How much data to halve the standard error?

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You currently estimate an average from n = 50 measurements. You want to halve your standard error (make the average twice as precise). How many total measurements do you need?

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Precision improves slowly, with the square root of the sample size. The standard error is 	ext{SE} = \frac{\sigma}{\sqrt{n}}, so the SE depends on \sqrt{n}, not n. Because the square root sits underneath, to cut the SE by some factor you must multiply the sample size by that factor squared. To halve the SE (a factor of 2), you need 2^2 = 4 times as much data: n{	ext{new}} = 4 	imes 50 = 200. You are not adding 50 more, you are quadrupling the whole sample. This is the harsh arithmetic of statistics: each extra digit of precision costs a lot more data than the last. Takeaway. SE shrinks lik…

How much data to halve the standard error?

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