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202 Part III: Analyzing Variance with ANOVA

Assessing the fit
To assess the fit of the two-way ANOVA models, you can use the R adjusted
2
(see Chapter 6). The higher this number is, the better (the maximum is 100
percent or 1.00). Notice that all the ANOVA tables in Figure 11-2 show a fairly
high R adjusted except for Figure 11-2c. In this table, none of the terms were
2
significant.

Multiple comparisons
In the case where you find that an interaction effect is statistically significant,
you can conduct multiple comparisons to see which combinations of Factors
A and B create different results in the response. The same ideas hold here as
do for multiple comparisons (covered in Chapter 10), except the tests can be
performed on all i * j interactions.

To perform multiple comparisons for a two-way ANOVA by using Minitab, enter
your responses (data) in Column 1 (C1), your levels of Factor A in Column 2 (C2),
and your levels of factor B in Column 3 (C3). Choose Stat>ANOVA>General
Linear Model. In the Responses box, enter your Column 1 variable. In Model,
enter C1 <space> C2 <space> C1*C2 (for the main effects and the interaction
effect, respectively; here, <space> means leave a space). Click on Comparisons.
In Terms, enter Columns 2 and 3. Check the Method you want to use for your
multiple comparisons (see Chapter 10), and click OK.

Are Whites Whiter in Hot Water?

Two-Way ANOVA Investigates

You use two-way ANOVA when you want to compare the means of n popula-
tions that are classified according to two different categorical variables (fac-
tors). For example, suppose you want to see how four brands of detergent
(Brands A, B, C, D) and water temperature (1 = cold, 2 = warm, 3 = hot) work
together to affect the whiteness of dirty t-shirts being washed. (Product-
testing groups can use this information as well as the detergent companies to
investigate or advertise how a detergent measures up to its competitors.)
Because this question involves two different factors and their effects on
some numerical (quantitative) variable, you know that you need to do a two-
way ANOVA. You can’t assume that water temperature affects whiteness of
clothes in the same way for each brand, so you need to include an interac-
tion effect of brand and temperature in the two-way ANOVA model. Because
brand of detergent has four possible types (or levels) and water temperature
has three possible values (or levels), you have 4 * 3 = 12 different combina-
tions to examine in terms of how brand and temperature interact. Those

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