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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?
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 : l 1 ¼ l 2 ¼ l 3
H 1 : l 1 l 2 l 3
The answer to this question is analogous to the decision rule used in this topic
for both the one-group t test and the two-group t test. You will recall that this rule
(See Sects. 4.1.6 and 5.1.8 ) was:
If the absolute value of t is less than the critical t, you accept the
null hypothesis.
or
If the absolute value of t is greater than the critical t, you reject the
null hypothesis, and accept the research hypothesis.
Now, here is the decision rule for ANOVA:
Objective: To learn the decision rule for the ANOVA F-test
The decision rule for the ANOVA F-test is the following:
If the value for F is less than the critical F-value, accept the null
hypothesis.
or
If the value of F is greater than the critical F-value, reject the null
hypothesis, and accept the research hypothesis.
Note that Excel tells you the critical F-value in cell G31: 3.32
Therefore, our decision rule for the honey bees AVOVA test is this:
Since the value of F of 8.19 is greater than the critical F-value of
3.32, we reject the null hypothesis and accept the
research hypothesis.
Therefore, our conclusion, in plain English, is:
There is a significant difference between the average number of sound
bursts per cycle between the three subspecies of honey bees.
Note that it is not necessary to take the absolute value of F of 8.19. The F-value
can never be less than one, and so it can never be a negative value which
requires us to take its absolute value in order to treat it as a positive value.
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