RESCALED SUM

RESCALED SUM (LET)

Let Subcommand

Compute the rescaled sum of a variable.

The rescaled sum has the formula:
\( \mbox{RSZ} = \frac{\sum_{i=1}^{N}{X_{i}}}{\sqrt{N}} \)

with N denoting the number of observations. This statistic has application in the ISO 13528 proficiency testing standard.

LET <par> = RESCALED SUM <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed rescaled sum is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <par> = DIFFERENCE OF RESCALED SUM <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the second response variable;
            <par> is a parameter where the computed difference of the rescaled sums is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the recaled sum of <y1> and <y2> and then computes the difference of the two sums.

LET A = RESCALED SUM Y1
LET A = RESCALED SUM Y1 SUBSET TAG > 2
LET A = DIFFERENCE OF RESCALED SUM Y1 Y2

The rescaled sum is sometimes used in the context of ISO 13528 proficiency studies for the case where there are multiple rounds of the proficiency study. Specifcally, the following two plots are sometimes generated
1. A plot of the rescaled sum versus the laboratory where the summation is over all rounds and all materials for a given laboratory. Laboratories with an absolute value greater than 2 are of possible concern (i.e., warning) and those with an absolute value greater than 3 are of concern (i.e., action signal). The advantage of this statistic is that it has the same interpretation as the z-scores. The disadvantage is that large magnitude z-scores of opposite sign can cancel each other.

2. A plot of the relative laboratory performance (RLP) versus the rescaled sum for all laboratories. A box is formed for the rescaled sum between -2 and 2 and for RLP between 0 and 1.5. Laboratories outside this box are identified as needing attention.

In some applications it may be desired to cap the value of outliers. This is most common when the response variable is a z-score or some other standardized score.

To specify this value, enter the command

LET CAPVALUE = <value>

where <value> is typically 3 or 4 (if the reponse data are z-scores or z-score type data). Note that the value represents an absolute value. For example, if CAPVALUE is 4, values greater than 4 will be set to 4 and values less than -4 will be set to -4.

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

None

MEAN	= Compute the mean of a variable.
STANDARD DEVIATION	= Compute the standard deviation of a variable.
SUM OF SQUARES	= Compute the sum of squares of a variable.
ROOT MEAN SQUARE	= Compute the root mean square error of a variable.

ISO 13528 Proficiency Testing

2012/2
2012/6: Added DIFFERENCE OF RESCALED SUM

 
SKIP 25
READ Y1 = 
LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100
LET SSQ = RESCALED SUM Y1
    

The result is -0.4749098.

 
SKIP 25
READ GEAR.DAT Y X
LET Y = ZSCORE Y
.
CHARACTER X BLANK
LINE BLANK SOLID
TIC MARK OFFSET UNITS DATA
X1TIC MARK OFFSET 0.5 0.5
.
LABEL CASE ASIS
Y1LABEL Rescaled Sum
X1LABEL Batch
RESCALED SUM PLOT Y X