Final answer:
The researcher should not perform a pooled variance t-test when the scores are not independent within the groups, as this violates one of the key assumptions of the test. The correct answer is 1) The scores are not independent within the groups
Step-by-step explanation:
A researcher is comparing two groups of 35 achievement scores and is considering conducting a pooled variance t-test. Among various scenarios, I would strongly advise the researcher NOT to conduct a pooled variance t-test when the scores are not independent within the groups. Independence of scores within each group is a crucial assumption for performing such a test.
When scores within the groups are not independent, it implies that there may be a relationship or interaction within the group that could affect the scores. This could result in biased estimates and violate one of the fundamental assumptions for many statistical tests, including the t-test, which assumes that observations within each group are independent of one another.
Other scenarios, such as differing variances between the groups and positive skewness of the achievement variable, although not ideal, do not necessarily preclude the use of a pooled variance t-test, depending on the severity of these issues. However, measures like transformations for skewness or using different tests more robust to variance differences might be more appropriate in these cases.