IQR vs Full Range: Choosing the Arm's Length Range

The arm’s length range is the conclusion of the study — but which range is a decision, and it is the decision a reviewer disputes most often, because every choice about the range moves the boundary the tested party is tested against. The OECD’s preference is the interquartile range (IQR). Indian practice also lives with the full range, and the mid-point sits in the middle of the argument. This page is the mechanics, the decision rules, and the documentation.

What the range actually does

The range defines the band of profit levels that, for the chosen PLI, the comparable evidence says is arm’s length for the tested party’s function. The tested party’s adjusted PLI is then placed against it:

• Inside — the price is supported; no adjustment is indicated.
• Outside — a signal, not a finding: the comparability analysis, the adjustments, or the pool needs a second look before anyone calls it an adjustment.

The range is a property of the pool and the method used to summarise the pool. Same pool, different range method, different boundary — which is why the choice belongs in the file with the pool, not as a footnote.

IQR mechanics, step by step

The IQR is the band between the first and third quartiles of the pool’s PLI values (OECD Ch. 3, para 6.104 — a statistical proxy, not a legal rule).

Worked example — nine adjusted OP/OC values: 3.2, 3.6, 4.0, 4.5, 4.8, 5.1, 5.4, 5.9, 6.3 (%).

1. Sort the values (already sorted).
2. Find the median: with n=9, the 5th value → 4.8.
3. Q1 = median of the lower half excluding the median: values 3.2, 3.6, 4.0, 4.5 → median = (3.6 + 4.0)/2 = 3.8.
4. Q3 = median of the upper half excluding the median: 5.1, 5.4, 5.9, 6.3 → median = (5.4 + 5.9)/2 = 5.65.
5. IQR: 3.80% – 5.65%, mid-point 4.73%.

Even counts. With n=8, there is no single middle value: the lower half is the first four values, the upper half the last four, and Q1/Q3 are each the median of their half. The same rule — “halve, then take the median of the half” — keeps the method consistent across pool sizes. (Different quartile conventions exist in statistics; pick one, apply it to every study, and say which one you used.)

Why the IQR. It is robust to the one or two companies that are in the pool but not truly comparable — the residual uncertainty of any qualitative screen. The full range is maximally sensitive to them; the IQR is the statistically honest middle. That robustness is exactly why the OECD prefers it as the first choice.

The full range in Indian practice

The full range (minimum to maximum of the pool) still appears in Indian studies, and in TPO reasoning, for three reasons:

1. Small pools. With five or six comparables, the IQR is thin and the full range is sometimes the only range with any width. (A pool that small is itself a search-design problem — but the range decision still has to be made.)
2. The “entered the full range” argument. When the tested party is outside the IQR but inside the full range, taxpayers (and, in disputes, the authorities) argue from the full range. The position is defensible as a secondary argument — it was never the OECD’s first choice.
3. TPO pools. A TPO rebuilding the pool with a different range method changes the boundary; knowing how both methods behave on your pool is part of audit readiness.

Choosing: the decision table

Situation	Range to document	Reason
Pool ≥ ~8 companies, clean qualitative screen	IQR	OECD first choice; robust; the default position
Pool 5–7 companies	IQR, with the full range shown alongside	The IQR is the position; the full range is the sensitivity analysis
Pool < 5 companies	Full range, with the limitation stated	The IQR has no meaningful width; the limitation is part of the conclusion
Tested party outside IQR, inside full range	IQR as the range; the outside position analysed	Do not silently switch range methods to change the conclusion — analyse the cause (unadjusted difference, pool, tested party)

The last row is the discipline that matters: the range method is fixed before the tested party’s number is placed, not chosen after. A study that documents “IQR considered; full range applied because the tested party fell outside the IQR” has documented its own weakness.

The mid-point, placed honestly

The mid-point (median for a symmetric pool; the arithmetic mean of Q1 and Q3 for the IQR) is a single-number estimate of the arm’s length result. Its legitimate uses:

• as a sensitivity inside the range analysis (“the tested party is within 30 bps of the mid-point”);
• where the authorities or the context (e.g. a settlement) operates from a single number.

Its illegitimate use is as the starting position of the study: a study built to hit the mid-point has inverted the method. The range comes from the pool; the tested party is placed in it; the mid-point describes the result.

Documenting the choice

The Local File’s range section needs exactly one compact block:

1. The pool — the adjusted PLI values, sorted, with the pool size.
2. The method — IQR (or full range), the quartile convention used, the stated reason from the decision table above.
3. The computation — Q1, Q3 (or min/max), mid-point, the worked numbers.
4. The placement — the tested party’s adjusted value, inside/outside, and what the placement means.

Four lines of substance. A TPO re-runs those four lines; if they run clean, the range argument is over before it starts.

FAQ

Is the IQR a legal requirement in India? No — it is the OECD’s statistical recommendation, and it is the position Indian practice increasingly treats as the default. The full range remains in active use, especially for small pools. Defensibility comes from the documented choice and the pool behind it, not from the label.

My pool has two obvious outliers. Do I drop them for the IQR? No — that is a qualitative decision and it belongs in the qualitative screen, with a company-specific reason. An “outlier” removed for the range statistics is the same range-management problem as a moved size band. If the company is not comparable, reject it at the stage that exists for that; if it is comparable, the IQR already contains the tolerance for it.

Which quartile convention should I use? Any consistent one. State it (“Q1/Q3 as the medians of the lower/upper halves excluding the overall median”) and apply it to every study. Reviewers challenge inconsistency across years far more often than the convention itself.