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8.2 How to Interpret the ANOVA Table Correctly
Objective : To interpret the ANOVA table correctly
ANOVA allows you to test for the differences between means when you have
three or more groups of data. This ANOVA test is called the F-test statistic, and is
typically identiﬁed with the letter: F.
The formula for the F-test is this:
F
Mean Square between groups (MS b ) divided by Mean Square within groups
(MS w )
¼
F
¼
MS b =
MS w
(8.1)
The derivation and explanation of this formula is beyond the scope of this Excel
Guide . In this Excel Guide , we are attempting to teach you how to use Excel , and we
are not attempting to teach you the statistical theory that is behind the ANOVA
formulas. For a detailed explanation of ANOVA, see Gould et al. (2002) and
Weiers (2011).
Note that cell D31 contains MS b ¼ 13.66, while cell D32 contains MS w ¼ 1.67.
When you divide these two ﬁgures using their cell references in Excel, you get
the answer for the F-test of 8.19 which is in cell E31. (Remember, Excel is more
accurate than your calculator!) Let’s discuss now the meaning of the ﬁgure:
F
8.19.
In order to determine whether this ﬁgure for F of 8.19 indicates a signiﬁcant
difference between the means of the three groups, the ﬁrst step is to write the null
hypothesis and the research hypothesis for the three subspecies of honey bees.
In our statistics comparisons, the null hypothesis states that the population
means of the three groups are equal, while the research hypothesis states that the
population means of the three groups are not equal and that there is, therefore, a
signiﬁcant difference between the population means of the three groups. Which of
these two hypotheses should you accept based on the ANOVA results?
¼
8.3 Using the Decision Rule for the ANOVA F-test
To state the hypotheses, let’s call SUBSPECIES A as Group 1, SUBSPECIES B as
Group 2, and SUBSPECIES C as Group 3. The hypotheses would then be:
H 0 :
m 1 m 2 m 3
H 1 :
m 1 6¼ m 2 6¼ m 3
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