# statistical estimation bias from rounded samples

Discussion in 'Scientific Statistics Math' started by Felipe G. Nievinski, Jan 5, 2012.

1. ### Felipe G. NievinskiGuest

Given a sample made of 6.13, 6.28, 6.34, the mean and standard
deviation are 6.25 and 0.11, respectively.

Now if each value in the sample is rounded to the closest integet
(6.0, 6.0, 6.0), standard formulae yield biased mean and standard
deviation: 6.0 and 0.0.

- Are you aware of better formulae for rounded samples?

Maybe one could consider each value as a separate estimate with a
standard deviation of 0.3 (standard deviation from 0.5-rounding of
uniformly distributed values), then propagate these as an additional
source of uncertainty. E.g., add 0.3^2/N to the sample variance?

This would account for the relatioship between the original standard
deviation and the rounding precision, i.e., if we round it less --
e.g., only to one decimal (6.1, 6.3, 6.3) -- then the bias is smaller:
mean and standard deviations are 6.24 and 0.12.

Thanks,
-Felipe.

Felipe G. Nievinski, Jan 5, 2012

2. ### Rich UlrichGuest

Yes. If the context deserves it.
Be sure to asterisk it and report it explicitly as "measurement
variance" or you will get some odd looks or hostility.

Rich Ulrich, Jan 5, 2012