 Dataplot Vol 2 Vol 1

# WEIGHTED ORDER STATISTIC MEAN

Name:
WEIGHTED ORDER STATISTIC MEAN (LET)
Type:
Let Subcommand
Purpose:
Compute the weighted order statistic mean of a variable.
Description:
The formula for the weighted order statistic mean is with Xi and Wi denoting the response variable and the weights variable, respectively.

Note that the Xi will be sorted while the Wi will not be sorted before applying this formula. That is, the Wi weight applies to the i-th order statistic, not the i-th response value. This is the main distinction between this command and the WEIGHTED MEAN command.

Syntax:
LET <par> = WEIGHTED ORDER STATISTIC MEAN <y> <w>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<w> is the weights varialbe;
<par> is a parameter where the weighted order statistic mean is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET WOS = WEIGHTED ORDER STATISTIC MEAN Y1 WEIGHT
LET WOS = WEIGHTED ORDER STATISTIC MEAN Y1 SUBSET TAG = 1
Default:
None
Synonyms:
None
Related Commands:
 WEIGHTED MEAN = Compute the weighted mean of a variable. WEIGHTED SUM = Compute the weighted sum of a variable. WEIGHTED STAND DEVIATION = Compute the weighted standard deviation of a variable. MEAN = Compute the mean of a variable. CONSENSUS MEANS = Perform a consensus means analysis.
Applications:
Consensus Means
Implementation Date:
2012/11
Program:
```
let y = data 1 4 9 16 25
let w = data 0 1 1 1 0
.
let b = weighted order statistic mean y w
```
The computed value of the statistic is 9.666667.
```let b = weighted order statistic mean y w
.
title case asis
title offset 2
title Bootstrap Plot for Weighted Order Statistic Means
label case ais
y1label Weighted Order Statistic Mean
x1label Bootstrap Sample
.
bootstrap sample 1000
set write decimals 5
bootstrap weighted order statistic mean plot y w
```
```
Bootstrap Analysis for the WEIGHTED ORDER STATISTICS MEAN

Response Variable One: Y
Response Variable Two: W

Number of Bootstrap Samples:                       1000
Number of Observations:                               5
Mean of Bootstrap Samples:                     10.55099
Standard Deviation of Bootstrap Samples:        4.92068
Median of Bootstrap Samples:                    9.66666
Minimum of Bootstrap Samples:                   1.00000
Maximum of Bootstrap Samples:                  25.00000

Percent Points of the Bootstrap Samples
-----------------------------------
Percent Point               Value
-----------------------------------
0.1    =        1.00000
0.5    =        1.00000
1.0    =        2.00000
2.5    =        2.00000
5.0    =        3.66666
10.0    =        4.66666
20.0    =        5.66666
50.0    =        9.66666
80.0    =       15.00000
90.0    =       16.66666
95.0    =       19.00000
97.5    =       22.00000
99.0    =       22.00000
99.5    =       25.00000
99.9    =       25.00000

Percentile Confidence Interval for Statistic

------------------------------------------
Confidence          Lower          Upper
Coefficient          Limit          Limit
------------------------------------------
50.00        7.00000       13.66666
75.00        4.66666       16.66666
90.00        3.66666       19.00000
95.00        2.00000       22.00000
99.00        1.00000       25.00000
99.90        1.00000       25.00000
------------------------------------------
``` Date created: 01/07/2013
Last updated: 01/07/2013