# Sampling Error

## Definition

In statistics, sampling error is incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics on the sample, such as means and quantiles, generally differ from the characteristics of the entire population, which are known as parameters. For example, if one measures the height of a thousand individuals from a country of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is typically done to determine the characteristics of a whole population, the difference between the sample and population values is considered an error. Exact measurement of sampling error is generally not feasible since the true population values are unknown; however, sampling error can often be estimated by probabilistic modeling of the sample.

## What is a ‘Sampling Error’

A sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data and the results found in the sample do not represent the results that would be obtained from the entire population. Sampling is an analysis performed by selecting by specific number of observations from a larger population, and this work can produce both sampling errors and nonsampling errors.

## Explaining ‘Sampling Error’

Sampling error can be eliminated when the sample size is increased and also by ensuring that the sample adequately represents the entire population. Assume, for example, that XYZ Company provides a subscription-based service that allows consumers to pay a monthly fee to stream videos and other programming over the web and that the firm want to survey homeowners who watch at least 10 hours of programming over the web each week and pay for an existing video streaming service. XYZ wants to determine what percentage of the population is interested in a lower-priced subscription service. If XYZ does not think carefully about the sampling process, several types of sampling errors may occur.

## Examples of Sampling Error

A population specification error means that XYZ does not understand the specific types of consumers who should be included in the sample. If, for example, XYZ creates a population of people between the ages of 15 and 25 years old, many of those consumers do not make the purchasing decision about a video streaming service, because they are not working full-time. On the other hand, if XYZ put together a sample of working adults who make purchase decisions, the consumers in this group may not watch 10 hours of video programming each week.

## Factoring in Nonsampling Error

XYZ also wants to avoid nonsampling errors, and these errors are caused by human error, such as a mistake made in the survey process. If one group of consumers only watches five hours of video programming a week and is included in the survey, that decision is a nonsampling error. Asking questions that are biased is another type of error.