I have a number of different large data capture processes with populations from 100,000 up to 4.5million forms.

I am wanting to determine the error rate in the capture process so am going to manually verify a number of forms against what was captured. I am using an assumption of 1% error rate, a confidence level of 99% with a confidence interval of 0.5% to calculate a sample size.

For the small process (100,000) the calculator comes out at 2440 forms. For the large process (4.5 million) the sample size goes up to 2499 forms (only 59 more).

Why is that number (59) so small? Is there a simple explanation for this?


The population size is largely irrelevant to power analysis, unless the sample is a large portion of the population. The calculations are based on the assumption of an infinite population and there is a finite population correction for estimating parameters:

$$FPC = \sqrt{\frac{N-n}{N-1}}$$

where N is the population and n is the sample size. When N is much larger than n, the FPC is so close to 1 that it can be ignored. The difference you got (59) is the part that would often be ignored.


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