Sampling and Sampling distributions

In Statistics, 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 the sample, such as sample mean) and the corresponding parameter (value of the 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 it is defined as \[\bar{x} – \mu\].

Exact calculation/ measurements of sampling error are not generally feasible as the true value of the population is usually unknown; 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 study should select sample(s) that are free from any bias, and the sample(s) are 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 sampling process error, but it is still possible that not all the randomized subjects/ objects are 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.

The potential Sources of Errors are:

Also Read: Sampling and Non-Sampling-Errors

Read more about Sampling-Error on Wikipedia

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Before differentiating the Sampling and Non Sampling Errors, let us define the Error term first.

The difference between an estimated value and the population’s 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 the 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 about how close the sample estimate is to the population’s true value.

Two Kinds of Errors: Sampling and Non Sampling Errors

There are two kinds of errors, namely (I) Sampling Errors and (II) Non Sampling Errors

1. Sampling Errors (random error)
2. Non-Sampling Errors (non-random errors)

Sampling Errors

A Sampling Error is the difference between the value of a statistic obtained from an observed random sample and the value of the corresponding population parameter being estimated. Let $T$ be the sample statistic used to estimate the population parameter; the sampling error is denoted by $E$  is  $E = T −\theta$. The value of Sampling Errors reveals the precision of the estimate. The smaller the sampling error, the greater 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

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, analyzing, and reporting the data, are all classified as non-sampling errors or non-random errors. These errors are present in a complete census as well as in the sampling survey.

One-by-One Comparison between Sampling and Non Sampling Errors

Feature	Sampling Error	Non-Sampling Error
Definition	Occurs due to differences between the sample and the population because only a subset is observed.	Occurs due to errors in data collection, processing, or analysis, regardless of sampling.
Cause	It can occur in both sample surveys and censuses.	Mistakes in survey design, measurement errors, respondent biases, data entry errors, etc.
Occurrence	Only in sample surveys (not in censuses).	It can be reduced by increasing the sample size or using better sampling techniques (e.g., stratified sampling).
Reduction	Can be reduced by increasing the sample size or using better sampling techniques (e.g., stratified sampling).	Reduced by improving survey methods, training enumerators, better questionnaire design, and data validation.
Examples	A sample mean differs from the population mean due to random selection.	– Interviewer bias – Misrecorded responses – Non-response errors – Processing mistakes
Type of Error	Random in nature (unavoidable but measurable).	Natural variation occurs because the sample is not a perfect representation of the population.

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