# Sampling Errors in Statistics: Definition, Types, and Calculation

![Sampling Error](https://www.investopedia.com/thmb/Bmo4lJrnc63UKSFBWleV0uq7i9k=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/SamplingError-4189704-Final-533c7191287b4b0e89fb11873679e08c.jpg)

*Sampling error can be minimized by increasing the sample size and redefining the target population. — Paige McLaughlin / Investopedia*

> **Definition**
>
> A sampling error occurs when a sample drawn from a population deviates from representing the true or entire population.

## What Is a Sampling Error?

Sampling is an analysis performed by selecting several observations from a larger population. The method of selection can produce both sampling errors and non-sampling errors. A sampling error is a deviation between the sampled value and the true population value.

### Key Takeaways

*   Even randomized samples will have some degree of sampling error because a sample is only an approximation of the population from which it is drawn.
*   The prevalence of sampling errors can be reduced by increasing the sample size.
*   In general, sampling errors can be placed into four categories: population-specific error, selection error, sample frame error, or nonresponse error.

## Understanding Sampling Errors

A sampling error is a deviation in the sampled value vs. the true population value. Sampling errors occur because the sample is not [representative](https://www.investopedia.com/terms/r/representative-sample.asp) of the population or is biased in some way. Even randomized samples will have some degree of sampling error because a sample is only an approximation of the population from which it is drawn.

## Calculating a Sampling Error

The [sampling error formula](https://www.investopedia.com/ask/answers/061715/how-do-i-calculate-standard-error-using-matlab.asp) is used to calculate the overall sampling error in statistical analysis. The sampling error is calculated by dividing the [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) of the population by the square root of the size of the sample and then multiplying the resultant with the Z-score value, which is based on the confidence interval.  

$\begin{aligned}&\text{Sampling Error}=Z\times\frac{\sigma}{\sqrt{n}}\\&\textbf{where:}\\&Z=Z\text{ score value based on the}\\&\qquad\ \text{confidence interval (approx}=1.96)\\&\sigma=\text{Population standard deviation}\\&n=\text{Size of the sample}\end{aligned}$  

## Types of Sampling Errors

There are different categories of sampling errors.

### Population-specific Error

A population-specific error occurs when a researcher doesn’t understand who to survey.

### Selection Error

Selection error occurs when the survey is self-selected, or when only those participants who are interested in the survey respond to the questions. Researchers can attempt to overcome selection errors by finding ways to encourage participation.

### Sample Frame Error

A sample frame error occurs when a sample is selected from the wrong population data.

### Nonresponse Error

A nonresponse error occurs when a useful response is not obtained from the surveys because researchers were unable to contact potential respondents (or potential respondents refused to respond).

## Eliminating Sampling Errors

The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

Consider that the average of a sample of 10 varies more than the average of a sample of 100. Steps can also be taken to ensure that the sample adequately represents the entire population.

Researchers might attempt to reduce sampling errors by replicating their study. This could be accomplished by taking the same measurements repeatedly, using more than one subject or multiple groups, or undertaking multiple studies.

Random sampling is an additional way to minimize the occurrence of sampling errors. Random sampling establishes a systematic approach to selecting a sample. For example, rather than choosing participants to be interviewed haphazardly, a researcher might choose those whose names appear first, 10th, 20th, 30th, 40th, and so on, on the list.

> **Fast Fact**
>
> One way to reduce the likelihood of sampling error is to use a larger sample size. The Monthly Employment Situation report, compiled each month by the U.S. Bureau of Labor Statistics, is calculated from a survey of 119,000 businesses and government agencies. Due to the enormous sample size, these surveys have an extremely low rate of sampling error.

## How Do Sampling Errors Apply to Real Life?

Sampling is often used by businesses and governments and in finance. It is relied on to make critical decisions and is particularly common in economic research.

Sampling helps companies predict [customer](https://www.investopedia.com/terms/c/customer.asp) behavior, estimate future [demand](https://www.investopedia.com/terms/d/demand.asp), and set prices. It also helps financial institutions detect [fraud](https://www.investopedia.com/terms/f/fraud.asp) by [auditing](https://www.investopedia.com/terms/a/audit.asp) transactions.

Sampling errors can affect the validity of their research findings and the quality of their data. They also won’t be as confident in their decision-making.

## Examples of Sampling Errors

Assume that XYZ Company provides a subscription-based service that allows consumers to pay a monthly fee to stream videos and other types of programming via an internet connection.

The firm wants to survey homeowners who watch at least 10 hours of programming via the internet per week and who 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.

A population specification error would occur if XYZ Company does not understand the specific types of consumers who should be included in the sample. For example, if XYZ creates a population of people ages 15 to 25, many of those consumers do not make the purchasing decision about a video streaming service because they may not work 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.

Selection error also causes distortions in the results of a sample. A common example is a survey that only relies on a small portion of people who immediately respond. If XYZ makes an effort to follow up with consumers who don’t initially respond, the results of the survey may change. Furthermore, if XYZ excludes consumers who don’t respond right away, the sample results may not reflect the preferences of the entire population.

## Sampling Error vs. Non-Sampling Error

Different types of errors can occur when gathering statistical data. Sampling errors are the seemingly random differences between the characteristics of a sample population and those of the general population. Sampling errors arise because sample sizes are inevitably limited. (It is impossible to sample an entire population in a survey or a census.)

> **Important**
>
> A sampling error can result even when no mistakes of any kind are made; sampling errors occur because no sample will ever perfectly match the data in the universe from which the sample is taken.

XYZ Company will also want to avoid [non-sampling errors](https://www.investopedia.com/terms/n/non-samplingerror.asp). These are errors that result during data collection and cause the data to differ from the true values. Non-sampling 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 non-sampling error. Asking biased questions is another type of error.  

## What Is Sampling Error vs. Sampling Bias?

In statistics, sampling means selecting the group that you will collect data from in your research.

Sampling errors are statistical errors that arise when a sample does not represent the whole population once analyses have been undertaken.

Sampling bias is the expectation, which is known in advance, that a sample won’t be representative of the true population—for instance, if the sample ends up having proportionally more women or young people than the overall population.

## Why Is Sampling Error Important?

Being aware of the presence of sampling errors is important because it can be an indicator of the level of confidence that can be placed in the results. Sampling error is also important in the context of a discussion about how much research results can vary.

## How Do You Find the Sampling Error?

In survey research, sampling errors occur because all samples are representative samples: a smaller group that stands in for the whole of your research population. It’s impossible to survey the entire group of people you’d like to reach.

It’s not usually possible to quantify the degree of sampling error in a study, since it’s impossible to collect the relevant data from the entire population you are studying. This is why researchers collect representative samples (and representative samples are the reason why there are sampling errors).

## What Is Sampling Error vs. Standard Error?

Sampling error is derived from the [standard error (SE)](https://www.investopedia.com/terms/s/standard-error.asp) by multiplying it by a Z-score value to produce a [confidence interval](https://www.investopedia.com/terms/c/confidenceinterval.asp).

The standard error is computed by dividing the standard deviation by the square root of the sample size.

## The Bottom Line

Sampling error occurs when a sample drawn from a population deviates somewhat from that true population. Large sampling errors can lead to incorrect estimates or inferences made about the population based on statistical analysis of that sample.

In general, sampling errors can be placed into four categories: population-specific error, selection error, sample frame error, or nonresponse error. A population-specific error occurs when the researcher does not understand who they should survey. A selection error occurs when respondents self-select their participation in the study. (This results in only those who are interested in responding, which skews the results.) A sample frame error occurs when the wrong subpopulation is used to select a sample. Finally, a nonresponse error occurs when potential respondents are not successfully contacted or refuse to respond.

> **Article Sources**
>
> 1.  U.S. Bureau of Labor Statistics. “[Current Employment Statistics—CES (National)](https://www.bls.gov/ces/).”