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Article 6. An introduction to hypothesis testing. 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}

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  • Dealing with paired parametric data

  • Comparing confidence intervals and p values

In covering these objectives the following terms will be introduced:

  • Parametric and non-parametric analysis

  • Paired z test

  • Paired t test

We have shown previously that statistical inference enables general conclusions to be drawn from specific data. For example estimating a population's mean from a sample mean. At first glance this may not appear important. In practice however the ability to make these estimations is fundamental to most medical investigations. These tend to concentrate on dealing with one or more of the following questions:

Have the observations changed with time and/or intervention?

Do two or more groups of observations differ from each other?

Is there an association between different observations?

To answer these questions many different types of statistical inference tests have been developed to deal with varying sample sizes and different types of data. Though the tests differ they have the common aim of assessing whether the null hypothesis is likely to be correct (box 1). They are known collectively as “tests of significance”.1

Box 1 The null hypothesis

There is no difference between the groups with respect to the measurement made.

The significance test chosen is dependent upon the type of data we are dealing with, whether it has a normal distribution and the type of question being asked.2 Once the distribution of the data is known, you can tell if the null hypothesis should be tested using parametric or non-parametric methods.

Parametric and non-parametric analysis


A normal distribution is a regular shape. As such it is possible to draw the curve exactly by simply knowing the mean, standard deviation and variance of the data. When considering a normal distribution of a population these features are known as parameters. Parametric analysis relies on the data being normally (or nearly) …

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  • * or estimated standard error of the mean (ESEM) if using a sample size < 100.4