1. Homogeneity of Variance
Pooling the variances doesn’t make sense when we cannot assume all of the sample
Variances are estimating the same value.
For two groups:
Levene (1960): replace all of the individual scores with either
then run a t-test or
F - test
Given: 1. Random and independent samples
2. Both samples approach normal distributions
Then: F is distributed with (n-large-1) and (n-small-1) df.
Null Hypothesis:
Alternate Hypothesis:

2. K independent groups:
Hartley: If the two maximally different variances are NOT significantly different,
Then it is reasonable to assume that all k variances are estimating the population variance.
The average differences between pairs will be less than the difference between the smallest
And the largest variance.
A and B are randomly selected pairs.
Thus:
will NOT be distributed as a normal F.
(k groups, n-1) df
Then, use
Table to test
Null Hypothesis:
Alternate Hypothesis:

3. Data Transformation: When Homogeneity of Variance is violated
Looking at the correlation between the variances (or standard deviations)
And the means or the squared means.
b) Use square root transformation
c) Use logarithmic transformation
d) Use reciprocal transformation