Question

1. Under what circumstances is it appropriate to run a one-tailed, as compared to a two-tailed Student’s T-test?
2. Under what circumstances is it appropriate to run a Paired T-test, as opposed to a Student’s T Test?
3. Under what circumstances is a one-sample T-test the correct one to run?

Answer 1

Under what circumstances is it appropriate to run a one-tailed, as compared to a two-tailed Student’s T-test?

We run one-tailed test for non-directional research hypothesis. Suppose we want to compare the means of two independent groups and determine whether one of the groups have lesser/greater average than the other group, we will use one-tailed test.

That is the alternative (research) hypothesis is any of the below, we will use one-tailed test.

or

Under what circumstances is it appropriate to run a Paired T-test, as opposed to a Student’s T Test?

When we compare two dependent or paired groups we use a Paired T-test. For example, we need to find whether the scores of students of a class in a examination improves after taking a new course. Same students scores were recorded before and after taking the course and thus the data are dependent and paired.

Under what circumstances is a one-sample T-test the correct one to run?

When we need to compare a group mean with a fixed hypothesized value, we use one-sample T-test. For example we need to test whether the average score of class is greater than the national average of 75. There is only one sample of students scores to be compared with a hypothesized value of 75.