61
ANOVA
– Analysis of Variance
Oneway ANOVA is used to compare three or more means; i.e.,
k
Ho
μ
μ
μ
⋅
⋅
⋅
=
=
2
1
:
.
If the null hypothesis is rejected, then there is a difference
somewhere; therefore, after rejecting the null hypothesis, follow the analysis with
either the Scheffe Test or Tukey Test.
ANOVA is a linear regression model.
Assumptions:
1.
Distributions are approximately normal (check for outliers and skewness).
2.
The samples are independent.
3.
The variances are homogeneous (check using the Ftest, pairwise).
Test statistic:
F = (between group variances)/(within group variances) with k – 1 degrees of
freedom in the numerator and N – k degrees of freedom in the denominator.
Recorded in the last column of the Table given below.
Results are generally given in Table form:
Source
Sum of Squares
df
Mean Square
F
Between groups
∑

=
2
)
(
x
x
n
SS
g
g
B
k  1
1
2

=
k
SS
S
B
B
2
2
W
B
S
S
Within groups
∑∑

=
2
)
(
g
W
x
x
SS
N  k
k
N
SS
S
W
W

=
2
Total
Add here
N  1
Between groups source is the factor; within groups source is the error.
If
the results are significant, the Fvalue in the table is in the rejection region when
compared to F(k  1, N  k), then the ANOVA should be followed with a
comparison pairwise between means by using either Scheffe Test or the Tukey
Test as follows:
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 Spring '11
 Bailey
 Normal Distribution, Variance, Null hypothesis, Tukey test

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