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In our example, the total sample size of the three groups is 33 since there are 11
bees in Group1, 10 bees in Group 2, and 12 bees in Group 3, and since there are
three groups, 33–3 gives a degrees of freedom for the ANOVA t-test of 30.
If you look up df = 30 in the t-table in Appendix E in the degrees of freedom
column (df), which is the second column on the left of this table, you will ﬁnd that
the critical t-value is 2.042.
Important note:
Be sure to use the degrees of freedom column (df) in Appendix E
for the ANOVA t-test critical t value
8.4.1.2 Stating the Decision Rule for the ANOVA t-Test
Objective: To learn the decision rule for the ANOVA t-test
Interpreting the result of the ANOVA t-test follows the same decision rule that
we used for both the one-group t-test (see Sect. 4.1.6 ) and the two-group t-test (see
If the absolute value of t is less than the critical value of t, we accept
the null hypothesis.
or
If the absolute value of t is greater than the critical value of t, we
reject the null hypothesis and accept the research hypothesis.
Since we are using a type of t-test, we need to take the absolute value of t. Since
the absolute value of -3.80 is greater than the critical t-value of 2.042, we reject
the null hypothesis (that the population means of the two groups are equal) and
accept the research hypothesis (that the population means of the two groups are
signiﬁcantly different from one another).
This means that our conclusion, in plain English, is as follows:
The average number of sound bursts per cycle for SUBSPECIES C was
signiﬁcantly greater than the average number of sound bursts per cycle for
SUBSPECIES B (16.75 vs. 14.66).
8.4.1.3 Performing an ANOVA t-Test Using Excel Commands
Now, let’s do these calculations for the ANOVA t-test using Excel with the ﬁle
you created earlier in this chapter: BEE12
A36: SUBSPECIES B vs. SUBSPECIES C
A38: 1/n B + 1/n C
A40: s.e. B vs. C
A42: ANOVA t-test
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