Biostatistics

350 CHAPTER 8 ANALYSIS OF VARIANCE
Dialog box:
Session command:
Stat ANOVA Twoway MTB > TWOWAY C1 C2 C3;
SUBC> MEANS C2 C3.
Type C1 in Response. Type C2 in Row factor and
Check Display means. Type C3 in Column factor and
Check Display means. Click OK.
Output:
Two-way ANOVA: C1 versus C2, C3
Analysis of Variance for C1
Source DF SS MS F P
C2 17 20238 1190 8.20 0.000
C3 3 2396 799 5.50 0.002
Error 51 7404 145
Total 71 30038
FIGURE 8.4.1 MINITAB procedure and output (ANOVA table) for Example 8.4.1.
8. Statistical decision. Since V:R: ¼ 5:50 is greater than 2.80, we are able
to reject the null hypothesis.
9. Conclusion. We conclude that there is a difference in the four
population means.
10. p value. Since 5.50 is greater than 4.98, the F value for a ¼ :005 and
df ¼ 40, the p value is less than .005.
Figure 8.4.2, shows the SAS ® output for the analysis of Example 8.4.1 and Figure 8.4.3
shows the SPSS output for the same example. Note that SPSS provides four potential tests.
The first test is used under an assumption of sphericity and matches the outputs in Figures
8.4.1 and 8.4.2. The next three tests are modifications if the assumption of sphericity is
violated. Note that SPSS modifies the degrees of freedom for these three tests, which
changes the mean squares and the p values, but not the V. R. Note that the assumption of
sphericity was violated for these data, but that the decision rule did not change, since all of
the p values were less than a ¼ :05.
&
Two-Factor Repeated Measures Design Repeated measures ANOVA is
not useful just for testing means among different observation times. The analyses are easily
expanded to include testing for differences among times for different treatment groups. As
an example, a clinic may wish to test a placebo treatment against a new medication
treatment. Researchers will randomly assign patients to one of the two treatment groups
and will obtain measurements through time for each subject. In the end they are interested