Question

Part one: What happens to the value of t as the pooled standard error gets larger?

Part two: Do we want the Levene's test for homogeneity of variances to be significant (p < .05) or non-significant (p > .05)? Why?

Answer 1

Part one: If the pooled standard error gets larger, the value of t (t-test statistic) gets smaller. This, in turns leads to the p-value getting larger and thus, reduction in the chance of rejection of the null hypothesis.

Part two: We want the Levene's test for homogeneity of variances to be non-significant (p > .05), which would mean that the null hypothesis of the equality of the variances of the 2 groups is not rejected. This would enable to use the 2 sample t-test for comparing the 2 group means, where the pooled standard error expression is used in the test statistic.