/*****************************************************************************
<     Macro  CALQNTIL calculates a quantile (such as the 95th percentile,
<     the first quartile, or by default the median) from grouped data
<     (a frequency distribution) by using linear interpolation to estimate
<     the exact location of the quantile within the target class of the
<     frequency distribution.  Modification by Roy Williams at MISER (Mass.
<     State Data Ctr.) of code originally produced by the California SDC.
>  Macro CalcMedian calculates a single median from a frequency distribution (a
>  one-dimensional SAS ARRAY of "grouped data") by using linear interpolation to
>  estimate the exact location of the median within the target class of the
>  frequency distribution.   Modification by Roy Williams at MISER (Mass. State
>  Data Ctr.) of code originally produced by the California SDC.
  *****************************************************************************/
< %MACRO CALQNTIL(QNTILE, N, LOWBOUND, FREQNCY, QDESIRED=0.50);
> %MACRO CalcMedian (Median, N, LowBound, Frequency, TotFreq) ;
  /*****************************************************************************
<    Parameters:
<              (first four parameters must be provided and in the given order)
<      QNTILE  (output) Estimated location of desired quantile (the name of the
<                       variable the result should be returned to)
<      N        (input) Number of classes in the frequency distribution
<      LOWBOUND (input) Array of size N, which contains the lower bounds of
<                       the N classes
<      FREQNCY  (input) Array of size N which contains the frequencies
<      QDESIRED (input) Quantile desired; e.g., 0.25, 0.5 (median), 0.75, etc.
<                       The median is the default.  See sample calls below.
>  Parameters must be provided in the given order:
>    Median   (output) Estimated location of median (the name of the
>                        variable the result should be returned to)
>    N         (input) Number of classes in the frequency distribution
>    LowBound  (input) Array of size N, which contains the lower bounds of
>                        the N classes
>    Frequency (input) Array of size N which contains the frequencies
>    TotFreq   (input) The total of the frequency distribution
  
<    Local variables (just SAS vars with unlikely names, not %LOCAL Macro vars):
<      _TOTFRQ_ is the total of the frequency distribution
<      _RUNSUM_ is the running sum while searching for the target class
<      _TRGFRQ_ is the frequency below the exact quantile desired
<      _SHARE_ is the estimated proportion of the target class above _TRGFRQ_
<      _WIDTH_ is the width of the target class
>  Local variables (just SAS vars with unlikely names, not %LOCAL Macro vars):
>    _RunningSum_ is the running sum while searching for the target class
>    _TargetFreq_ is the frequency below the median (1/2 of the total frequency)
>    _Share_ is the estimated proportion of the target class above _TargetFreq_
>    _Width_ is the width of the target class
  *****************************************************************************/
< _TOTFRQ_ = SUM (OF &FREQNCY[*]) ;
  
< if _TOTFRQ_ = 0 then &QNTILE = . ; /* empty frequency distribution */
<   else do ;
<      _TRGFRQ_ = _TOTFRQ_ * &QDESIRED ;
> IF &TotFreq = 0
>   THEN &Median = . ; /* empty frequency distribution */
>   ELSE DO ;
>     _TargetFreq_ = &TotFreq * 0.5 ;
  
  /* Compute cumulative distribution until target exceeded */
<      _RUNSUM_ = 0 ;
<      do i = 1 to &N while (_RUNSUM_ < _TRGFRQ_) ;
<          _RUNSUM_ = _RUNSUM_ + &FREQNCY[i] ;
<        end ;
<      i = i - 1 ; /* since loop goes one past the target class */
>     _RunningSum_ = 0 ;
>     DO i = 1 TO &N while (_RunningSum_ < _TargetFreq_) ;
>       _RunningSum_ = _RunningSum_ + &Frequency[i] ;
>     END ;
>     i = i - 1 ; /* since loop goes one past the target class */
  
< /*   linearity assumption rarely reasonable in top and bottom classes */
<      if i = &N or i = 1 then &QNTILE = . ;
<         else do ;
<            _SHARE_ = (_RUNSUM_ - _TRGFRQ_) / &FREQNCY[i] ;
<            _WIDTH_ = &LOWBOUND[i+1] - &LOWBOUND[i] ;
<            &QNTILE = &LOWBOUND[i+1] - _WIDTH_ * _SHARE_ ;
<           end ;
<   end ;
< %MEND CALQNTIL ;
< 
> /*  linearity assumption rarely reasonable in top and bottom classes */
>     IF i = &N OR i = 1 
>       THEN &Median = . ;
>       ELSE DO ;
>         _Share_ = (_RunningSum_ - _TargetFreq_) / &Frequency[i] ;
>         _Width_ = &LowBound[i+1] - &LowBound[i] ;
>         &Median = &LowBound[i+1] - _Width_ * _Share_ ;
>       END ;
> END ;
> %MEND CalcMedian ;
>  
  /*****************************************************************************
< Sample calls: (Macro definition must be placed BEFORE Macro call).
> Sample call (Median Age of Latinos, both sexes, male & female,
>  used in Census2000 SF1 profiles Age-2, AgeRace-H, and Race-H): 
> (Macro definition must be placed BEFORE Macro call).
  
< * Median Ages of Hispanic Persons from Table P15 in STF3 ;
<     array agecat [31] _temporary_ (0,1,3,5,6,7,10,12,14,15,16,17,18,19,
<                       20,21,22,25,30,35,40,45,50,55,60,62,65,70,75,80,85) ;
<     array agehispm [31] P015_01 - P015_31 ;
<     array agehispf [31] P015_32 - P015_62 ;
<     %CALQNTIL(medhm, 31, agecat, agehispm)
<     %CALQNTIL(medhf, 31, agecat, agehispf)
> ARRAY PCT12LowBounds [103] _TEMPORARY_ (0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
>    16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
>    41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
>    66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
>    91,92,93,94,95,96,97,98,99,100,105,110) ;
> ARRAY P12LowBounds [23] _TEMPORARY_ (0, 5,10, 15,18, 20,21,22, 25,30,35,40,
>                                     45,50,55, 60,62, 65,67,    70,75,80,85) ;
> ARRAY P12Hmale [23] P12Hi3 -P12Hi25 ;
> ARRAY P12Hfeml [23] P12Hi27-P12Hi49 ;
> ARRAY P12HBoth [23] ; * if not already defined ;
> DO age = 1 TO 23 ;
>   P12HBoth[age] = P12Hmale[age] + P12Hfeml[age] ;
> END ;
  
< * Median Incomes (needed when generating STF3 data for custom areas) ;
<     array inccat [25] _temporary_ (0,5000,10000,12500,15000,17500,20000,
<             22500,25000,27500,30000,32500,35000,37500,40000,42500,45000,
<             47500,50000,55000,60000,75000,100000,125000,150000) ;
<     array hhinc [25] P080_01 - P080_25 ;
<     array fminc [25] P107_01 - P107_25 ;
<     array uiinc [25] P110_01 - P110_25 ;
<     IF CUSTOM THEN DO ; * if 'custom' is true (non-0) for this observation ;
<                        %CALQNTIL(P080A, 25, inccat, hhinc) 
<                        %CALQNTIL(P107A, 25, inccat, fminc) 
<                        %CALQNTIL(P110A, 25, inccat, uiinc) 
<                    END ;
> IF Custom THEN DO ; * if 'Custom' is true (non-0) for this observation ;
>     %CalcMedian (P13Hi1, 23, P12LowBounds, P12HBoth, P12Hi1) 
>     %CalcMedian (P13Hi2, 23, P12LowBounds, P12Hmale, P12Hi2) 
>     %CalcMedian (P13Hi3, 23, P12LowBounds, P12Hfeml, P12Hi26) 
> END ;
  *****************************************************************************/