I still don't understand. Where does the 8 in your example come from?
Where do the boundaries of your bins come from; are they assumptions or
is the questions asked as a set of ranges? (e.g. do you earn less x$,
between xx$ and xxx$, etc?)
--- Brooks Taggert J <[email protected]> wrote:
> Thanks to Steve and Maarten for the suggestions. I might be missing
> something but it doesn't seem as though there isn't an easy
> implementation.
>
> For clarification here is what is meant by fractional median.
>
> Explanation of Fractional Median
>
> Using the median becomes problematic when the data set contains large
> numbers of repeated values. In the case of SEI scores, the student
> can
> only choose 1 of 5 values, and so, by design, the set of SEI scores
> of
> most classes contains large groups of the same value. And so, if the
> regular median were calculated, there would only be a few possible
> results for all classes/instructors. The fractional median is used to
> provide a wider range of possible results, while still maintaining
> some
> of the desirable properties of the regular median. In terms of the
> mathematics, the fractional median provides a more continuous range
> of
> outcomes instead of the discrete set possible with the regular
> median.
>
> Here is the basic idea (and an example): To arrive at a continuous
> set
> of outcomes, one assumes that each data value is the center of the
> true
> set of values that could have been measured. For example, when a
> student
> selects a 3 instead of a 2 or a 4, one can assume that if the student
> were allowed to choose any numerical value from the real line, they
> would have selected something between 2.5 and 3.5, and since they
> were
> not allowed to list their exact observation, they selected the
> nearest
> choice, in this case a 3.
>
> We call this range of values associated with each observable
> measurement
> (choice) a bin or a cell. The cell for the choice 1 is .5 to 1.5, for
> a
> 2 it is 1.5 to 2.5, etc. We now want to calculate the fractional
> median,
> which estimates what the median would have been if the student could
> have selected any real value (not just the 5 choices given). First we
> determine what cell the standard median lives in. The fractional
> median
> will be a value from the cell that contains the standard median. We
> then
> determine how far into the cell the median actually is (again
> assuming
> they could have selected any value in the cell). This gives the
> fractional median.
>
> Example Data Set: two 2's, nine 3's, eight 4's, and eight 5's. (I
> picked
> an odd number of values because it is a little tricky, the even
> number
> case is a bit easier.)
>
> This is a total of 27 measurements (student scores). Half of 27 is
> 13.5,
> and so if we look for the thirteen and a half value, we end up
> looking
> between two 4's. So the median is a 4, which comes from the cell
> ranging
> from 3.5 to 4.5, and so the fractional median will be between 3.5 and
> 4.5.
>
> The fractional median in this case will be 3.5 plus the percentage of
> the distance into the cell the middle value represents. So if it were
> the case that the true median was the middle 4, then the percentage
> of
> the distance into the cell would be 50%= .5, thus the fractional
> median
> would be a 3.5+.5=4 (so the median equals the fractional median in
> this
> situation). In our example, the 4 that represents the true median
> would
> be between the 2nd and 3rd four (the 2.5th four, let's say) of the
> eight
> 4's in the cell, which is 2.5/8 ths of the way into the cell. Now,
> since
> 2.5/8=.3125, the fractional median for this example would be
> 3.5+.3125=3.8125. Note: if more of the 3's were 4's, then the "middle
> 4"
> would be a greater distance into the cell, resulting in a higher
> fractional median (but the regular median would still be 4).
>
>
> TJ
>
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of Steven
> Samuels
> Sent: Saturday, January 17, 2009 2:58 PM
> To: [email protected]
> Subject: Re: st: Fractional Median
>
> -pctile- with the -altdef- option gives an interpolated percentile
> different from that in -sum-. See if that's what you need.
>
> -Steve
>
> --- Brooks Taggert J <[email protected]> wrote:
> > My university uses the fractional median when calculating scores
> from
> > student evaluation of instructors. I'm helping us move
> electronically
> > and in the process was using Stata to do some of the statistics.
> > Strangely I can't find an easy method (ie a pre-built ado) to
> > calculate the fractional median, nor can I find a reference
> anywhere.
>
> > Am I missing something?
> >
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
*
* For searches and help try:
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* http://www.ats.ucla.edu/stat/stata/
