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Article 8. An introduction to hypothesis testing. Non-parametric comparison of two groups—1
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 non-parametric data

• Dealing with small samples of nominal data

In covering these objectives the following terms will be introduced:

• χ2 test

• Fisher's exact test

• Yates's correction

In the previous article the basic principles behind comparing two groups was discussed. The t test was also shown to play an important part in this process when dealing with parametric data. As it is a versatile test, it can be used to compare independent groups and paired groups as well as give an estimate of a population mean when a sample is known. In contrast, when dealing with non-parametric data, several tests have to be used. Fortunately though the same principles apply.

As these non-parametric tests do not assume the distribution of the data is normal, they can be used on a much wider spectrum of results. The cost of this is they lack power and are mainly tests of significance. Consequently they will tell if a difference exists but not how big it is (table 1).

View this table:
Table 1

Contrast of parametric and non-parametric tests in two group comaparisons

There are many non-parametric tests and choosing the most appropriate one can be difficult. Studying published papers can add to the confusion because tests are selected for a variety of reasons, including personal preferences. Furthermore, calculations are commonly carried out with the aid of computer software. As a result there is a risk that the unwary can produce a figure with a p value that is in fact meaningless because the wrong test has been used.

For those unfamiliar with statistics the way forward is to talk to someone who knows about the subject. To make these meetings more useful, the next two articles will concentrate on the common non-parametric tests used for two groups comparisons (table 2).

View this table:
Table 2

Table of non-parametric tests …

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