# Sampling

A sample is anything less than the full population.
The population is the group of items for which information is being collected.
For certain information such as opinions and attitudes it is impossible to carry out a complete survey and in these cases a sample is preferred.

A sample is selected and the relevant statistics are then used to estimate the statistics for the whole population.
These are often referred to as Descriptive Statistics.

Given a choice we would always use the whole population for our analysis but sometimes this is just not possible or practical.
In these situations we are forced to work with a sample to draw conclusions.
The validity and accuracy of our conclusion relies entirely on how good our sample is, and therefore it is imperative that we can obtain a good sample
From a good sample generalisations can be made with some confidence.

Statistical Analysis is often done on a sample and not on a whole population
A sample must represent the whole of the population and not be biased in any way
You always want to choose a sample that will be as representative as possible.
As a general rule the larger the sample the better it is.

Information obtained from a sample will be of interest, but it is usually used to try and deduce information about the entire population
In statistics, this is called making inferences.

biased samples ??

### Different Types of Random Sampling

Random is this context means that all the items in the population have an equal chance of being selected
Systematic Sampling
Stratified Sampling
Cluster Sampling - Relies on natural groups
Quota Sampling - The selection is not random and requires human instinct

Quasi-Random sampling
Importance sampling

These can be divided into two categories
1) probability sampling
2) non probability sampling

### Sampling with or without replacement

Unrestricted random sampling is carried out "with replacement".
This means that the unit selected is replaced before the next unit is selected.
In sampling "without" replacement only those units not previously selected can be selected the next next time.
In applied statistics it is assumed that sampling is without replacement.
Sampling without replacement is often called "simple random sampling" or "simple probability sampling".