OMB Meeting Book - January 8, 2015

54

Even for the normal distribution, the robust estimates of variation are biased by several percent for reasonable sample sizes and are of very low efficiency compared to the sample standard deviation. This is a step price to pay for protection from outliers. The mean results do reasonably reproduce the originating distribution (with the small bias obvious at the mode):

Standard Normal Distribution

0.0 0.1 0.2 0.3 0.4

Normal MAD IQR

Density

-4

-2

0

2

4

z

4

23

Recommended to OMB by Committee on Statistics: 07-17-2013 Reviewed and approved by OMB: 07-18-2013