# 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.