In this chapter, we move from one-way ANOVA to two-way ANOVA. Two-way ANOVA also compares the means of several populations, but these populations can now be classified in two ways or are the combinations of factor levels in a two-factor experiment. Here are some examples. See if you can identify how these groups are classified in two ways.

• Does haptic feedback in a game controller help navigate a video game obstacle course? Does the effect of the feedback vary depending on the difficulty of the course? A group of researchers have study participants navigate an obstacle course under different levels of difficulty and using different types of controllers.
• How do consumers perceive calorie and size descriptors on single-serve snack packs? Nabisco investigates the perceptions of Oreo snack packs that are either 100 or 99 calories and that consist of either mini or mega sandwich cookies.
• Does the facing direction (left or right) of a product in an advertisement affect its perceived worth? Does this effect vary depending on the advertisement’s temporal focus (past or future)? A group of researchers investigate this through a set of experiments.¹

Many of the key concepts of two-way ANOVA are similar to those of one-way ANOVA, but the presence of two factors to classify the groups also introduces some new ideas. We once more assume that the data are approximately Normal and that groups may have different means but the same standard deviation; we again pool to estimate this common standard deviation; and we again use F statistics for significance tests.

The major difference between one-way ANOVA and two-way ANOVA is in the FIT term in our DATA=FIT+RESIDUAL conceptual model. As a result, we devote the first section of this chapter to a careful study of this term, and we find much that is both new and useful. This is followed by a section devoted to inference.