statistical estimation bias from rounded samples

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

  1. 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.

    Felipe G. Nievinski, Jan 5, 2012
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  2. Felipe G. Nievinski

    Rich Ulrich Guest

    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
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