Talk:Sheppard's correction

Under- or over-estimation? Suggestion
The text says binning causes under-estimation. Sheppards correction is negative, implying a downward correction. Either the text should say 'over-estimation' or the correction needs to be added rather than subtracted ...

IIRC the negative correction is the correction normally given in this context so it looks like the text needs amending. — Preceding unsigned comment added by Slrellison (talk • contribs) 18:17, 29 January 2016 (UTC)

nonsense deleted
The following paragraph is nonsense and I deleted it:
 * When data is grouped, moments are calculated using the mid-points of the groups. This tends to underestimate moments of even order. Sheppard's correction treats the data as spread evenly throughout each group. This is done by adding to the discrete distribution of the grouped variable, an independent random variable uniformly distributed between −0.5c and 0.5c, where c is the class width.

Rounding data to the nearest unit causes an overestimate of the variance if the data is normally distributed because the rounding error is negatively correlated with the observed value. That is why Sheppard's correction reduces the estimated variance. For the uniform distribution the opposite is true: rounding causes variance to be underestimated and the exact opposite correction must be done. So it's a biased correction. The last sentence in the paragraph deleted and quoted above is the opposite of the truth.

The observation in the comment by user: Slrellison above is entirely correct. Michael Hardy (talk) 21:45, 16 June 2016 (UTC)