 30 girls in Year 8—but there is no main effect of gender (homework was completed by 100 boys vs. 100 girls) and no main effect of year (homework was completed by 100 students from Year 3 and 100 from Year 8).

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