Article Text

Article 7. An introduction to hypothesis testing. Parametric comparison of two groups—2
1. P Driscoll,
2. F Lecky
1. Accident and Emergency Department, Hope Hospital, Salford M6 8HD, UK
1. Correspondence to:Mr Driscoll, Consultant in Accident and Emergency Medicine (pdriscoll{at}hope.srht.nwest.nhs.uk)

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## Objectives

• Dealing with unpaired (independent) parametric data

• Discuss common mistakes using the t test

In covering these objectives the following terms will be introduced:

• Unpaired z test

• Unpaired t test

• One and two tailed tests

In the previous article we discussed the comparison of paired (dependent) data.1 These result when there is a relation between the groups, for example investigating the before and after effects of a drug on the same group of patients. The key measurement here is the difference between each pair. If this comes from a population that is normally distributed the mean difference can be calculated along with the standard error of the mean (SEM). The 95% confidence intervals for the true mean difference can then be derived along with the p value for the null hypothesis (table 1).

View this table:
Table 1

Comparison of two groups using z and t-tests

When there is no relation between the groups, the data are called “unpaired” or “independent”. A common example of this is the controlled trial where the effect of an intervention on one group is compared with a control group without the intervention. Here the selection of the experimental group does not tell you which people will be in the control group. They are therefore independent of one another.

It is useful to note at this stage that when you compare groups you are taking into account two variations. One is due to the difference between subjects within the same group and is called the intra-group variation. The other results from the difference between the groups and so is known as the inter-group variation. With paired data the difference in subjects is removed because each subject acts as its own control. Consequently you are simply measuring the inter-group variation. In contrast, when using unpaired data, both these variations have an …

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## Footnotes

• * or estimated standard error of the mean (ESEM) if using a sample size < 100.2