Sampling Error

Fundamentals of Social Statistics by Adam J. McKee

Whenever a sample is drawn, only that part of the population that is included (by definition!) in the sample is measured.  The idea is to use the sample to represent the entire population.  Because of this, there will always be some error in the data, resulting from those members of the population who were not measured.  This discrepancy between what we observe in the sample and what is true in the population is known as sampling error.

Random sampling procedures always result in some degree of sampling error.

The more people we include (the larger our sample is), the more accurately the sample will reflect the population, and the less sampling error we will have.  If a census is performed (a 100 percent sample is a census), there will be no sampling error.

Selecting a large sample size does not correct for errors due to bias.

When newspapers print things like “the margin of error is plus or minus three percent,” it seems to suggest that the results are accurate to within the stated percentage.  This view of it is completely wrong and grossly misleading.  That is not to say anything bad about the media; they merely want to warn people about sampling error.  However, most readers are not trained in statistical methods and may fail to assume that all surveys—all data coming from samples—are estimates.  Estimates may be wrong.

Let us take a public opinion poll with a 4% margin of error as an example.  (We use percentages in this example because they are very easy in intuitive in interpretation.  Keep in mind that these basic ideas apply to any statistic computed from a sample).  If we continue to take random samples from the population 100 times, then the results would fall within that confidence interval 95% of the time.  That means that if you asked a question from this poll 100 times, 95 of those times the percentage of people giving a particular answer would be within 4 points of the percentage who gave that same answer in this poll.  Why only 95% of the time?  In reality, the margin of error is what statisticians call a confidence interval.  The math behind it is much like the math behind the standard deviation.

Key Terms

Nonprobability Sampling, Convenience Sampling, Quota Sampling, Margin of Error, Confidence Interval

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Last Modified:  09/20/2023

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