Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Sampling Error Definition, Example, Formula | Basic Statistics

Sampling Error Definition, Example, Formula

Sampling error also called estimation error 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 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 parameter then the sampling error is $\bar{x} – \mu$.

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.

Sampling Error

Sampling Error

Cause 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 NonSampling Errors

Sampling and NonSampling Errors

Sampling and NonSampling Errors

The difference between an estimated value and the population true value is called an error. Since a sample estimate is used to describe a characteristic of a population. A sample being only a part of population cannot provide a perfect representation of the population, no matter how carefully the sample is selected. Generally it is seen that an estimate is rarely equal to the true value and we may think that how close will the sample estimate be to the population true value. There are two kind of errors

  1. Sampling Errors (random error)
  2. Non sampling errors (non random errors)
  1. Sampling Errors
    A Sampling Errors is the difference between the value of a statistic obtained from an observed random sample and the value of corresponding population parameter being estimated.Let T be the sample statistic used to estimate the population parameter , the sampling error denoted by E  is  $E = T −θ$. The value of Sampling Errors reveals the precision of the estimate. Smaller the sampling error, the greater will be the precision of the estimate.The sampling error can be reduced:

    i)   By increasing the sample size
    ii)  By improving the sampling design
    iii) By using the supplementary information

  2. Non-Sampling Error
    The errors that are caused by sampling the wrong population of interest and by response bias as well as those made by an investigator in collecting analysis and reporting the data are all classified as non-sampling error or non-random errors. These error are present in a complete census as well as in sampling survey.


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