Paired-sample and two-sample hypothesis tests
Paired-sample and two-sample hypothesis tests
Paired-Sample Hypothesis Tests
Definition and Use
- A paired-sample hypothesis test (also known as the matched pairs test) is a statistical procedure used for comparing two related or dependent groups.
- This test is ideally suited for cases involving repeated measurements on a single sample or two samples that have been matched for specific characteristics.
- Examples include measuring performance of a group before and after an intervention, or comparing twins on a trait of interest.
Data Assumptions
- The observations must be dependent and paired in some way.
- The differences between the paired observations should be reasonably normally distributed.
Test Procedure
- The primary step involves calculating the differences between the paired observations.
- Then the differences are tested to determine if they are significantly different from zero.
- The null hypothesis usually states that the mean difference between the paired observations is zero.
- A significant test outcome indicates that the mean of the differences is significantly different from zero.
Two-Sample Hypothesis Tests
Definition and Use
- A two-sample hypothesis test is a statistical procedure used for comparing the means of two independent and unrelated groups.
- These are often used in experiments or studies where the two groups are exposed to different conditions or represent different demographic groups.
Data Assumptions
- The two samples should be independent of each other.
- They should be drawn from populations that each have a normal distribution, and the variances of the populations should be equal.
- However, if these assumptions are not met, non-parametric alternatives such as the Mann-Whitney U test can be used.
Test Procedure
- The null hypothesis typically states that the means of the two populations are equal.
- The alternative hypothesis, on the other hand, postulates that the population means are not equal.
- A significant test result indicates that the means of the two groups are significantly different from each other.