The Two Sample Paired t -test

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

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

Do people earn more aftergetting a qualification?

Do people watch more TVafter getting satellite TV?

For example suppose peoplewith raised blood pressure are given a new drug which it is supposedreduces blood pressure. To test this, people are put on a two weekcourse of drugs and their blood pressures are compared before andafter. 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 meandifference,(thereis 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 hypothesisis

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

The mean difference,


We calculate

2.785 >1.833 so we rejectThedrug does lower blood pressure.