Question

In a two independent sample t-test with non-pooled data, when S_large/S_small is greater than 2:

A) Pooled data is preferred
B) Non-pooled data is preferred
C) S_large/S_small has no impact on the choice of data
D) ANOVA should be used instead

Answer 1

For a two-independent sample t-test with non-pooled data when S_large/S_small > 2, non-pooled data is preferred because this indicates a significant difference in variances. The correct approach for paired measurements is a test of dependent means, as seen in the anxiety levels example. The correct option is B.

Step-by-step explanation:

When conducting a two-independent sample t-test with non-pooled data, the ratio S_large/S_small is compared to a threshold of 2 to decide on the variance equality. If S_large/S_small is greater than 2, this indicates a significant difference in sample variances which suggests that non-pooled data is preferred. Pooled data assumes equal variances, so when this assumption doesn't hold (S_large/S_small > 2), non-pooled data that does not assume equality of variances is the better choice for statistical accuracy.

In the case of hypothesis testing on matched or paired samples, the correct statement is that two measurements are drawn from the same pair of individuals or objects, and two sample means are compared to each other, making the answer choice D (both b and c) true.

For the provided data concerning anxiety levels, the correct test is a test of dependent means, as the measurements are paired and taken from the same students at two different times.