WINSORIZE

WINSORIZE (LET)

Let Subcommand

Winsorize a variable.

The computation of many statistics can be heavily influenced by extreme values. One approach to providing a more robust computation of the statistic is to Winsorized the data before computing the statistic.

To Winsorized the data, tail values are set equal to some specified percentile of the data. For example, for a 90% Winsorization, the bottom 5% of the values are set equal to the value corresponding to the 5th percentile while the upper 5% of the values are set equal to the value corresponding to the 95th percentile.

Note that Winsorization is not equivalent to simply throwing some of the data away. This is because the order statistics are not independent.

LET <y2> = WINSORIZE <y1>        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the response variable;
              <y2> is a variable where the computed Winsorized values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET Y2 = WINSORIZE Y1
LET Y2 = WINSORIZE Y1 SUBSET TAG > 2

The analyst must specify the percentages to Winsorize in each tail. This is done by defining the internal variables P1 (the lower tail) and P2 (the upper tail). For example, to Winsorize 10% of each tail, do the following:
LET P1 = 10
LET P2 = 10
LET Y2 = WINSORIZE Y1

None

None

WINSORIZED MEAN	= Compute a Winsorized mean.
WINSORIZED VARIANCE	= Compute the Winsorized variance.
WINSORIZED STANDARD DEVIATION	= Compute a Winsorized standard deviation.
WINSORIZED COVARIANCE	= Compute a Winsorized covariance.
WINSORIZED CORRELATION	= Compute a Winsorized correlation.
VARIANCE	= Compute the variance.
BIWEIGHT MIDVARIANCE	= Compute the biweight midvariance.

Robust Data Analysis

7/2002

LET Y1 = CAUCHY RANDOM NUMBERS FOR I = 1 1 100 
LET P1 = 10 
LET P2 = 10 
LET Y2 = WINSORIZE Y1 
LET A1 = EXTREME Y1 
LET A2 = EXTREME Y2