What is a random sample?
Date: 2015-10-07; view: 463.
Sample
Population
What is the difference between a sample and a population?
In statistics we make a distinction between two concepts: a population a sample.
A population is any entire collection of people, animals, plants or things from which we may collect data. It is the entire group we are interested in, which we wish to describe or draw conclusions about.
In order to make any generalisations about a population, a sample, that is meant to be representative of the population, is often studied. For each population there are many possible samples. A sample statistic gives information about a corresponding population parameter. For example, the sample mean for a set of data would give information about the overall population mean.
It is important that the investigator carefully and completely defines the population before collecting the sample, including a description of the members to be included.
Example
The population for a study of infant health might be all children born in the UK in the 1980's. The sample might be all babies born on 7th May in any of the years.
A sample is a group of units selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions about the larger group.
A sample is generally selected for study because the population is too large to study in its entirety. The sample should be representative of the general population. This is often best achieved by random sampling. Also, before collecting the sample, it is important that the researcher carefully and completely defines the population, including a description of the members to be included.
Example
The population for a study of infant health might be all children born in the UK in the 1980's. The sample might be all babies born on 7th May in any of the years
Arandom sample is one where the researcher insures (usually through the use of random numbers applied to a list of the entire population) that each member of that population has an equal probability of being selected. Random samples are an important foundation of Statistics. Almost all of the mathematical theory upon which Statistics are based rely on assumptions which are consistent with a random sample.
Purely random samples are hard to achieve in the real world, but many times you can come close. The biggest problem is that you may not have a complete list of the population that you want to randomly draw from. The telephone book for a city, for example, will list most households, but will exclude those who do not have a telephone, those who have unlisted numbers, and most recently, those who use a cell phone instead of a land phone for all their calls (cell phone numbers are usually not in the telephone book).
A second barrier to purely random samples is that for some people in the population, you will find it difficult or impossible to locate them. People who work unusual hours or who travel a lot may end up getting selected in the sample, but may never be around to answer the telephone.
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