In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, a sample

Sampling (statistics)

In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....

 is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component. Random sampling can also refer to taking a number of independent observations from the same probability distribution, without involving any real population.
The sample usually is not a representative of the population from which it was drawn— this random variation in the results is termed as sampling error

Sampling error

-Random sampling:In statistics, sampling error or estimation error is the error caused by observing a sample instead of the whole population. The sampling error can be found by subtracting the value of a parameter from the value of a statistic...

. In the case of random samples, mathematical theory is available to assess the sampling error. Thus, estimates obtained from random samples can be accompanied by measures of the uncertainty associated with the estimate. This can take the form of a standard error

Standard error (statistics)

The standard error is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate....

, or if the sample is large enough for the central limit theorem

Central limit theorem

In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...

 to take effect, confidence intervals may be calculated.

Types of random sample

• A simple random sample
  Simple random sample
  In statistics, a simple random sample is a subset of individuals chosen from a larger set . Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has...
  
   is selected so that all samples of the same size have an equal chance of being selected from the entire population.
• A self-weighting sample, also known as an EPSEM (Equal Probability of Selection Method) sample, is one in which every individual, or object, in the population of interest has an equal opportunity of being selected for the sample. Simple random samples are self-weighting.
• Stratified sampling
  Stratified sampling
  In statistics, stratified sampling is a method of sampling from a population.In statistical surveys, when subpopulations within an overall population vary, it is advantageous to sample each subpopulation independently. Stratification is the process of dividing members of the population into...
  
   involves selecting independent samples from a number of subpopulations, group or strata within the population. Great gains in efficiency are sometimes possible from judicious stratification.
• Cluster sampling
  Cluster sampling
  Cluster Sampling is a sampling technique used when "natural" groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups and a sample of the groups is selected. Then the required information is...
  
   involves selecting the sample units in groups. For example, a sample of telephone calls may be collected at by first taking a collection of telephone lines and collecting all the calls on the sampled lines. The analysis of cluster samples must take into account the intra-cluster correlation which reflects the fact that units in the same cluster are likely to be more similar than two units picked at random

Methods of producing random samples

• Random number table
  Random number table
  Random number tables have been used in statistics for tasks such as selected random samples. This was much more effective than manually selecting the random samples...
  
  
• Mathematical algorithms for pseudo-random number generators
• Physical randomization devices such as coins, playing cards or sophisticated devices such as ERNIE
  Ernie
  Ernie is a fictional character, a Muppet on the Public Broadcasting Service's long-running children's television show, Sesame Street. He and his roommate Bert form a comic duo that is one of the program's centerpieces, with Ernie acting the role of the naïve troublemaker and Bert the world-weary foil...
  
  

See also

• Randomness
  Randomness
  Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....
  
  
• Sampling (statistics)
  Sampling (statistics)
  In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
  
  
• Survey sampling
  Survey sampling
  In statistics, survey sampling describes the process of selecting a sample of elements from a target population in order to conduct a survey.A survey may refer to many different types or techniques of observation, but in the context of survey sampling it most often involves a questionnaire used to...
  
  
• Statistical population
  Statistical population
  A statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest...