topic Re: What should be done FIRST: DEMEANING or WINSORIZING? in Statistical Procedures

What should be done FIRST: DEMEANING or WINSORIZING?

jjsingh04 — Fri, 05 Jun 2020 02:50:30 GMT

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

Re: What should be done FIRST: DEMEANING or WINSORIZING?

PGStats — Fri, 05 Jun 2020 03:12:38 GMT

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.

Re: What should be done FIRST: DEMEANING or WINSORIZING?

Rick_SAS — Sat, 06 Jun 2020 10:19:42 GMT

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.

Re: What should be done FIRST: DEMEANING or WINSORIZING?

jjsingh04 — Sat, 20 Jun 2020 18:43:39 GMT

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

J.J.

Re: What should be done FIRST: DEMEANING or WINSORIZING?

jjsingh04 — Sat, 20 Jun 2020 18:44:46 GMT

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

J.J.