# Mathematics and Statistics - Sampling methods

## Introduction

Please note:  this material is derived from http://www.coventry.ac.uk/ec/~nhunt/meths/index.html

### Why Sample?

When organisations require data they either use data collected by somebody else (secondary data), or collect it themselves (primary data). This is usually done by SAMPLING, that is collecting data from a representative SAMPLE of the population they are interested in.

A POPULATION need not be human.  In statistics we define a population as the collection of ALL the items about which we want to know some characteristics. Examples of populations are hospital patients, road accidents, pet owners, unoccupied property or bridges. It is usually far too expensive and too time consuming to collect information from every member of the population, exceptions being the General Election and The Census, so instead we collect it from a sample.

The population we want to know about is called the TARGET POPULATION, as it is the one we are interested in and targeting. Identifying the target population is not always as easy as it might appear, and once identified there are many practical difficulties. If your target population is cat owners how do you find a list of them?

If it is to be of any use the sample must represent the whole of the population we are interested in, and not be biased in any way. This is where the skill in sampling lies: in choosing a sample that will be as representative as possible.  As a general rule the larger the sample, the better it is for estimating characteristics of the population. It's easier to estimate the mean height of men by measuring 50 of them rather than just 2.

However, in practice one is constrained by TIME and COST.

Although information about our sample will be of immediate interest, the point of collecting it is usually to deduce information about the entire population. In statistics this is called making INFERENCES.  If such inferences are to be reliable then the sample must be truly representative of the population, i.e. free from bias.

The basis for selecting any sample is the list of all the subjects from which the sample is to be chosen - this is the SAMPLING FRAME.  Examples are the Postcode Address File, the Electoral register, telephone directories, membership lists, lists created by credit rating agencies and others, and maps. A problem, of course, is that the list may not be up to date.  In some cases a list may not even exist.

Please note:  this material is derived from http://www.coventry.ac.uk/ec/~nhunt/meths/index.html.