Objectives

• Discuss the principles of statistical inference

• Quantifying the probability of a particular outcome

• Discuss clinical versus statistical significance

In covering these objectives we will introduce the following terms:

• Population and sample

• Parameter and statistic

• Null hypothesis and alternative hypothesis

• Type I and II errors

The previous two articles discussed summarising data so that useful comparisons can be made. Another common problem encountered is estimating a value in a larger group based upon information collected from a small number of subjects. To see how statistics can be used to achieve this, it is helpful to begin by reviewing the meaning of five commonly used terms:

• Population and sample

• Parameter and statistic

• Element

The word “population” describes a large group that includes every possible case. In contrast, a “sample” is a smaller group of subjects who are part of the population. Therefore the population of UK emergency departments would have every emergency department in the UK whereas those in the north west would represent a sample.

A value measured in a population is known as a “parameter”. Consequently the trolley waiting time in UK emergency departments would be a parameter. The term “statistic” is used to denote the same variable when it is measured in a sample. Finally each separate observation in either a population or sample is called an “element” and it is often labelled with the letter X. The number of elements in a population is given the letter N and in a sample, n.

It is often not possible to record all the elements of a population. For example, a study investigating the peak flow in asthmatic patients attending UK emergency departments cannot review every patient. …