4
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):
-4
-2
0
2
4
0.0
0.1
0.2
0.3
0.4
Standard Normal Distribution
z
Density
Normal
MAD
IQR
Recommended to OMB by Committee on Statistics: 07-17-2013
Reviewed and approved by OMB: 07-18-2013
23
54
