A within-sample share cancels an unknown scale factor but it does NOT make two studies comparable - the same eviction reads as 0.20 over a genome-wide denominator and 0.67 over a promoter-only one, in the same cells on the same day
also called the share denominator · why 0.67 and 0.20 are the same result
Measuring what fraction of a signal sits at a set of places is the right way to compare treated and untreated samples when you have no yardstick. But the fraction depends on what you divide by, so two people can measure the same thing correctly and get numbers three times apart.
The same thing, for a scientist
This graph holds `concept-q117-a-within-sample-share-is-the-cross-condition-comparison-that-survives-a-missing-scale-factor`, and that concept is right: a share `x_i / sum(x)` cancels an unknown per-sample scale factor `k` exactly, as does a within-sample rank, while a fold change carries the unrecoverable ratio `k_v/k_d`. **What it does not do is make two studies' shares comparable, and this beat measured the size of that problem by accident.** The same menin eviction, in the same RS4;11 samples, on the same day [E1]: | denominator | held set | MENIN share ratio | |---|---|---:| | 21,461 deposited RefGene TSS windows | top 1% = 215 windows | **0.6697** | | 1,389,514 genome-wide 2 kb bins (input > 0, not blacklisted) | top 0.1% = 1,390 bins | **0.1999** | **A factor of 3.35, from the denominator alone.** And the ceiling-free statistic barely moves: the fraction of the held set still in its own top is 0.205 over the TSS denominator and 0.1058 genome-wide - a factor of 1.9 - while the fraction losing rank is 0.847 and 0.9151, a factor of 1.08. **Why.** A share is `signal at the set / signal everywhere in the universe`. A promoter-only universe is almost entirely occupied by the factor being measured, so there is very little unoccupied space for evicted signal to move into and the share has nowhere to fall. A genome-wide universe is 97% background and the share can fall the whole way. **The share statistic's dynamic range is a property of the universe, not of the biology.** **Three rules follow, and the second is the one that bites.** 1. **State the universe with every share.** "Share of total coverage" is not a statistic until the denominator is named: how many regions, of what size, filtered how. 2. **Never compare a share across studies with different universes.** This beat's headline replication of Q117 (0.1999 against 0.179) is only meaningful because the universe was deliberately rebuilt to match: 2 kb bins, input > 0, blacklist-filtered, top 0.1%. Had it been read off the convenient deposited promoter table it would have read 0.67 against 0.179 and looked like a failure to replicate. 3. **Prefer the rank-membership statistic for cross-study comparison.** `fraction of the held set still in its own top X%` moved by 1.9-fold across a 65-fold change of universe, against the share's 3.35-fold, and it has no ceiling problem that a percentile-shift statistic has. It is the statistic this beat leads with for that reason.
The related trap in the other direction: a rank statistic at its ceiling
Q117 found that its pre-registered rank statistic was structurally incapable of detecting a KDM2B gain, because KDM2B was already at the 99.685th percentile of its own distribution at the fusion's sites in DMSO. It added a share statistic for that reason.
This beat hit the mirror image. Its pre-registered null was matched on the DMSO percentile decile, and the held set is the top 1% - one tenth of its own decile, with the other nine tenths much weaker and free to fall further. The pre-registered null therefore moved more than the held set and the E2 statistic came out negative for every track, which is an artefact of the matcher. Replaced with a rank-neighbourhood null (+/-400 ranks), recorded as a deviation.
So the pairing is: a share needs its universe declared, and a rank needs its headroom declared. Neither statistic is safe on its own and this beat reports both for every claim.
AND THE COST OF THE SHARE STATISTIC: it is blind to a uniform global loss
This is the price of cancelling the scale factor and it is not stated in the concept this beat inherits.
A within-sample share is a statement about SHAPE, not about amount. If a drug removed a factor uniformly from every site in the genome, every share would be unchanged and the share ratio would be exactly 1.0. So a share ratio near 1 has two readings - nothing left and everything left - and only an external calibrant distinguishes them. That calibrant is the scale factor, which is the thing that is missing.
This matters for a specific number in this beat. The DOT1L tracks' unnormalised totals over the deposited TSS table fall to 0.283 (MOLM13), 0.333 (RS4;11) and 0.470 (ML-2) of their DMSO values, while the MOLM13 DOT1L share ratio at its own top 1% is 0.9108 and its retention is 0.721. Read as a share, MOLM13's DOT1L barely moves. Read as a total, it loses 70%. Both are true, and the honest statement is that DOT1L in MOLM13 falls roughly UNIFORMLY rather than site-selectively - which is exactly the pattern a share statistic cannot quantify and can only detect as an absence of reshaping.
The totals are library-depth-confounded and cannot be used as amounts. So for a uniform loss, this dataset has no valid statistic at all, and that is the honest bound on every retention claim in this beat: the MLL1-N-reactive material that stays is unchanged in its DISTRIBUTION, and its total amount is unmeasurable here.
| definition | A within-sample share cancels an unknown per-sample scale factor but its dynamic range is set by the universe it is computed over, so shares from different universes are not comparable quantities. |
|---|---|
| worked example | RS4;11 MENIN under VTP-50469: 0.6697 over 21,461 promoter windows, 0.1999 over 1,389,514 genome-wide 2 kb bins. |
| preferred cross study statistic | fraction of the held set still in its own top X% (ceiling-free and scale-free); report the share beside it with its universe named |
| status | run |
- Is there a universe-invariant eviction statistic? A ratio of the held set's share to a class-matched null's share partially normalises the universe (0.1999/0.4531 = 0.44 genome-wide) and was computed here but not compared across universes. One line of code.
- How much of this project's existing cross-study occupancy comparison rests on shares from mismatched universes? No sweep was run; the search token would be 'share of total' and 'fraction of signal' across the analyses directory.
- A share ratio near 1.0 is consistent with total retention and with total uniform loss. Nothing in GSE127507 distinguishes them, so every 'retained' claim in this beat is a claim about distribution and not amount. The only fix is a calibrant: a spike-in, or an internal reference region established to be drug-invariant by an independent measurement.
the 0.1999 figure is only comparable to Q117's 0.179 because the genome-wide universe was deliberately rebuilt to match; the promoter-only denominator gives 0.6697 for the same eviction
extends that concept with what a share does NOT buy: comparability across universes, and any sight of a uniform global loss
the worked example is this beat's own headline: 0.6697 over a promoter denominator and 0.1999 over a genome-wide one, same cells, same day
the hypothesis's central retention claim is a claim about distribution and not amount, because a share is blind to a uniform loss