Use the samples to make informal inferences about the population.

**Methods of collecting data**

**1.1 Taking a census**

A census involves observing every member of a population and is used if the size of the population is small or if extreme accuracy is required.

**Advantages**

It should give a completely accurate result, a full picture.

**Disadvantages**

Very time consuming and expensive. It cannot be used when testing process destroys article being tested information is difficult to process because there is so much of it.

**1.2 Sampling**

Sampling involves observing or testing a part of the population. It is cheaper but does not give such a full picture.

The size of the sample depends on the accuracy desired (for a varied population a large sample will be required to give a reasonable accuracy).

**1.2.1 Simple random sampling**

Every member of the population must have an equal chance of being selected

.**1.2.2 Using random number tables**

To take a simple random sample of size n from a population of N sampling units first make a list and give each member of the population a number. Then use random number tables to select the sample.

We ignore any numbers which do not refer to a member of the population – for example using three figure random numbers for a population numbered from 001 to 659 we would ignore numbers from 660 to 999.

Also we ignore the second occurrence of the same number.

**Advantages **The numbers are truly random and free from bias. It is easy to use each member has a known equal chance of selection.

**Disadvantages**

It is not suitable when the sample size is large.

**1.2.3 Lottery sampling**

A sampling frame is needed – identifying each member of the population. The name or number of each member is written on a ticket (all the same size, colour and shape), and the tickets are all put in a

container which is then shaken. Tickets are then drawn without replacement.

**Advantages**

The tickets are drawn at random. It is easy to use. Each ticket has a known chance of selection (considered as constant as long as the sample size is much smaller than the total number of tickets).

**Disadvantages**

It is not suitable for a large sample a sampling frame is needed.

**1.2.4 Systematic sampling**

First make an ordered list, and divide into equal groups each of size 50 (or xx). Second select every 50th (or xx) member from the list. In order to make sure that the first on the list is not automatically selected random number tables must be used to select the member in the first group, then select every 50th (or ??) after that. Used when the population is too large for simple random number sampling.

**Advantages**

Simple to use. Suitable for large samples

**Disadvantages**

Only random if the ordered list is truly random. it can introduce bias

**1.2.5 Stratified sampling**

First divide the population into exclusive (distinct) groups or strata and then select a sample so that the proportion of each stratum in the sample equals the proportion of that stratum in the population.

Used when

The sample is large and the population divides naturally into mutually exclusive groups.

**Advantages**

It can give more accurate estimates (or a more representative picture) than simple random number sampling when there are clear strata present. It reflects the population structure.

**Disadvantages**

Within the strata the problems are the same as for any simple random sample if the strata are not clearly defined they may overlap.

**1.2.6 Sampling with and without replacement**

Simple random sampling is sampling without replacement in which each member of population can be selected at most once. In sampling with replacement each member of the population can be selected more than once: this is called unrestricted random sampling.

**1.2.7 Quota sampling**

This is a non-random method. First decide on groups into which the population is divided and a number from each group to be interviewed to form quotas. Then go out and interview and enter each result into the relevant quota.

If someone refuses to answer or belongs to a quota which is already full then ignore that persons reply and continue interviewing until all quotas are full. Used when it is not possible to use random methods – for example when the whole population is not known (homeless in a big city).

**Advantages**

can be done quickly as a representative sample can be obtained with a small sample size costs are kept to a minimum administration is fairly easy.

**Disadvantages **It is not possible to estimate the sampling errors (as it is not a random process) interviewer may not put into correct quota non-responses are not recorded it can introduce interviewer bias.

**1.2.8 Primary data**

Primary data is data collected by or on behalf of the person who is going to use the data.

**Advantages**

Collection method is known, accuracy is known , exact data needed are collected

**Disadvantages**

Costly in time and effort

**1.2.9 Secondary data**

Secondary data is data not collected by or on behalf of the person who is going to use it. The data are second-hand – e.g. government census statistics.

**Advantages**

Cheap to obtain, large quantity available (e.g. internet) Much has been collected year on year and can be used to plot trends

**Disadvantages**

Collection method may not be known, accuracy may not be known. it can be in a form which is difficult to handle bias is not always recognised.