## 1. Paired T tests

**What Is It?**

Paired T-tests are used to compare the means of two populations where the observations have been taken in pairs one from each population. They can also be referred to as 'dependent samples T-tests'. For a T-test to be applicable the differences need to be roughly normally distributed. This means that while the test is applicable when the differences are not normally distributed it is not applicable in cases where you have extreme outliers.

The test is set up such that the working assumption is that the differences in the means of the 2 samples is zero. The test output is a P value which gives a probability that this is correct and that the differences in the means of the 2 distributions is zero - this is a 'null hypothesis'.

The formula for the test is

A typical use for this sort of test would be:

1. To compare two methods of measuring the same thing, especially in observational studies where you are concerned about and want to try to minimise the impact of confounding factors on the results.

2. To compare before and after results for for a specific set of subjects, for example blood pressure before and after taking a blood pressure mediation.

**How Do I Carry Out A T-test?**

Step One:

Calculate the difference between each of the two pairs of observations.

Step Two:

Using these differences to calculate a mean

Step Three:

Work out the standard deviation of these differences, and so the standard error of the mean difference

Step Four

Use the results of the calculations in Steps One, Two and Three above to calculation the T-statistic.

this is calculated as the mean of the differences divided by the standard error of the mean difference

Step Five

This T value can then be looked up on a table of T-distributions to obtain the P value for the test. The P value will need to be compared to a distribution with n-1 degress of freedom.

**How Would I Carry One Out In SPSS?**

When you have entered your data into SPSS it is simple to use it to calculate the P value. Simply click COMPARE and choose MEANS from the menu, and then choose the appropriate T test, in this case paired, from the menu.