The RANK Procedure

# PROC RANK Statement

 PROC RANK ;

Specify the input data set DATA=
Create an output data set OUT=
Specify the ranking method

Compute fractional ranks FRACTION or NPLUS1

Partition observations into groups GROUPS=

Compute normal scores NORMAL=

Compute percentages PERCENT

Compute Savage scores SAVAGE
Reverse the order of the rankings DESCENDING
Specify how to rank tied values TIES=

Note:

You can specify only one ranking method in a single PROC RANK step.

DATA=SAS-data-set

specifies the input SAS data set.

 Restriction: You cannot use PROC RANK with an engine that supports concurrent access if another user is updating the data set at the same time. Restriction: For in-database processing to occur, it is necessary that the data set specification refer to a table residing on a supported DBMS. Main discussion: Input Data Sets
DESCENDING

reverses the direction of the ranks. With DESCENDING, the largest value receives a rank of 1, the next largest value receives a rank of 2, and so on. Otherwise, values are ranked from smallest to largest.

 Featured in:
FRACTION

computes fractional ranks by dividing each rank by the number of observations having nonmissing values of the ranking variable.

 Alias: F Interaction: TIES=HIGH is the default with the FRACTION option. With TIES=HIGH, fractional ranks are considered values of a right-continuous, empirical cumulative distribution function. See also: NPLUS1 option
GROUPS=number-of-groups

assigns group values ranging from 0 to number-of-groups minus 1. Common specifications are GROUPS=100 for percentiles, GROUPS=10 for deciles, and GROUPS=4 for quartiles. For example, GROUPS=4 partitions the original values into four groups, with the smallest values receiving, by default, a quartile value of 0 and the largest values receiving a quartile value of 3.

The formula for calculating group values is as follows:

FLOOR is the FLOOR function, rank is the value's order rank, k is the value of GROUPS=, and n is the number of observations having nonmissing values of the ranking variable for TIES=LOW, TIES=MEAN, and TIES=HIGH. For TIES=DENSE, n is the number of observations that have unique nonmissing values.

If the number of observations is evenly divisible by the number of groups, each group has the same number of observations, provided there are no tied values at the boundaries of the groups. Grouping observations by a variable that has many tied values can result in unbalanced groups because PROC RANK always assigns observations with the same value to the same group.

 Tip: Use DESCENDING to reverse the order of the group values. Featured in: Partitioning Observations into Groups Based on Ranks
NORMAL=BLOM | TUKEY | VW

computes normal scores from the ranks. The resulting variables appear normally distributed. n is the number of observations that have nonmissing values of the ranking variable for TIES=LOW, TIES=MEAN, and TIES=HIGH. For TIES=DENSE, n is the number of observations that have unique nonmissing values. The formulas are as follows:

 BLOM yi=-1((ri-3/8)/(n+1/4)) TUKEY yi=-1((ri-1/3)/(n+1/3)) VW yi=-1((ri)/(n+1))
In these formulas, -1 is the inverse cumulative normal (PROBIT) function, ri is the rank of the ith observation, and n is the number of nonmissing observations for the ranking variable.

VW stands for van der Waerden. With NORMAL=VW, you can use the scores for a nonparametric location test. All three normal scores are approximations to the exact expected order statistics for the normal distribution (also called normal scores). The BLOM version appears to fit slightly better than the others (Blom 1958; Tukey 1962).

 Interaction: If you specify the TIES= option, then PROC RANK computes the normal score from the ranks based on non-tied values and applies the TIES= specification to the resulting score. Restriction: Use of the NORMAL= option will prevent in-database processing.
NPLUS1

computes fractional ranks by dividing each rank by the denominator n+1, where n is the number of observations that have nonmissing values of the ranking variable for TIES=LOW, TIES=MEAN, and TIES=HIGH. For TIES=DENSE, n is the number of observations that have unique nonmissing values.

 Aliases: FN1, N1 Interaction: TIES=HIGH is the default with the NPLUS1 option. See also: FRACTION option
OUT=SAS-data-set

names the output data set. If SAS-data-set does not exist, PROC RANK creates it. If you omit OUT=, the data set is named using the DATAn naming convention.

 Interaction: When in-database processing is being performed and OUT= also refers to a supported DBMS table and if both IN= and OUT= reference the same library, then all processing can occur on the DBMS with results directly populating the output table. In this case, no results will be returned to SAS.
PERCENT

divides each rank by the number of observations that have nonmissing values of the variable and multiplies the result by 100 to get a percentage. n is the number of observations that have nonmissing values of the ranking variable for TIES=LOW, TIES=MEAN, and TIES=HIGH. For TIES=DENSE, n is the number of observations that have unique nonmissing values.

 Alias: P Interaction: TIES=HIGH is the default with the PERCENT option. Tip: You can use PERCENT to calculate cumulative percentages, but you use GROUPS=100 to compute percentiles.
SAVAGE

computes Savage (or exponential) scores from the ranks by the following formula (Lehman 1998):

 Interaction: If you specify the TIES= option, then PROC RANK computes the Savage score from the ranks based on non-tied values and applies the TIES= specification to the resulting score.
TIES=HIGH | LOW | MEAN | DENSE

specifies how to compute normal scores or ranks for tied data values.

HIGH

assigns the largest of the corresponding ranks (or largest of the normal scores when NORMAL= is specified).

LOW

assigns the smallest of the corresponding ranks (or smallest of the normal scores when NORMAL= is specified).

MEAN

assigns the mean of the corresponding rank (or mean of the normal scores when NORMAL= is specified).

DENSE

computes scores and ranks by treating tied values as a single-order statistic. For the default method, ranks are consecutive integers that begin with the number one and end with the number of unique, non-missing values of the variable that is being ranked. Tied values are assigned the same rank.

Note:   CONDENSE is an alias for DENSE.

 Default: MEAN (unless the FRACTION option or PERCENT option is in effect). Interaction: If you specify the NORMAL= option, then the TIES= specification applies to the normal score, not to the rank that is used to compute the normal score. Featured in: See also: Treatment of Tied Values

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