# Sampling Error Definition, Example, Formula

In Statistics, sampling error also called estimation error which is the amount of inaccuracy in estimating some value that is caused by only a portion of a population (i.e. sample) rather than the whole population. It is the difference between the statistic (value of the sample, such as sample mean) and the corresponding parameter (value of population, such as population mean) is called the sampling error. If $\bar{x}$ is the sample statistic and $\mu$ is the corresponding population parameter then the sampling error is defined as $\bar{x} – \mu$.

Exact calculation/ measurements of sampling error is not feasible generally as the true value of population is unknown usually, however it can often be estimated by probabilistic modeling of the sample.

Causes of Sampling Error

• The cause of the Error discussed may be due to the biased sampling procedure. Every research should select sample(s) that is free from any bias and the sample(s) is representative of the entire population of interest.
• Another cause of this Error is chance. The process of randomization and probability sampling is done to minimize the sampling process error but it is still possible that all the randomized subjects/ objects are not the representative of the population.

Eliminate/ Reduce the Sampling Error

The elimination/ Reduction of sampling error can be done when a proper and unbiased probability sampling technique is used by the researcher and the sample size is large enough.

• Increasing the sample size
The sampling error can be reduced by increasing the sample size. If the sample size $n$ is equal to the population size $N$, then the sampling error will be zero.
• Improving the sample design i.e. By using the stratification
The population is divided into different groups containing similar units.

Also Read: Sampling and Non-Sampling Errors Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

### 3 Responses

1. bague diamant says:

great article, very nice

• Syed says:

Hi,

I have followed your MCQs (https://itfeature.com/statistical-sources-2/statistics-mcqs/sampling/mcqs-sampling) and I have question regarding one of the question in it (Question no 10).

You have marked E as a right answer in the pdf while in the definition you have named it as sampling error, I suppose the right answer is B (as per your definition). Please help with the confusion.

Thanks.

• Muhammad Imdad Ullah says:

please search the term such as “statistical error” or “error in statistics”.

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