 Dataplot Vol 2 Vol 1

# WINSORIZED VARIANCE

Name:
WINSORIZED VARIANCE (LET)
Type:
Let Subcommand
Purpose:
Compute the Winsorized variance of a variable.
Description:
The standard variance estimate can be heavily influenced by extreme values. The Winsorized variance compensates for this by setting the tail values equal to a certain percentile value. For example, for a 90% Winsorized variance, 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. Then the standard variance formula (HELP VARIANCE for details) is applied.
Syntax:
LET <par> = WINSORIZED VARIANCE <y1>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the response variable;
<par> is a parameter where the computed Winsorized variance is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = WINSORIZED VARIANCE Y1
LET A = WINSORIZED VARIANCE Y1 SUBSET TAG > 2
Note:
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 A = WINSORIZED VARIANCE Y
Note:
Support for the Winsorized variance has been added to the following plots and commands:

WINSORIZED VARIANCE PLOT
BOOTSTRAP WINSORIZED VARIANCE PLOT
JACKNIFE WINSORIZED VARIANCE PLOT
CROSS TABULATE WINSORIZED VARIANCE PLOT
DEX WINSORIZED VARIANCE PLOT
WINSORIZED VARIANCE INTERACTION STATISTIC PLOT
WINSORIZED VARIANCE INFLUENCE CURVE
TABULATE WINSORIZED VARIANCE
CROSS TABULATE WINSORIZED VARIANCE
LET ... = CROSS TABULATE WINSORIZED VARIANCE
Default:
None
Synonyms:
None
Related Commands:
 WINSORIZE = Winsorize a variable. WINSORIZED STANDARD DEVIATION = Compute a Winsorized standard deviation. WINSORIZED MEAN = Compute a Winsorized mean. WINSORIZED COVARIANCE = Compute a Winsorized covariance. WINSORIZED CORRELATION = Compute a Winsorized correlation. VARIANCE = Compute the variance. BIWEIGHT MIDVARIANCE = Compute the biweight midvariance.
Applications:
Robust Data Analysis
Implementation Date:
7/2002
Program 1:
```
LET Y1 = CAUCHY RANDOM NUMBERS FOR I = 1 1 100
LET A1 = VARIANCE Y1
LET P1 = 10
LET P2 = 10
LET A2 = WINSORIZED VARIANCE Y1
```
Program 2:
```SKIP 25 