Dispersion: The Spread of the Comparables Distribution
Dispersion defined: the spread of the comparables’ PLI values around the centre — the width read, the consistency signal and the pool-quality documentation.
Definition
Dispersion is the spread of the comparables’ PLI values around the centre — how tightly (or loosely) the pool’s members cluster on the PLI. It is the distribution’s consistency signal: the tight dispersion (the members clustered, the narrow IQR) is the pool that agrees on the PLI — the comparability is strong, the range is the pool’s consistent position; the wide dispersion (the members spread, the wide IQR) is the pool that does not agree — the comparability is mixed, the range is wide, and the width is itself the documentation’s question (the comparability adjustments that should have narrowed it, the set quality the width describes).
Tight dispersion: 2.6 2.7 2.8 2.8 2.9 3.0 3.1 (the IQR narrow —
the pool agrees; the range is the consistent position)
Wide dispersion: 1.2 2.1 2.8 3.4 4.2 5.1 6.8 (the IQR wide —
the pool disagrees; the width is the documentation’s
question: the adjustments, the set quality)| The read | The content |
|---|---|
| The IQR width | The p75 − p25 (the range’s width) — the primary dispersion measure, relative to the median (the width as a share of the mid-point: the 2.1%–3.4% IQR on the 2.8% median is the ~46% width) |
| The consistency signal | The tight width (the pool agrees on the PLI — the comparability strong, the members’ functions/assets/risks genuinely similar) against the wide width (the pool mixed — the members’ differences not fully screened out, or the adjustment not applied) |
| The documentation use | The width stated in the benchmarking annex (the IQR, the width, the relative width) — the pool-quality read, the significance note’s companion, the TPO’s “is this pool comparable?” answer |
The working read (the IQR vs full range guide): the dispersion is the quality read on the range — the range (the IQR) is the standard, the dispersion is the confidence in the standard. The wide-dispersion pool is not automatically the bad pool (the genuine economic difference among the comparables — the product mix, the scale — is the spread the comparability explains), but it is the pool the documentation must explain: the width’s cause (the members’ differences, the adjustment applied, the set’s character) stated, so the range’s width is the comparability’s honest result, not its unexamined artifact. The benchmarking mistakes self-audit carries the wide-unexplained-width as the pool-quality row.
Example
The pool (12 members, the adjusted PLIs): the IQR is 2.1%–3.4% (the width 1.3 points, ~46% of the 2.8% median) — the moderate dispersion. The read: the members cluster around the median with the expected spread (the product mix variation, the scale difference — the comparability factors the qualitative screen documented per member). The annex states: the IQR, the width, the relative width, the width’s cause (the members’ differences, the working-capital adjustment applied, the outlier treated) — the pool-quality read, the significance note’s companion. The tested party at 2.9% (inside, 0.1 above the mid-point) — the position in a pool whose consistency is documented, not assumed.
See also
FAQ
Is a wide dispersion a defect in the pool? Not automatically — the wide dispersion is the genuine economic difference among the comparables (the product mix, the scale, the asset structure — the comparability factors that differ among the members) where the difference is the economics, not the screening failure. The defect is the wide dispersion unexplained (the width with no cause stated, the members’ differences not screened, the adjustment not applied) — the mistake list row. The documentation’s job is the width’s cause: the tight width (the consistent pool) stated, the wide width (the mixed pool) explained — the comparability’s honest result either way.
Dispersion or significance — how are the two reads different? The significance is the set-size adequacy (the number of members, the range’s reliability on the n); the dispersion is the spread measure (the values’ clustering, the range’s width and its cause). The thin set (the small n, the significance question) can have the tight dispersion (the few members agree — the reliability still questioned on the n); the large set (the adequate n, the significance met) can have the wide dispersion (the many members disagree — the comparability questioned on the spread). The two reads are independent, and the documentation carries both: the size (the significance) and the width (the dispersion), each with its cause.
Where does the dispersion read appear in the documentation? In the benchmarking annex’s range block: the IQR (the bounds, the construction), the mid-point (the median), the width (the p75 − p25, the relative width), the width’s cause (the members’ differences, the adjustment applied, the outlier treated, the set’s character), and the tested party’s position (the IQR relation, the mid-point distance). The pool-quality read — the significance (the size) and the dispersion (the width) together — is the TPO’s “is this pool comparable?” answer, stated in the file rather than argued in the proceeding.
Run the screens as a study, not a spreadsheet
Quartyl applies the method, PLI and screening steps above as a pipeline — and keeps a documented reason for every exclusion.
Related docs
Interquartile Range (IQR): The OECD Arm's Length Range
The interquartile range defined: the band between the first and third quartiles of the comparable pool — the OECD\'s preferred construction of the arm's length range.
Read docStatistical Significance: Is the Comparables Set Big Enough?
Statistical significance in benchmarking: the set-size adequacy question — the minimum set, the TPO’s first ask, and the documentation that answers it.
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