Homogeneity assumption

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Homogeneity assumption Lets return to the
assumption of homogeneity of variance. When group
sizes are balanced, this assumption is not
critical. However, even so there are several
simple tests we can use to check this
assumption. In SPSS and SAS tests are built in
to ANOVA. It is typical to use Levenes test,
which you learned about with the t test. This
test is available in SPSS and SAS. Two other
tests are Cochrans C and Hartleys Fmax.
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Homogeneity assumption Cochrans C is a ratio of
the largest group variance to the sum of the
sample variances. Specifically The Fmax
statistic is a ratio as well, but it compares the
largest sample variance to the smallest one.
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Homogeneity assumption For our sample we can
compute C C 11.2/(2.51011.2) 11.2/23.7
0.47 We need to compare this to a special table,
where the df are k the number of groups (here
it is 3) and (nj-1) where nj is the group size.
We will use nj5 even though one group has 6
cases. So the test has df 3 and 4.
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Here is the full table for your use.
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Homogeneity assumption For our sample we can
compute Fmax Fmax 11.2/2.5 4.48 Again we
compare this to another special table, with df
k the number of groups (here it is 3)
and (nj-1) where nj is the group size. We will
again use nj5. So the test has df 3 and 4.
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(No Transcript)
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Here is the full table for your use.
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Recall again that we are testing equality
(homogeneity) of variance across populations,
and H0 ?N2 ?M2 ?P2 ?e2 The critical
value for C is 0.7457 and for Fmax it is
15.5. Our sample values are C 0.47 and
Fmax4.48. In both cases our sample statistics
are lower than the critical values and we fail to
reject H0. The homogeneity of variance
assumption is reasonable for these data.