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Geometric Mean and Harmonic Mean in SAS

Posted on 2007-04-11
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Last Modified: 2013-11-16
How does one compute Geometric Mean of a column in a SAS dataset? Also Harmonic mean?
It seems possible to compute GM of a row in SAS, but that would require using PROC TRANSPOSE. I couldn't find how to compute this directly for one or more columns. It seems  surprising that this fairly mundane descriptive statistic.

thanks in advance.

- stochastic
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Question by:stochastic
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by:andymcooper
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Stochastic,

You're right - proc means will not do this. Why not???
Anyway, I think will the following SAS code will.
Note - comment out all lines using PRODUCT if you have a lot of variables >1, otherwise the numbers get too big!

/* dataset to try code on */
data tst;
  length VAR 8.;
  do VAR=1 to 10;
    output;
  end;
run;

/* datastep to calculate all sorts of means */
data tst_m (keep=ARITHMETIC_MEAN GEOMETRIC_MEAN_A GEOMETRIC_MEAN_B HARMONIC_MEAN);
  set tst end=EOF;
  retain COUNT PRODUCT SUM SUM_LOGS SUM_INV;
 
  length COUNT PRODUCT SUM SUM_LOGS SUM_INV ARITHMETIC_MEAN GEOMETRIC_MEAN_A GEOMETRIC_MEAN_B HARMONIC_MEAN 8.;
 
  LOG_VAR = log(VAR);

  /* initialise to 0 */
  if _N_=1 then do;
    COUNT= 0 ;
    PRODUCT=1;
    SUM_LOGS = 0;
    SUM =0 ;
    SUM_INV = 0;
  end;

  /* note - product gets too big in most cases, so sum logs instead */
  COUNT=COUNT+1;
  PRODUCT=PRODUCT*VAR;
  SUM_LOGS=SUM_LOGS+LOG_VAR;
  SUM=SUM+VAR;
  SUM_INV=SUM_INV+1/VAR;

  if EOF then do;
    ARITHMETIC_MEAN = SUM/COUNT;
    GEOMETRIC_MEAN_A = PRODUCT**(1/COUNT);
    GEOMETRIC_MEAN_B = exp((1/COUNT)*SUM_LOGS);
    HARMONIC_MEAN = 1/(SUM_INV/COUNT);
    output;
  end;
run;
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andymcooper earned 500 total points
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Stochastic,

Just thought that you may need to calculate means for each category in a dataset. The following code works like a proc means with a by statement. It works the same way as the previous code, but stores the results into temporary arrays as it goes along.

%let NCATS = 4;

data tst (keep=VAR CAT);
  length VAR 8.;
  do i=1 to 10;
    CAT = 1;
    VAR = i;
    output;
  end;
  do CAT=2 to &NCATS;
    do i=1 to 10;
      VAR = ranuni(1);
      output;
    end;
  end;
run;

/* calculate different sorts of means, and split the results by CAT */
/* note this only works if the categories are numeric variables */
/* if not, convert them to one using an informat */

proc sort data=tst; by CAT; run; quit;

data tst_m (keep=CAT ARITHMETIC_MEAN GEOMETRIC_MEAN_A GEOMETRIC_MEAN_B HARMONIC_MEAN);
  set tst end=EOF;
  by CAT;

  /* setup arrays */
  array COUNT{&NCATS} _temporary_;
  array PRODUCT{&NCATS} _temporary_;
  array SUMS{&NCATS} _temporary_;  
  array SUM_LOGS{&NCATS} _temporary_;  
  array SUM_INV{&NCATS} _temporary_;  

  length ARITHMETIC_MEAN GEOMETRIC_MEAN_A GEOMETRIC_MEAN_B HARMONIC_MEAN 8.;
 
  LOG_VAR = log(VAR);

  /* initialise to 0 */
  if first.CAT then do;
    COUNT{CAT}= 0 ;
    PRODUCT{CAT}=1;
    SUM_LOGS{CAT} = 0;
    SUMS{CAT} =0 ;
    SUM_INV{CAT} = 0;
  end;

  /* note - product gets too big in most cases, so sum logs instead */
  /* store all sums and counts in temporary arrays, at the position for this category */
  COUNT{CAT}=COUNT{CAT}+1;
  PRODUCT{CAT}=PRODUCT{CAT}*VAR;
  SUM_LOGS{CAT}=SUM_LOGS{CAT}+LOG_VAR;
  SUMS{CAT}=SUMS{CAT}+VAR;
  SUM_INV{CAT}=SUM_INV{CAT}+1/VAR;

  if EOF then do;
    /* output arrays into a long dataset */
    do CAT=1 to &NCATS;
      ARITHMETIC_MEAN = SUMS{CAT}/COUNT{CAT};
      GEOMETRIC_MEAN_A = PRODUCT{CAT}**(1/COUNT{CAT});
      GEOMETRIC_MEAN_B = exp((1/COUNT{CAT})*SUM_LOGS{CAT});
      HARMONIC_MEAN = 1/(SUM_INV{CAT}/COUNT{CAT});
      output;
    end;
  end;
run;

Andy
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by:stochastic
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andymcooper,

I apologize for the delayed response. Thanks for your suggestions, I will try them out. Meanwhile
I'm accepting your comment as a solution. What remains is the curiosity about why this isn't a built-in feature.

- stochastic
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