Sampling Error Formula: Definition, Formula, Calculation & Solved Examples

Sampling Error means the difference between the sample mean and the population mean. Sampling error represents the uncertainty related to the test statistic as a result of taking an incomplete sample from a population instead of an entire population. Sampling error is also termed sampling variability or insampling variability. Sampling Error describes the variation that might be expected by taking different sets of observations in a study. The larger the sample size, the easier it is to calculate sampling error, but the smaller the impact of sampling error is likely to be. In statistical surveys, we find sampling error is observed when the true value of the population parameter differs from the estimated value. The difference between these two values is called ‘Sampling Error’.

Key Terms: Sampling Error, Sampling, Sample Size, Variation, Mean, Population, Census, Statistical Error, Deviation

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Definition of Sampling Error

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A sampling error means that the results obtained from a sample are different from the actual results that can be obtained from the entire population. This can often occur when an analyst decides not to survey an entire population and instead selects a small sample of subjects. The results that are returned by analyzing this small sample are not necessarily identical to what would be obtained if the entire population were surveyed rather than a sample.

It is important to consider whether there is likely to be any significant impact on the results of your study given its scale and the characteristics of those you are surveying; if not, then there may be little or no benefit in calculating sampling error.

Sampling Error

Read More: Mean and Variance of Random Variable

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Role of Sample Size

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The biggest difference between a sample study and a full census of the population is the size of the statistical error. The smaller your sample, the greater the difference between the result and what it would be if you had asked everyone in the population. With a larger sample, that error gets smaller but only in proportion to the square root of n. For example, doubling your sample size will reduce your sampling error by 40%.

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Formula For Sampling Error

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Calculations of the sampling error is vital while you are drawing the statistical inference from a huge population but cannot afford to test it physically. This is because many organizations, governments, etc. don't conduct census due to their large population size and depend on a sample of the population for their decision-making process.

Sampling error is the difference between the sample statistic and the parameter of the population. Estimating this error gives you some idea of how close your sample estimate is to the true population value. This formula is easily understandable.

Sampling Error = Z × σ/√n Where

• Z score value based on the confidence interval
• σ denotes the population standard deviation
• n denotes the sample size

Sampling Error Formula

Read More: Difference Between Variance and Standard Deviation

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Step By Step Calculation of Sampling Error

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The sample error is a form of error that occurs in experiments and surveys when the data which is collected doesn't represent and depict the whole population. For example, it is essential to obtain data from various parts of the country whereas you only focus on one specific region. This mistake can be corrected by accurately determining the representative sample size with knowledge and information while eliminating biases.

• First, the population is defined and the sampling frame is determined. Then a sample size is chosen which should be greater than 10% of the value of the population.
• Next, the precise frequency isn’t important because it is too cumbersome to calculate so one just approximates. Finally, probability sampling techniques are used to obtain a random sample
• The size of a population is referred to as n. Sampling error refers to the differences that exist between sample means and the true population mean.
• When sampling error is small, then this would indicate a closer resemblance between sample means and the true population mean. In order to realize this, we must obtain information through sampling and consequently analyze results by making inferences on those results using statistics.
• Sampling error is a measurement of the individual errors in a sample.
• A high standard deviation is an indicator that the data points are more spread out, and hence indicate less precision.

Population and Sample

The amount of sampling error depends on the sampling method used, along with its size. There are four main steps to determining sampling error:

1. defining your population,
2. selecting a sample size,
3. selecting a sampling method
4. calculating the margin of error in your sample

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Things to Remember

• Sampling error means that a number of the observations or data picked out of a list will vary on where they are chosen, which lead to two types of sampling errors which are an estimation and non-sampling errors.
• In a sample survey, the difference between the sample statistic and the population parameter is known as sampling error. A larger population size reduces the margin of error.
• Calculating sampling error becomes simple when it is taken as the first step towards the calculation of the confidence interval.
• It is done by comparing an estimated value to a chosen theoretical value and describing the error in terms of missing values, known values and estimated values.
• Sampling error is an error that occurs due to the use of unavailable population data in the sample.
• Non-sampling errors happen because of a multitude of factors, including limited resources, such as time and budget, inaccurate data collection procedures, and problems with questionnaires or survey design.

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