## The Two Sample Paired t -test

The paired t test is typically used to analyse whether there is a before and after difference. It is the same population before and after, and the difference for each individual is measured and a mean difference found and analysed for significance. For example:

Do patients with high blood pressure see a fall in drug pressure after taking a drug?

Do people earn more after getting a qualification?

Do people watch more TV after getting satellite TV?

For example suppose people with raised blood pressure are given a new drug which it is supposed reduces blood pressure. To test this, people are put on a two week course of drugs and their blood pressures are compared before and after. The results are illustrated in the following table.

Person | A | B | C | D | E | F | G | H | I | J |

Before | 164 | 122 | 166 | 162 | 152 | 114 | 136 | 142 | 154 | 190 |

After | 150 | 120 | 148 | 137 | 152 | 122 | 132 | 138 | 142 | 170 |

Difference | -14 | -2 | -18 | -25 | 0 | 8 | -4 | -4 | -12 | -20 |

Suppose to test mean difference,(there is no difference in blood pressure before and after taking the drug)we carry out a hypothesis test at the 10% level.

The null hypothesis is

The alternative hypothesis is

This is a two tailed test so we look in the statistical tables forwith10-1=9 degrees of freedom ie

The mean difference,

We calculate

2.785 >1.833 so we rejectThe drug does lower blood pressure.