Percentile: The Position in the Comparables Distribution

Definition

The percentile is the position in the sorted distribution: the p50 is the value at which 50% of the pool’s members sit below (the median), the p25 the value at which 25% sit below, the p75 the value at which 75% sit below. The IQR (the arm’s length range, the OECD’s convention) is constructed from the p25 and the p75 — the middle 50% of the distribution — with the median between them as the mid-point. The percentiles are the coordinates of the standard: the range’s bounds, the centre, and the tested party’s position, all stated as percentiles of the pool.

The pool’s adjusted PLIs (n members, sorted ascending):
  p5 … p25 ────── p50 (median) ────── p75 … p95
         │◄──────────  the IQR  ──────────►│
         the arm’s length range (p25–p75)
         the tested party’s position: inside / outside, the p-position

The percentile	The content
p25 / p75	The IQR’s bounds — the arm’s length range (the OECD’s convention); the tested party inside = the price accepted, outside = the adjustment question
p50 (the median)	The mid-point — the position measure inside the range (the distance, the direction)
p5 / p95 (the convention)	The full-range practice’s bounds (where the full range is the stated convention — the IQR vs full range guide); the tails’ treatment, the outlier question
The tested party’s p-position	The tested party’s adjusted PLI’s position in the pool (the p62, the p40) — the documented position, the appeal’s coordinate

The working read (the IQR vs full range guide): the standard is the percentile convention, stated — the IQR (the p25–p75) as the OECD’s default, the full range (the p5–p95, or the min–max on the stated basis) where the practice states it — and the tested party’s position in the convention (the IQR relation, the mid-point distance, the p-position). The percentile is the coordinate language the documentation speaks: the range, the centre, the position, all as percentiles of the pool’s distribution, on the adjusted values, on the stated method.

Example

The pool (12 comparables, the adjusted PLIs sorted): the p25 is 2.1%, the p50 (median) is 2.8%, the p75 is 3.4% — the IQR is 2.1%–3.4%. The tested party’s adjusted PLI is 3.1% — its position in the pool is the p62 (between the median and the p75): inside the IQR, 0.3 points above the mid-point. The documentation states: the IQR (the bounds, the construction), the mid-point (the median), the tested party’s position (inside, the p62, the +0.3 distance) — the coordinates, on the adjusted values, on the stated method (the multi-year averaging where the study runs on the averaged values).

See also

• Median · Interquartile Range (IQR)
• IQR vs Full Range
• Outlier

FAQ

How are the percentiles computed on a small pool? On the sorted values, the standard interpolation (the linear interpolation between the ordered values, the convention stated) — the 12-member pool’s p25 is the value at the 25th percentile of the 12 sorted values (the interpolation between the 3rd and 4th, on the standard method). The small-pool caution is the statistical significance question (the set size’s adequacy, the TPO’s first ask) — the percentile computation is mechanical; the adequacy of the set it runs on is the judgement the documentation carries.

IQR percentiles or full-range percentiles — which is the standard? The IQR (the p25–p75) is the OECD’s convention — the arm’s length range, the default. The full range (the p5–p95, or the min–max on the stated basis) is the practice variant, stated where used (the IQR vs full range guide has the convention’s choice and the documentation of it). The percentiles are the coordinates; the convention is the choice — stated, applied, the tested party’s position in it.

Does the tested party’s own p-position matter, or only the IQR relation? The IQR relation is the standard (inside = accepted, outside = the adjustment question); the p-position is the documented coordinate — the appeal’s and the TPO’s shared reference (the tested party at the p62, 0.3 above the mid-point, is the file’s stated position). The documentation carries both: the relation (the standard) and the position (the coordinate) — the p-position is what the adjustment’s arithmetic runs on where the tested party is outside (the distance to the bound, the direction).