Quadrupling the data to double the z-score

Question

At n = 1000 days of data, a strategy's z-statistic for a nonzero mean is z = 1.0, so it is not significant. The per-day edge is fixed and will not change. Using only the way z scales with sample size, how many days would be needed to push the z-statistic to 2.0, and why?

Accepted Answer

The scaling. For a fixed per-day edge, the z-statistic grows with the square root of the sample size: z \propto \sqrt{n}. To double z from 1.0 to 2.0, you must double \sqrt{n}, which means multiplying n by 2^2 = 4: n{	ext{new}} = 4 	imes 1000 = 4000 	ext{ days}. Sanity check. At n = 1000, z = 1.0 means the constant of proportionality is 1.0 / \sqrt{1000}. At n = 4000, z = (1.0/\sqrt{1000}) 	imes \sqrt{4000} = 1.0 	imes \sqrt{4} = 2.0. Confirmed. What it teaches. Buying more statistical significance is expensive and gets more expensive the further you go. Going from z = 1 to z = 2 costs 3…

Quadrupling the data to double the z-score

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