Microsoft Office Tutorials and References
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2. Find 1/n 2 þ
1/n 3 (since both groups have a different number of bees in them, this
becomes: 1/10
0.18
3. Multiply MS w times the answer for step 2 (1.67 x 0.18
1/12
0.10
0.08
þ
¼
þ
¼
0.31)
¼
4. Take the square root of step 3 (SQRT (0.31)
¼
0.55
¼
5. Divide Step 1 by Step 4 to ﬁnd ANOVA t (
3.80)
Note: Since Excel computes all calculations to 16 decimal places, when you use
2.09 / 0.55
3.78 in two decimal
places, but Excel’s answer will be much more accurate because it is always in 16
decimal places.
Now, what do we do with this ANOVA t-test result of
3.80 ? In order to
interpret this value of
3.80 correctly, we need to determine the critical value of
t for the ANOVA t-test. To do that, we need to ﬁnd the degrees of freedom for the
ANOVA t-test as follows:
8.4.1.1 Finding the Degrees of Freedom for the ANOVA t-test
Objective : To ﬁnd the degrees of freedom for the
ANOVA t-test.
The degrees of freedom (df) for the ANOVA t-test is found as follows:
df
take the total sample size of all of the groups and subtract the number of groups
¼
k where k
¼
the number of groups)
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.
¼
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
Sect. 5.1.8):
If the absolute value of t is less than the critical value of t, we accept the null
hypothesis.
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