Page 216 - Statistics II for Dummies

200 Part III: Analyzing Variance with ANOVA

Interpreting the results:

Numbers and graphs

The drug study example involves four people in each treatment combination
of three possible dosage levels (10mg, 20mg, and 30mg per day) and two pos-
sible 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.

Notice that each ANOVA table in Figure 11-2 shows the degrees of freedom
for dosage is 3 – 1 = 2; the degrees of freedom for times per day is 2 – 1 = 1;
the degrees of freedom for the interaction term is (3 – 1) * (2 – 1) = 2; the
degrees of freedom for total is 3 * 2 * 4 – 1 = 23; and the degrees of freedom
for error is 3 * 2 * (4 – 1) = 18.

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.)

Here’s how the graphs from Figure 11-1 match up with the output in Figure 11-2:
✓ In the ANOVA table for Figure 11-2a, you see that the interaction term
isn’t significant (p-value = 0.526), so the main effects can be studied. The
p-values for dosage (Factor A) and times taken (Factor B) are 0.000 and
0.001, indicating both Factors A and B are significant; this matches the
plot in Figure 11-1a.
✓ In Figure 11-2b, you see that the p-value for interaction is significant
(p-value = 0.000), so you can’t examine the main effects of Factors A and
B (in other words, don’t look at their p-values). This represents the situ-
ation in Figure 11-1e.
✓ Figure 11-2c shows nothing is significant. The p-value for the interac-
tion term is 0.513; p-values for main effects of Factors A (dosage) and B
(times taken) are 0.926 and 0.416, respectively. These results coincide
with Figure 11-1d.
✓ Figure 11-2d matches Figure 11-1b. It has no interaction effect (p-value =
0.899); dosage (Factor A) is significant (p-value = 0.000), and times per
day (Factor B) isn’t (p-value = 0.207).
✓ Figure 11-2e matches Figure 11-1c. The interaction term, dosage * times
per day, isn’t significant (p-value = 0.855); times per day is significant
with p-value 0.000, but dosage level isn’t significant (p-value = 0.855).

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