Rank Transformation with mean=0 and std=1

[Yegen]

Hi all,

I am trying to rank transform a data by year (i.e., rank transformation within cross-section) such that the rank transformed that has a mean of 0 and a standard deviation of 1. 

Here is what I have so far, but I am not able to force proc transform to rank transform the data so that SAS rank transforms the data by having mean=0 and std=1:

data work.have;
 infile cards expandtabs truncover;
 input id year value;
 cards;
 1 2001 0.4
 2 2001 0.3
 3 2001 0.4
 4 2001 0.8
 5 2001 0.9
 6 2001 0.8
 7 2001 0.8
 1 2002 0.3
 2 2002 0.9
 3 2002 0.1
 4 2002 0.9
 5 2002 0.2
 6 2002 0.9
 7 2002 0.9
;
run;

/*    I want to rank the variable "value" by year such that it has a mean=0 and a std=1 			    */
/*    Please note that the rank needs to be performed within each year (i.e., within the cross-seciton) */
proc rank data=work.have out=work.have_ranked;
   by year;
   var value;
   ranks valueRank;
run;

/* 	Results */ 
proc sql;
	create table work.want as 
	select distinct year, mean(value) as average, std(value) as standard_dev
	from work.have_ranked
	group by year;
quit;
	

Any suggestions will be appreciated!

[PaigeMiller · Accepted solution]

---

@Yegen wrote:

Hi all,

I am trying to rank transform a data by year (i.e., rank transformation within cross-section) such that the rank transformed that has a mean of 0 and a standard deviation of 1. 

Here is what I have so far, but I am not able to force proc transform to rank transform the data so that SAS rank transforms the data by having mean=0 and std=1:

data work.have;
 infile cards expandtabs truncover;
 input id year value;
 cards;
 1 2001 0.4
 2 2001 0.3
 3 2001 0.4
 4 2001 0.8
 5 2001 0.9
 6 2001 0.8
 7 2001 0.8
 1 2002 0.3
 2 2002 0.9
 3 2002 0.1
 4 2002 0.9
 5 2002 0.2
 6 2002 0.9
 7 2002 0.9
;
run;

/*    I want to rank the variable "value" by year such that it has a mean=0 and a std=1 			    */
/*    Please note that the rank needs to be performed within each year (i.e., within the cross-seciton) */
proc rank data=work.have out=work.have_ranked;
   by year;
   var value;
   ranks valueRank;
run;

/* 	Results */ 
proc sql;
	create table work.want as 
	select distinct year, mean(value) as average, std(value) as standard_dev
	from work.have_ranked
	group by year;
quit;
	

Any suggestions will be appreciated!

---

PROC RANK gives you unstandardized ranks, not what you want, hence the next step. Use PROC STDIZE to transform the rank numbers so that they have mean 0 and variance 1.

[Rick_SAS]

Ranks of unique values will be integers 1, 2, 3, ....

It sounds like you want to standardize the values to have mean=0 and std=1. You can do that with PROC STDIZE:

/*    I want to rank the variable "value" by year such that it has a mean=0 and a std=1 			    */
/*    Please note that the rank needs to be performed within each year (i.e., within the cross-seciton) */
proc stdize data=work.have out=work.have_ranked;
   by year;
   var value;
run;

proc means data=have_ranked;
class year;
var value;
run;

proc print data=have_ranked;
run;

[Yegen]

Thanks for your helpful replies, @Rick_SAS and @PaigeMiller. I am trying to follow a prior study that claims that they were using a normalized (to have a mean of 0 as well as a unit standard deviation) rank-transformation. Since they were not explicitly mentioning that they standardized the data to have a zero mean and a unit std, I am not sure if your suggestion @Rick_SAS would produce the same as a normalized rank-transformation?

[Yegen]

@Rick_SAS and @PaigeMiller, I have tried to use both of your suggestions and the results seem to be similar although the transformed values are different:

data work.have;
 infile cards expandtabs truncover;
 input id year value;
 cards;
 1 2001 0.4
 2 2001 0.3
 3 2001 0.4
 4 2001 0.8
 5 2001 0.9
 6 2001 0.8
 7 2001 0.8
 1 2002 0.3
 2 2002 0.9
 3 2002 0.1
 4 2002 0.9
 5 2002 0.2
 6 2002 0.9
 7 2002 0.9
;
run;

/*    I want to rank the variable "value" by year such that it has a mean=0 and a std=1 			    */
/*    Please note that the rank needs to be performed within each year (i.e., within the cross-seciton) */
proc rank data=work.have out=work.have_ranked;
   by year;
   var value;
   ranks valueRank;
run;

PROC STANDARD DATA=have_ranked MEAN=0 STD=1 OUT=have_ranked1;
	by year;
	VAR valueRank value;
RUN;

proc means data=have_ranked1;
class year;
var value valueRank;
run;

proc print data=have_ranked1;
run;

I wanted to see if the rank tranformed values will be similar to the non-rank transformed values after standardizing the data. They seem pretty similar, but not exactly the same.  

[Reeza]

Does your data have ties?

[PaigeMiller]

---

@Yegen wrote:

@Rick_SAS and @PaigeMiller, I have tried to use both of your suggestions and the results seem to be similar although the transformed values are different:

I wanted to see if the rank tranformed values will be similar to the non-rank transformed values after standardizing the data. They seem pretty similar, but not exactly the same.  

---

Pretty similar, but not exactly the same? I don't know what that means, you need to show us what you did and what the different results are.

From what I can see, @Rick_SAS and my suggestion are the same, and should produce the same results.

[Yegen]

@PaigeMiller, I think @Rick_SAS suggested that I should use directly the variable "value" in the standardization rather than using the "valueRank" variable. When I use the "value" and "valueRank" variables in the standardization, I get different "standardized values". 

@Reeza, there was no mentioning in the paper that I am following whether they have adjusted for ties. So I assume no adjustments were made there..