# Explain the concept of sampling error

### October 27, 2019

Explain the concept of sampling error
In [statistics], sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or [sample (statistics)/sample], of that population. Since the sample does not include all members of the population, statistics on the sample, such as means and quartiles, generally differ from the characteristics of the entire population, which are known as parameters. For example, if one measures the height of a thousand individuals from a country of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is typically done to determine the characteristics of a whole population, the difference between the sample and population values is considered an [Errors and residuals|error]. The exact measurement of sampling error is generally not feasible since the true population values are unknown.

sampling error
A sampling error is a problem in the way that members of a population are selected for research or data collection, which impacts the validity of results. Numerically, a sampling error expresses the difference between results for the sample and estimated results for the population.

Subjects are selected through several different methods, broadly categorized as probability-based or non-probability-based. Probability-based methods are considered to yield the most valid results because each member of a population has an equal chance of selection; as long as a sufficiently large sample is selected, the group should be representative of the population.

No sampling method is infallible. In simple random sampling, considered to be the most foolproof method, subjects for the sample are randomly selected from the entire population to create a subset.

Even in this case, however, the sample size is an issue. In general, a larger group of subjects will be more representative of the population. Imagine, for example, a study in which thirty subjects are selected from a population of a thousand random selection could not ensure that the sample would represent the population.

Other sampling errors include:
Non-response: Subjects may fail to respond, and those who respond may differ from those who don't in significant ways.
Self-selection: If subjects volunteer, that may indicate that they have a particular bias related to the study, which can skew results.
Sample frame error: A non-representative subgroup may be selected as a sample.
Population specification error: The researcher fails to identify the population of interest with enough precision.

A sufficiently large sample size, randomized selection and attention to study design can all help to improve the validity of data.

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