The Paired t Test

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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 forwith 10-1=9 degrees of freedom ie

The mean difference,

We calculate

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

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