Comparing two means

Questions about the difference between two means can sometimes be answered using two different types of data.

Two independent samples
Measurements are made from two samples of individuals from the groups whose means are to be compared. A 2-sample t-test will compare the means.
One paired sample
The 'individuals' can be re-defined as pairs of related values from the two groups, and a single sample of these pairs can be collected. A paired t-test can be performed on the differences to compare the means.

The paired data usually give more accurate results.

Car repair costs from two garages

This simulation demonstrates the potential benefits from using paired data instead of two independent samples.

Matched pairs in experiments

In an experiment, the experimental units can sometimes be grouped into pairs that are similar in some way. These are called matched pairs.