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Chapter 16: One-Way Analysis of Variance
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Note:
We will be able to test for independence later in the chapter.
Section Review
Next we will discuss how we use the
F
distribution to help perform the test
of hypothesis for a one-way ANOVA.
16-5 The
F
-Distribution and the
F
Test Statistic
The
F
-distribution
will enable us to statistically compare different (at least
three) population means for the One-Way ANOVA procedures.
Under the assumption that the null hypothesis given in
Section 16-4
is true
for a one-way ANOVA, the test statistic of analysis of variance will follow
an
F-
distribution
. The
F-
distribution is obtained by computing the ratio of
two chi-square distributions and thus has a numerator as well as a
denominator degrees of freedom associated with it. The numerator degrees
of freedom is
-1 and the denominator degrees of freedom is
–
, where
is the number of populations from which samples are obtained or
treatments and
is the combined sample size from these
populations (total
data values).
Example 16-8:
In
Example 16-1
, what are the numerator and denominator
degrees of freedom if a one-way analysis of variance was run on the data
collected for the experiment?
Solution:
From the information given in
Example 16-1
, the number of
populations which were sampled is
= 4 and the combined sample size is
= 10 + 9 + 10 + 7 = 36. Thus, the numerator degrees of freedom is
– 1 =
4 -1 = 3, and the denominator degrees of freedom is
–
= 36 – 4 = 32.
e-Self Review