What should be done FIRST: DEMEANING or WINSORIZING?

[jjsingh04]

As shown in the following example, the order of operations--demeaning vs. winsorizing--makes a big difference in the results. Which should I do first? 

In the example below, we're starting with the 10 observations: 0, 0, 50, 50, 50, 50, 70, 70, 80, and 80. In the columns/procedure on the left, we demean first, In the columns/procedure on the right, we winsorize first. (I normally winsorize at the 1% and 99% levels--not 10% and 90%, but had to use the latter numbers for the sake of simplicity in the example.) 

Thanks! 

	Observed X	Demeaned X	Winsorized (10%,90%)		Observed X	Winsorized (10%,90%)	Demeaned X
	0	-50	0		0	50	-8
	0	-50	0		0	50	-8
	50	0	0		50	50	-8
	50	0	0		50	50	-8
	50	0	0		50	50	-8
	50	0	0		50	50	-8
	70	20	20		70	70	12
	70	20	20		70	70	12
	80	30	20		80	70	12
	80	30	20		80	70	12
Mean:	50			Mean:		58

[PGStats · Accepted solution]

If the purpose of these operations is to protect against outliers, you should winsorize before centering, because outliers can have a very large influence on the mean used for centering. So, better remove them first.

[Rick_SAS]

To echo PGStasts, the Winsorized mean is a robust estimate of location. If your goal is to center the data in a robust way, use a robust estimate.  If you are going to scale the data, use a robust estimate of scale.

[jjsingh04]

Thanks very much Rick! What you and PG are saying makes perfect sense! 

J.J.

[jjsingh04]

Thanks very much PG! What you and Rick are saying makes perfect sense! 

J.J.