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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.

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homogeneity of variance
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:

slide2

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:

slide3

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