Question

When would you use FPC? Please list an example.

Remember, if we have a large, but finite population and we are taking a small sample of it, we need to use the FPC.

For example: let's say 1,000 students took this class in the last 3 years in all ways, i.e. on-line, in a traditional classroom during a normal semester, and during the summer terms. Let's say that since Finance majors have a lot more math in many of their courses, I would expect them to have higher grades. Let's say that there were 100 Finance majors that took the course. Should I use the FPC? Yes. The sample is small relative to the population.

Can you think of an example?

Answer 1

The Finite Population Correction Factor (FPC) is used when you sample without replacement from more than 5% of a finite population. It’s needed because under these circumstances, the Central Limit Theorem doesn’t hold and the standard error of the estimate (e.g. the mean or proportion) will be too big. In basic terms, the FPC captures the difference between sampling with replacement and sampling without replacement.

Most real-life surveys involve finite populations sampled without replacement. For example, you might perform a telephone survey of 10,000 people; once a person has been called, they won’t be called again

A downside of using the FPC is that it can cause uncertainty when applying the results to a larger population, so you should be careful when making inferences.

The general formula is:

FPC = ((N-n)/(N-1))^1/2  

• N = population size,
• n = sample size.

If the calculated value for the FPC is close to 1, it can be ignored. As the sample size falls under 5%, the value becomes somewhat insignificant (an FPC is .998 for a sample of 50).