Sampling is cheaper and faster than a census, which requires data for the entire population.
As mentioned earlier, however, different samples selected from the same population will give different results because these samples contain different elements. Because of this discrepancy, we speak of a sampling error.
Suppose we need to find the sampling error for the mean. Suppose there is also no non-sampling 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 sample distribution lesson, the following 5 values apply to the entire population and μ = 86.4
80 85 85 90 92
Suppose we choose a random sample of three values from this population. For example, suppose the values are 85, 90, and 92
x̄ = (85 + 90 + 92) / 3 = 267/3 = 89
Sampling error = x̄ – μ = 89 – 86.4 = 2.6
The mean estimated from the sample is 2.6 higher than the mean from the population.
Note that sampling errors occur randomly. However, nonsampling errors are the result of human error.
For example, suppose that when we collect the sample above, we mistakenly include 92 as 91.
As a result, the sample mean is x̄ = (85 + 90 + 91) / 3 = 266/3 = 88.66
As a result, the sampling error is now x̄ – μ = 89 – 88.66 = 0.34
0.34 doesn’t really represent the sampling error as we already calculated it to be 2.6.
The difference between 2.6 and 0.34 or 1.26-0.26 or 2.26 is the non-sampling error since the value of 2.26 was due to human error.
For the population and sample in this lesson, sampling error = 2.6 and non-sampling error = 2.26