A ratio-of-ratios combines four independent tracks and a pair ratio combines two, so its noise floor is wider by a factor of root two in log space - and cycles 101 and 102 scored two ratio-of-ratios against a pair floor. Applying the correction to the measured 9.4% peak floor gives 13.5%: VTP's 1.3% stays comfortably inside, and SGC0946's 22.8% stays outside but its margin falls from '2-6x outside' to 1.7x
also called the order-of-quantity correction · four tracks are not two · the root-two floor
Comparing two measurements doubles the random error; comparing two comparisons doubles it again. Two of this project's results compared two comparisons but judged them against a yardstick built from a single comparison, which made them look more solid than they are. Both conclusions still hold, but one of them by a much smaller margin than was reported.
The same thing, for a scientist
**A same-condition pair ratio combines two independent tracks. A ratio-of-ratios combines four.** In log space, if one track's share at a stratum carries variance s^2, a pair ratio carries 2s^2 and a ratio-of-ratios 4s^2. The floor for the second is therefore **sqrt(2) times wider in log space** than the floor for the first. **Cycles 101 and 102 computed two ratio-of-ratios and judged both against a pair floor.** | quantity | tracks | value | deviation | floor used then | correct floor now | |---|---:|---:|---:|---:|---:| | VTP-50469 ratio-of-ratios, C1 vs NT | 4 | 1.0134 | **1.34%** | 4-10% | **13.5%** | | SGC0946 ratio-of-ratios, C1 vs NT | 4 | 0.7724 | **22.76%** | 4-10% | **13.5%** | | FLAG DMSO C1/NT | 2 | 0.8374 | 16.26% | 4-10% | 9.4% | **Both verdicts survive and one of them is materially weaker.** VTP's 1.34% is now 10 times inside its floor rather than 3-7 times inside - a strengthening. SGC's 22.76% was described as *"2-6x outside it"*; against the correct 13.5% it is **1.7x outside**, a margin of 9.3 percentage points. **The direction is unchanged; the confidence attached to it should not be.** **The correction is the smaller half of the story.** The larger half is that the floor being corrected was measured at the wrong stratum and from the wrong assay - both handled in the companion entries. This entry exists because the order-of-quantity error is independent of those two and would still apply if the floor had been perfect.
The derivation, so it can be checked rather than believed
Let x_i = log(share of track i at stratum s), with independent errors of variance s^2.
- Pair ratio
A/B:log ratio = x_A - x_B, variance2s^2, so typical magnitude~ sqrt(2) s. - Ratio-of-ratios
(A/B)/(C/D):log = x_A - x_B - x_C + x_D, variance4s^2, typical magnitude~ 2s.
Ratio of the two typical magnitudes: 2s / (sqrt(2) s) = sqrt(2). In multiplicative terms, if the measured pair floor is 1 + f, the ratio-of-ratios floor is 2^(sqrt(2) * log2(1+f)) - 1. For f = 0.0937 this gives 0.1350.
In cycle 102's design the four tracks of each ratio-of-ratios are four distinct libraries - NT-DMSO, NT-drug, C1-DMSO, C1-drug - so the independence assumption is met for each one individually. The two ratio-of-ratios share their two DMSO tracks with each other, so the VTP and SGC figures are correlated and should not be treated as two independent observations of anything.
Where else this applies
Any quantity of the form (treated/untreated) in condition 1, over (treated/untreated) in condition 2 takes the wider floor. That includes every 'does the drug do the same thing in the resistant genotype' statistic in this thread.
A difference of differences on a log scale has the same structure and the same correction. A three-track quantity - for instance one shared control - carries variance 3s^2 and a factor of sqrt(1.5), not sqrt(2); count the distinct libraries, not the ratios.
| script | analyses/the-same-condition-noise-floor/run.py |
|---|---|
| status | run |
| result summary | Ratio-of-ratios floor = 2^(sqrt(2)*log2(1+pair_floor)) - 1. With the measured 9.37% peak pair floor this is 13.50%. VTP 1.34% inside; SGC0946 22.76% outside by 9.26 points, downgraded from '2-6x outside' to 1.7x. |
| pair floor TOP | 0.0937 |
| ratio of ratios floor TOP | 0.135 |
| vtp ror deviation | 0.0134 |
| sgc ror deviation | 0.2276 |
| sgc margin | 0.0926 |
- The claim this most weakens is that a DOT1L inhibitor displaces the fusion MORE than a menin inhibitor in a resistance genotype - a result that, if taken at face value, argues for DOT1L inhibition as a menin-inhibitor-resistance strategy. It is still outside the floor, but by 1.7-fold rather than the 2-6-fold that was reported, and it rests on n = 1 per arm.
- Conversely the correction strengthens the reassuring result - that the menin inhibitor evicts the fusion identically in the resistant genotype - which is the finding this project uses to argue that an occupancy-based pharmacodynamic assay would score a resistant cell as a complete responder. A stronger version of that is a worse problem for trial design, not a better one.
- How much of the 9.4% peak floor is systematic (and therefore partially cancelling in a ratio-of-ratios) and how much is random (and therefore additive)? Two same-condition pairs of the same assay would separate them; GSE299100 has only one per assay.
- Does any other entry in this corpus compare a four-track quantity against a two-track floor? No sweep has been run, and the error is invisible in a results file that records only the final ratio.
- E1established confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.dataset
Cycle 102 records VTP_ratio_of_ratios = 1.0134 and SGC_ratio_of_ratios = 0.7724 for the C1-versus-NT contrast, describes the first as INSIDE and the second as '2-6x OUTSIDE' a floor of 4-10% derived from two input PAIR ratios, and the underlying FLAG shares it reports (NT DMSO 0.008412, NT VTP 0.006355, C1 DMSO 0.007045, C1 VTP 0.005393) confirm each ratio-of-ratios is built from four distinct libraries.
What this evidence cannot show
Internal repository sources. The four-library composition is inferred from the share table rather than from a stated track list, but the four shares are four distinct numbers from four named GSM accessions, so the inference is direct.
Evidence that argues against this (1)
- If the four libraries were processed as two batches grouped by drug, the DMSO and drug errors would be correlated and the variance would be below 4s^2, making sqrt(2) an overcorrection. Cycle 102 checked this directly and found the opposite: the SRA accessions SRX23818684/685/687/688 and BioSamples SAMN40239754/755/757/758 are grouped by GENOTYPE, not by drug. Grouping by genotype leaves the drug contrast uncorrelated, so the four-independent-track assumption is the right one here. source 2026
- E2strong confidence 4 of 5: Replicated in peer-reviewed work by more than one group.dataset
The measured same-condition pair floor at the top 0.1% stratum is 9.37%, which propagates to 13.50% for a four-track ratio-of-ratios; against it, VTP's 1.34% is inside and SGC0946's 22.76% is outside with a margin of 9.26 percentage points.
What this evidence cannot show
The 9.37% is a single observed deviation from one pair, not an estimated standard deviation, so treating it as a typical magnitude and scaling it is an order-of-magnitude argument rather than a confidence interval. With n = 1 pair per assay no interval is available. The MLL1 pair gives 8.83% at the same stratum, which would propagate to 12.7%, so the choice between the two antibody arms moves the answer by under a point.
Evidence that argues against this (1)
- The correction can be argued the other way for the VTP case: if the two genotypes' DMSO tracks share a systematic IP-efficiency term, part of it cancels in the ratio-of-ratios, which would make the true floor NARROWER than the pair floor rather than wider. That cancellation is exactly why a ratio-of-ratios is used. Whether it dominates the added variance depends on how much of the 9.4% is systematic and how much random, and nothing here separates those - a second same-condition pair would. source 2026