# Sampling and nonsampling errors

This lesson will show the difference between sampling and nonsampling errors. Using a sample in order to get information about a population is often better than conducting a census for many reasons.

Sampling is less costly and it can be done more quickly than a census which requires data for the entire population.

However, as already stated, different samples selected from the same population will give different results because these samples contain different elements. Because of this discrepancy, we say that there is a sampling error.

Sampling error definition

Sampling error is the difference between the value of a sample statistics and the value of the population parameter.

Suppose, we need to find the sampling error for the mean. Suppose also there is no nonsampling error which we define below.

Let x̄ be the mean for a sample

Let μ be the mean of the population

Sampling error = x̄ - μ

For example, in the lesson about sampling distribution, the 5 scores below are for the entire population and μ = 86.4

80         85          85          90              92

Suppose we choose a random sample of three scores from this population. Assume that the scores are 85, 90, and 92

x̄  = (85 + 90 + 92)/3  = 267 / 3 = 89

Sampling error  = x̄ - μ = 89 - 86.4  =  2.6

The mean score estimated from the sample is 2.6 higher than the mean score from the population.

Nonsampling errors definition

Any collection errors, recording errors, and/or tabulation errors are called nonsampling errors.

Notice that sampling errors occur because of chance. However, nonsampling errors are the result of human mistakes.

Now suppose when collecting the sample above, we mistakenly record 92 as 91.

As a result, the sample mean is x̄  = (85 + 90 + 91)/3  = 266 / 3 = 88.66

Consequently, the sampling error is now x̄ - μ = 89 - 88.66  =  0.34

0.34 does not really represent the sampling error since we already calculated it as 2.6.

The difference between 2.6 and 0.34 or 1.26 - 0.26  or 2.26 is the nonsampling error because the value of 2.26 occurred as a result of human mistake.

For the population and sample in this lesson, sampling error = 2.6 and nonsampling error = 2.26

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