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The
F-ratio is used to determine whether the variances in two independent samples are equal.
If the F-ratio is not statistically significant, you may assume there is homogeneity of
variance
and employ the standard t-test
for the difference of means. If the F-ratio is statistically significant, use an
alternative t-test computation such as the Cochran and Cox method.
Problem: Given the following summary statistics, are the
variances equal?
Sample
A  =20 n=10
Sample
B =30 n=30
Set
the Rejection Criteria
Determine
the degrees of freedom (df) for each sample
df
= n1 - 1 (numerator = n for sample with larger variance)
df
for numerator (Sample
B) = 29
df
= n2 - 1 (denominator = n for sample with smaller variance)
df
for denominator (Sample
A) = 9
Determine
the level of confidence -- alpha
Consult
F-Distribution table for df = (29,9), alpha.05
Fcv=
2.70
Compute
the Test Statistic
where
 = largest variance
 = smallest
variance
 
Compare
The
test statistic with the f critical value (Fcv) listed in the F distribution. If the
F-ratio
equals or exceeds the critical value, the null hypothesis (Ho)  (there
is no difference between the sample variances) is rejected. If there is a difference in
the sample variances, the comparison of two independent means should involve the use of
the Cochran and Cox method or one of several alternative techniques.
The
test statistic (1.50) did not meet or exceed the critical value (2.70). Therefore, there
is no statistically significant difference between the variance
exhibited in Sample
A and the variance exhibited in Sample B. Assume homogeneity of variance
for tests of the difference between sample means.
Software Output Example
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