Microsoft Office Tutorials and References
In Depth Information
H 0 : l 2 ¼ l 3
H 1 : l 2 l 3
For Group 2 vs. Group 3, the formula for the ANOVA t-test is:
ANOVA t ¼ X 1 X 2
s : e : ANOVA
ð 8 : 2 Þ
where
s
1
n 1
þ 1
n 2
s : e : ANOVA ¼
MS w
ð 8 : 3 Þ
The steps involved in computing this ANOVA t-test are:
1. Find
the
difference
of
the
sample
means
for
the
two
groups
(14.66 -
16.75 =-2.09).
2. Find 1/n 2 ? 1/n 3 (since both groups have a different number of bees in them,
this becomes: 1/10 ? 1/12 = 0.10 ? 0.08 = 0.18
3. Multiply MS w times the answer for step 2 (1.67 9 0.18 = 0.31)
4. Take the square root of step 3 (SQRT (0.31) = 0.55
5. Divide Step 1 by Step 4 to ﬁnd ANOVA t (-2.09/0.55 =-3.80)
Note:
Since Excel computes all calculations to 16 decimal places, when you use
Excel for the above computations, your answer will be -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 ¼ take the total sample size of all of the groups and subtract the
number of groups in your study ð n TOTAL k where k ¼ the
number of groups Þ
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