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Chapter 9: Going One-Way with Analysis of Variance
for females was 47.8 inches; the mean for males was 56.5 inches. The t-statistic
for the difference in the two means (females – males) is t = –2.23, which has a
p-value of 0.039 (see last line of Figure 9-1 output). At a level of α = 0.05, this dif-
ference is significant (because 0.039 < 0.05). You conclude that males and
females differ with respect to their mean watermelon seed spitting distance.
And you can say males are likely spitting farther because their sample mean
was higher.
Figure 9-1:
A t-test
Two-sample T for females vs males
comparing
N
StDev
Mean
SE Mean
mean water-
2.9
10
females
9.02
47.80
2.7
56.50
8.45
10
males
melon seed
spitting
Difference = mu (females) – mu (males)
distances You can see the results of the t-test in Figure 9-1. The mean spitting distance 163
Estimate for difference: –8.70000
for females
95% CI for difference: (–16.90914, –0.49086)
versus T–Test of difference = 0 (vs not =): T–Value = –2.23 P–Value = 0.039 DF = 18
males.
Evaluating More Means with ANOVA
Now that you can compare two independent populations inside and out, at
some point two populations will not be enough. Suppose you want to com-
pare more than two populations regarding some response variable (y). This
idea kicks the t-test up a notch into the territory of ANOVA. The ANOVA pro-
cedure is built around a hypothesis test called the F-test, which compares
how much the groups differ from each other, compared to how much variabil-
ity is in each group. In this section, I set up an example of when to use ANOVA
and show you the steps involved in the ANOVA process. You can then apply
the ANOVA steps to the following example throughout the rest of the chapter.
Spitting seeds: A situation
just waiting for ANOVA
Before you can jump into using ANOVA, you must figure out what question
you want answered and collect the necessary data.
Suppose you want to compare the watermelon seed spitting distances for
four different age groups: 6–8, 9–11, 12–14, and 15–17. The hypotheses for
this example are Ho: µ 1 = µ 2 = µ 3 = µ 4 versus Ha: At least two of these means