Question

When hypothesis testing, when might you use a related sample versus an independent sample? Provide examples of both population to illustrate the differences.

Answer 1

When the samples are not independent but the sample observations are paired together, i.e. the pair of observations(x_i ,y_i) corresponding to the same sample unit, we have to use related sample.

The related samples are used when we want to test the significance or effect of treatment on the same sample units.

Example : Suppose we want to test the effect of extra mathematics classes on the test score of students. We can conduct a test and record the test scores before the classes and again we can conduct the test and record the test scores after attending the extra mathematics classes to compare the the test scores and know whether the extra mathematics classes are effective in increasing test scores.

Here the sample units are students, we record the test score of same student before and after the classes. that means the samples are related samples.

Independent Samples: When sample units are independent of each other , i.e. the effect of treatment on ith sample unit does not effect the jth sample unit.

Example : Suppose we want to test the effect of extra mathematics classes on the test score of students between two sections of grade 2 . So we conduct a test and record the test score of Section A and section B students.

Here the scores of students of section A is independent of scores of students of section B.