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# Sampling Error

In statistics, it is the most common practice to take probability samples of very large population. Although, the random selection process is considered to be the best way of getting a representative sample from a population, it cannot guarantee a perfect sample. We must acknowledge that even the best of the samples will be a little deviated from the actual population. This deviation is termed as sampling error. This error occurs when the sample is chosen randomly, rather than focusing on each subject in the population.

 Related Calculators Sampling Error Calculator calculate percent error calculate standard error Error Function Calculator

## Formula

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The sampling error occurs during the estimation of statistical characteristics of given population. A sample being unable to include all the elements of a population, the other statistical measures like mean, median, quartile etc. get deviated from the characteristics of whole population. This is defined as the sampling error. For instance: to determine average height of 1 million citizens of a country, if a statistician takes the average of the height of 1000 randomly chosen people, then it is quite evident that the average height of 1 million people would not be same as the average height of 1000 people.

The sampling error does occur very commonly. However, it can be reduced or eliminated by increasing the sample size and by ensuring that the sample represents whole population. There are different kinds of sampling errors. There are several methods of determining them. The most common formula for estimating sampling error is

Sampling Error =  $\frac{(Standard\ Deviation)}{\sqrt{(Sample\ Size)}}$

Or

$SE$ =  $\frac{S}{\sqrt N}$

## Sampling Error & Non Sampling Error

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An error that occurs in the data due to the process of sample collection and considering a sample from the population instead of taking entire population is known as sampling error. On the other hand, the non-sampling error occurs in data due to the factors other than choosing a sample.

Sampling error and non-sampling error both are the reasons for deviation of the estimated statistical measures from the true values. If either of them occurs in a data, then the estimations from different samples of same sample size may vary from one sample to another and it is more likely that each estimate deviates from the actual value of population parameter.

The non-sampling errors may cause bias in surveys or polls. There are several different kinds of non-sampling errors.

In short, the term non-sampling is used to represent all the sampling errors that do not occur due to random selection of a sample from the population. To quantify a non-sampling error is much more complicated than to quantify a sampling error.

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