Percentiles (finally getting to understand it).

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Well I think I've finally  worked out what the=20
"SPSS Statistical Algorithms" text must have meant.

I think it's the following simple C func.

double=20
pctileSPSS(double *x, size_t n, double q)
{

  double tp =3D (n + 1) * q -1;
  int lo;
 =20
  lo =3D (int) floor(tp);

  qsort(x, n, sizeof(double), cmp);

  assert( lo >=3D-1);
  assert(lo <=3D (int) n);

 if ( lo > n - 1)=20
   return x[n-1];

 if ( lo =3D=3D -1 )=20
   return x[0];

  return x[lo] + (x[lo+1]-x[lo]) * (tp-lo);
}


This seems to return the same answers as all the available SPSS
examples.  As Michael mentioned however it is inelegent to put it
politely!!

Percentiles near the 50th are fine, but the others get squeezed away
from the median.  And so there has to be the two special cases to cope
with percentiles near 0 and 100  (for a small data set, the 85th
percentile will be the same as the 100th) .

Quite frankly it's a croc!  I much prefer Michael's definition (also
used by R), which doesn't use any special cases.

I suggest that PSPP uses the R definition unless the
--bug-for-bug-spss-compatibility option was requested.

John




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