Question

When should a paired​ t-test be performed instead of a​ two-sample t-test? A paired​ t-test should be performed instead of a​ two-sample t-test when the variable of interest is categorical. A paired​ t-test should be performed instead of a​ two-sample t-test when the observations within each sample are dependent. A paired​ t-test should be performed instead of a​ two-sample t-test when the samples taken are independent of each other. A paired​ t-test should be performed instead of a​ two-sample t-test when the sample sizes are small and the data in each population are not normally distributed. A paired​ t-test should be performed instead of a​ two-sample t-test when each observation in one group has a dependence on a particular observation in the other group.

Answer 1

Correct option:

A paired​ t-test should be performed instead of a​ two-sample t-test when each observation in one group has a dependence on a particular observation in the other group.

Explanation:

The paired t-test (also known as the dependent t-test or paired sample t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

We use the paired t-test if we have two measurements on the same item, person or thing. We should also use this test if we have two items that are being measured with a unique condition.

For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.

Or, examining the effect of a special course of calculus on the students by collecting their scores before and after the course.

In a paired t-test every observation of one group is related to a specific observation on the other groups.

Consider the second example provided above.

Suppose student A received a 50 in the calculus test before the special course and a 80 after the special course. This implies that the score of students A in group 1 (before course group) is related to the score of student A in group 2 (after course group).

Thus, the correct option is:

"A paired​ t-test should be performed instead of a​ two-sample t-test when each observation in one group has a dependence on a particular observation in the other group."