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.
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,
2.785 >1.833 so we rejectThedrug does lower blood pressure.