The minimal impact of population size on power and precision

Steve Simon

2001-01-19

*Dear Professor Mean

Dear Skeptical,

It is surprising

The best analogy I have heard about sampling goes something like: “Every cook knows that it only takes a single sip from a well-stirred soup to determine the taste.” It’s a nice analogy because you can visualize what happens when the soup is poorly stirred.

With regards to why a sample size characterizes a population of 10 million and a population of 10 thousand equally well

Finite Population Correction factor (fpc)

When the size of the sample becomes a large fraction of the size of the population

The formula for fpc is.

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where N is the size of the population and n is the size of the sample. If fpc is close to 1

The following table shows what the fpc in four different situations would be.

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When the sample size is 50

A good rule of thumb is to use the fpc when the sample is 10% or more of the population.

Be cautious about using the fpc. Frequently you want to generalize to a larger population than the one you sampled from. You may have restricted the population out of convenience

For example

Summary

Uncle Gene wants an explanation of why a sample for a population of 10 million people doesn’t have to be much larger than a sample for a population of 10 thousand people. Professor Mean provides an analogy to taking a single sip from a well stirred soup. He then presents the finite population correction factor and shows that it does not make much of a difference unless your sample is a large fraction of the total population.

Further reading

  1. **[Yes

You can find an earlier version of this page on my original website.