PERCENTAGE RANK

PERCENTAGE RANK (LET)

Let Subcommand

Compute the percentage ranks of a variable.

The percentage rank is computed as

with R_i and N denoting the rank of the i-th element and the number of observations, respectively.

Ranks are frequently used in nonparametric statistical analysis. Some analysts like to the think of the ranks in terms of percentages.

LET <y2> = PERCENTAGE RANK <y1>
                     <SUBSET/EXCEPT/FOR qualification>
where <y1> is a response variable;
            <y2> is a variable where the percentage ranks are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET PERCRANK = PERCENTAGE RANK Y1

Ties are assigned an average rank. For example, if the 2nd and 3rd highest values are equal, each is assigned a rank of 2.5.

None

None

RANK	= Rank the elements in a variable.
RANK2	= Rank the elements in a variable when there are one, two, or three group-id variables.
RANK INDEX	= Rank the elements in a variable where each rank will be assigned a unique integer value.
SORT	= Sort the elements in a variable.
SORTC	= Sort the elements in a variable and carry one or more variables along.

ISO 13528, First Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2005, p. 24.

Nonparametric statistics

2012/1

 
let y1 = norm rand numb for i = 1 1 20
let y2 = rank y1
let y3 = percentage rank y1
.
set write decimals 3
print y1 y2 y3
    

The following output is generated.

---------------------------------------------
             Y1             Y2             Y3
---------------------------------------------
         -1.073          1.000          2.500
          0.573         17.000         82.500
         -0.873          2.000          7.500
          0.233         13.000         62.500
         -0.455          6.000         27.500
         -0.525          5.000         22.500
         -0.705          4.000         17.500
          0.032         11.000         52.500
          1.190         19.000         92.500
          0.269         15.000         72.500
         -0.149          9.000         42.500
         -0.196          8.000         37.500
         -0.243          7.000         32.500
         -0.840          3.000         12.500
         -0.103         10.000         47.500
          0.418         16.000         77.500
          0.263         14.000         67.500
          0.898         18.000         87.500
          0.034         12.000         57.500
          1.587         20.000         97.500