st: Median calculation for interval data

[Chris Ruebeck <ruebeckc@lafayette.edu>]

I have written an ado file to calculate a version of the median for  
interval data as described below.  A synopsis: when there are many  
observations with the median value, we may believe there is some  
information in the distribution of observations above, below, and  
within the median value.

My question for Statalist: is there an existing Stata ado file that I  
could have used?

I would also appreciate any comments on the method that I used.

Thanks,
Chris


Method: Calculate the fraction of the median interval above the  
median interval's lower bound necessary to have half of all  
observations above and half below, assuming that in the median  
interval the observations are evenly distributed.  Thus, if there are  
25 observations above the median interval and 75 observations below  
it, 80 observations in it, and the median interval is [10, 15), then  
the "median" is

	10 + (15-10)*((25 + 80 + 75)/2 - 75)/80 = 10.9375.


capture program drop intervalMedian
program define intervalMedian, rclass
	syntax if, ///
		  lowlim(varname numeric) /// Lower limit of interval
		  hholds(varname numeric) // Number of households in this interval
	preserve
	marksample touse
	keep if `touse'
	keep `lowlim' `hholds'
	tempvar runSum /// The runing sum
		  markMed /// 0, -1, 2 marker for below, median, above
		  upper // upper limit of interval

	// Get the upper limit for each one
	sort `lowlim'
	generate `upper' = `lowlim'[_n+1]

	// Find the median interval
	generate `runSum' = sum(`hholds') // Final observation is total
	local halfObs = `runSum'[_N]/2 // The index of the median
	generate `markMed' = `runSum' - `halfObs' // Negative below median  
interval
	replace `markMed' = cond(`markMed'<0,0,2) // Marks at & above median  
interval
	sort `markMed' `lowlim' // Already in this order, but Stata doesn't  
know
	by `markMed': replace `markMed' = -1 if _n==1 & `markMed'==2 // The  
median

	// Collect values necessary for calculation (could be 1 line instead  
of 3)
	sort `markMed' // The median interval is now the first observation
	local countBelow = `runSum' - `hholds' // # below median interval
	local intervalBelow = `halfObs' - `countBelow' // # below median in  
interval
	local theMedian = (`intervalBelow'/`hholds')*(`upper' - `lowlim') +  
`lowlim'
	return local median `theMedian'
	display "The median: `theMedian'"

	restore
end
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