Question

For an Independent Samples T-test, what are we looking for when the output gives us the significance for Levene’s test for equal variance? Which significance value do we choose and when?

Answer 1

Levene's test ( Levene 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.

The hypotheses for Levene’s test are:

("the population variances of group 1 and 2 are equal")
  ("the population variances of group 1 and 2 are not equal")

This implies that if we reject the null hypothesis of Levene's Test, it suggests that the variances of the two groups are not equal; i.e., that the homogeneity of variances assumption is violated.

This test for homogeneity of variance provides an F-statistic and a significance value (p-value). We are primarily concerned with the significance value – if it is greater than 0.05 (i.e., p > .05), our group variances can be treated as equal. However, if p < 0.05, we have unequal variances and we have violated the assumption of homogeneity of variances.

The Levene test rejects the hypothesis that the variances are equal if

• W > F_{α, k-1, N-k}

What are we looking for when the output gives us the significance for Levene’s test for equal variance?

When ths output is significance means p-value < 0.05 then we we have unequal variances and we have violated the assumption of homogeneity of variances.

If the Levene's Test for Equality of Variances is statistically significant, which indicates that the group variances are unequal in the population, you can correct for this violation by not using the pooled estimate for the error term for the t-statistic, but instead using an adjustment to the degrees of freedom using the Welch-Satterthwaite method.

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