Page 213 - Intermediate Statistics for Dummies

17_045206 ch11.qxd 2/1/07 10:15 AM Page 192
192
Part III: Comparing Many Means with ANOVA
j
of A and B) and i
(m – 1) degrees of freedom from MSE (mean sum of
* *
squares for error), respectively. (Recall that i and j are the number of levels
of A and B, and m is the sample size at each combination of A and B.) You
basically want to see whether more of the total variability in the y’s can be
explained by the AB term compared to what is left in the error term. A large
value of F means that the AB term is significant, and you leave it in the model.
If the interaction term isn’t significant, you take the AB term out of the model,
and you can explore the effects of factors A and B separately regarding the
MS A
response variable y. The test for Factor A uses the test statistic F =
MSE
which has an F-distribution with i – 1 degrees of freedom from MS A (mean sum
(m – 1) degrees of freedom from MSE (mean
of squares for factor A) and i
j
* *
MS B
,
sum of squares for error), respectively. Testing for factor B uses F =
MSE
which has an F-distribution with j – 1 and i
j
(m – 1) degrees of freedom.
* *
The results you can get from testing the terms of the ANOVA model are the
same as those represented in Figure 11-1. They’re all provided in Minitab ,
output outlined in the next section, including their sum of squares, degrees
of freedom, mean sum of squares, and p-values for their appropriate F-tests.
Running the Two-Way ANOVA Table
The ANOVA table for two-way ANOVA includes the same elements as the
ANOVA table for one-way ANOVA (see Chapter 9). But where in the one-way
ANOVA you had one line for Factor A’s contributions, now you add lines for
the effects of Factor B and the interaction term AB. Minitab calculates the
ANOVA table for you as part of the output from running a two-way ANOVA.
In this section, you can figure out how to interpret the results of a two-way
ANOVA, assess the model’s fit, and use a multiple comparisons procedure, using
the drug-data study.
Interpreting the results: Numbers and graphs
The drug-study example has, say, four people in each treatment combination of
three possible dosage levels (10, 20, 30mg per day) and two possible times for
taking the drug (one time per day and two times per day). The total sample
size is 4 3 2 = 24. I made up five different data sets in which the analyses
* *
represent each of the five scenarios shown in Figure 11-1. Their ANOVA tables,
as created by Minitab, are shown in Figure 11-2.
The order of the graphs in Figure 11-1 and the ANOVA tables in Figure 11-2 isn’t
the same. Can you match them up? (I promise to give you the answers, so keep
reading.)