# Confidence Interval for Paired Means

The testing method of paired means  is used to compare the means of two variables for a single group. It is often referred to as the paired difference  test since it tests whether the difference between two variables within the single group. It is important to note that since the data is “paired” it is not independent. The confidence interval for a paired means test may determine with a specific amount of confidence where the mean difference value should fall.

First step is to calculate the difference:

d = y1 – y2

In order to run a paired test the following conditions must be met:

• Random Sampling
• 10% (data must represent less than 10% of total population)
• Nearly Normal (histogram of the differences should appear fairly normal)

Provided that all of these conditions are met, we can compute the confidence interval to any specified degree of confidence using the following formula and the degrees of freedom, df = nd – 1:

$(\bar{d} \pm t^*_{df} (\frac{s_d}{\sqrt{n_d}}))$

As previously stated this confidence interval gives, to a certain confidence, where the actual mean difference should fall and thus can be used to provide evidence to support a hypothesis test conclusion. A good example of how a paired means test is executed can be seen by following this link. This wikipedia page goes in depth to describe how this method of hypothesis testing can be used and how the confidence interval plays a role.