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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 |
Accepted Solutions
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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.
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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.
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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.
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Thanks very much Rick! What you and PG are saying makes perfect sense!
J.J.
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Thanks very much PG! What you and Rick are saying makes perfect sense!
J.J.