# 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**.