How to Calculate Interpolated Median (IM) Using Syntax

[asp778ACU-2]

Dear SPSS Base Gurus,

I am trying to work something out which I am sure SPSS can do to calculate
the IM
N = total number of valid responses to the question
M = the standard median of the scores
N1 = number of scores less than M (strictly less, not equal)
N2 = number of scores equal to M

https://spu.edu/depts/insdev/interpolated_median_explanation.pdf
 
But I am not sure how to translate the IM formula above into the syntax.
Attached dummy survey data set list that required interpolated median for Q1
and Q2.
What I try to achieve populate IM figures using syntax.
As I am newbie with very basic knowledge of SPSS, any enlightenment will be
appreciated.

SampleData.sav
<http://spssx-discussion.1045642.n5.nabble.com/file/t341643/SampleData.sav>
Thanks in advance.




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[Art Kendall]

Is this what you are looking for?


GET
  FILE='C:\Users\Art\AppData\Local\Temp\SampleData.sav'.
DATASEt NAME ExampleData.
DISPLAY DICTIONARY.
VARIABLE LEVEL Q1 Q2 (ORDINAL).
*Perhaps even interval.
NUMERIC MyScore (f3.1).
*using MEAN to get a summative score with the same meaning as the response
scale.
COMPUTE MYScore=Mean.2(Q1 to Q2).
FREQUENCIES VARIABLES = Q1 Q2 MyScore /STATISTICS =ALL.
NUMERIC NewVar (F2).
RECODE MyScore(Missing=Copy)(4.0 THRU HI =2)(1 THRU 3.9999 =1)(ELSE = -1)
INTO NewVar.
VALUE LABELS NewVar
    -1 'Oops weird result'
    1 'Below Median'
    2 'At or above Median'.
MISSING VALUES NewVar (LO THRU -1).
CROSSTABS TABLES = MyScore BY NewVar.



-----
Art Kendall
Social Research Consultants
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[Art Kendall]

Since the score is at least ordinal, why not use both the mean and median in
your reasoning?

In SPSS click <Help> theu enter "RANK"

then paste this after the syntax I posted before.
RANK VARIABLES=Q1 /RANK INTO RMEAN /TIES=MEAN.
RANK VARIABLES=Q1 /RANK INTO RCONDS /TIES=CONDENSE.
RANK VARIABLES=Q1 /RANK INTO RHIGH /TIES=HIGH.
RANK VARIABLES=Q1 /RANK INTO RLOW /TIES=LOW.
DESCRIPTIVES VARIABLES= RMEAN TO RLOW /statistics=ALL.




-----
Art Kendall
Social Research Consultants
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[Bruce Weaver]

I understood things differently from Art.  The following is quite rough and
ready, but I think it does what you describe.  (VECTOR and LOOP might be
tidier than DO-REPEAT, but I don't have a lot of time to mess around with it
any further right now.)  

HTH.


GET FILE='C:\Temp\SampleData.sav'.

* Get Nvalid and ordinary median for each question.
AGGREGATE
  /OUTFILE=* MODE=ADDVARIABLES
  /BREAK=
  /Nvalid1 Nvalid2 = NU(Q1 Q2)
  /med1 med2 = MEDIAN(Q1 Q2).

* n1 = number of scores less than Median (strictly less, not equal)
* n2 = number of scores equal to Median.

DO REPEAT n1 = n1Q1 n1Q2 / n2 = n2Q1 n2Q2 / med = med1 med2.
 COMPUTE n1 = Q1 LT med.
 COMPUTE n2 = Q1 EQ med.
END REPEAT.

* Sum those flag variables to convert them to counts.
AGGREGATE
  /OUTFILE=* MODE=ADDVARIABLES OVERWRITE=YES
  /BREAK=
  /n1Q1 n2Q1 n1Q2 n2Q2 = SUM(n1Q1 n2Q1 n1Q2 n2Q2).
FORMATS n1Q1 n2Q1 n1Q2 n2Q2 (F5.0).
DESCRIPTIVES n1Q1 n2Q1 n1Q2 n2Q2.

* Compute interpolated median (IM).

DO REPEAT
 IM = IM1 IM2 /
 med = med1 med2 /
 N = Nvalid1 Nvalid2 /
 n1 = n1Q1 n1Q2 /
 n2 = n2Q1 n2Q2.
DO IF n2 EQ 0.
 COMPUTE IM = med.
ELSE.
 COMPUTE IM = med-0.5+((0.5*N-n1)/n2).
END IF.
END REPEAT.
DESCRIPTIVES med1 med2 IM1 IM2.




asp778ACU-2 wrote

> Dear SPSS Base Gurus,
>
> I am trying to work something out which I am sure SPSS can do to calculate
> the IM
> N = total number of valid responses to the question
> M = the standard median of the scores
> N1 = number of scores less than M (strictly less, not equal)
> N2 = number of scores equal to M
>
> https://spu.edu/depts/insdev/interpolated_median_explanation.pdf
>  
> But I am not sure how to translate the IM formula above into the syntax.
> Attached dummy survey data set list that required interpolated median for
> Q1
> and Q2.
> What I try to achieve populate IM figures using syntax.
> As I am newbie with very basic knowledge of SPSS, any enlightenment will
> be
> appreciated.
>
> SampleData.sav
> &lt;http://spssx-discussion.1045642.n5.nabble.com/file/t341643/SampleData.sav&gt; 
> Thanks in advance.
>
>
>
>
> --
> Sent from: http://spssx-discussion.1045642.n5.nabble.com/
>
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>  (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
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> INFO REFCARD





-----
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Bruce Weaver
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"When all else fails, RTFM."

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[Art Kendall]

Since the score is at least ordinal, why not use both the mean and median in
your reasoning?

In SPSS click <Help> theu enter "RANK"

then paste this after the syntax I posted before.
RANK VARIABLES=Q1 /RANK INTO RMEAN /TIES=MEAN.
RANK VARIABLES=Q1 /RANK INTO RCONDS /TIES=CONDENSE.
RANK VARIABLES=Q1 /RANK INTO RHIGH /TIES=HIGH.
RANK VARIABLES=Q1 /RANK INTO RLOW /TIES=LOW.
DESCRIPTIVES VARIABLES= RMEAN TO RLOW /statistics=ALL.



-----
Art Kendall
Social Research Consultants
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[asp778ACU-2]

Many thanks for the enlightenment and sharing back bone syntax.

I shall cook survey data using scripts provided and wish me luck how it goes
.

As I am number crunch (e.g.: BI analyst by trade) and not statistician so I
just follow the tradition using the hard complicated way  - Interpolated
Median Score rather than using the old school (e.g.: basic statistics –
median, etc).







-----
Andre
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