Hand-considered hypotheses, 2901–3000
Measurement science only. Traceability, reference materials, interlaboratory comparison, uncertainty budgets, conformity decisions. Each entry was written on its own and given its own logical form, printed with it: some claim a quantity is misattributed, some assert a bound, some an inversion, some a hidden term, some an artefact that mimics a real effect. None has been tested. Estimates are marked where a number is a judgement rather than a measurement.
The traceability chain
Misattribution
H2901. A calibration certificate's stated uncertainty is routinely read as a property of
the artefact, yet for artefacts calibrated by comparison it is mostly a property of the
comparator and the transfer standard used at that visit. The artefact inherits the comparison's
error but not its uncertainty structure, so one block can carry two different uncertainties from
two laboratories and neither need be wrong. Re-calibrating a single batch by two routes and
decomposing the two budgets term by term, rather than comparing their totals, shows which terms
are shared and which belong to the block.
Hidden term
H2902. Comparing end standards carries a term from elastic indentation at the two contact
faces, and because the probing force is fixed by the comparator the term is constant and is
absorbed silently into the assigned length. The artefact then appears to change length when it
moves to a comparator with a different probing force, and the change follows the force
difference rather than any material property. Extrapolating a series of measurements on one
artefact to zero probing force isolates the indentation term without a material model.
Identity
H2903. Repeatability and drift of a comparator are one autocorrelated process, and the
line between them is drawn by the averaging time the operator happens to choose; because a
single noise source supplies both numbers, a laboratory can report excellent repeatability and
poor drift from the same record by moving the line. Computing the structure function across lag
times shows whether a plateau exists at all, and where none does the two figures are an artefact
of the split.
Bound
H2904. The uncertainty a laboratory can honestly attach to a disseminated value is
bounded below by its drift rate multiplied by the time since the last calibration, however good
the comparison was. A comparison fixes the value now; the interval turns a rate into an offset
that grows without further information. Calibrating a set of standards at two intervals and
plotting assigned uncertainty against elapsed time should give a slope equal to the drift rate,
and a slope near zero would falsify the claim.
Threshold
H2905. A digital indicator parked near a code boundary behaves as a quantizer rather than
as a noisy sensor, and the change of regime happens where the noise is about one least
significant digit (estimate). Below that, repeated readings cycle through a short deterministic
pattern that looks like exceptional stability. Recording ten thousand readings with the input
held within a tenth of a digit of a boundary distinguishes a cycle from a distribution.
Reversal
H2906. Adding parameters to a calibration model improves agreement at the measured points
and worsens it between them, and the worsening grows faster than the improvement once the model
has more parameters than the instrument has physical error sources. The interpolated correction
then becomes least trustworthy where no data exist, which is most of the range. Fitting models
of increasing order to one dataset and checking each against an independently measured midpoint
exposes the crossover.
Count
H2907. Pairwise measurement of n artefacts yields at most n-1 independent differences,
and what remains is a single scale factor the differences cannot constrain, so any reported
matrix with more independent entries has been assembled with an assumption, usually that one
artefact is exact. A rank test on the measured difference matrix identifies which assumption was
made and whether the report admits making it.
Artefact mimics effect
H2908. Apparent thermal expansion of a gauge block in air can be the growth of the
interferometer's dead path instead of the block's own expansion, and the sign differs between a
single-arm and a differential arrangement. Both produce a linear drift against temperature, so
one thermometer cannot separate them. Reversing the beam path so the dead path shortens while
the block lengthens, at the same heating rate, separates them cleanly.
Scale argument
H2909. The dominant error in short-length calibration is angular: the comparator's tilt
multiplied by the offset from the measuring axis grows relative to the length as the artefact
shortens, so an instrument excellent at one metre can be poor at one millimetre. Measuring a
graduated series from a millimetre to a metre on one comparator, and plotting error against the
offset-to-length ratio, isolates the angular term from the scale term.
Inversion of standard practice
H2910. The usual pyramid of reference standard, then working standard, then instrument
inserts a transfer whose stability can be worse than the comparator's own resolution. Comparing
the instrument directly with the reference, both at one temperature, removes a link instead of
adding one. Doing both routes on the same afternoon and differencing the results measures the
transfer's contribution directly rather than assuming it small.
Selection effect
H2911. Consensus values are commonly computed from participants who completed every
round, and completion correlates with the stability being estimated, so the consensus leans
toward stable laboratories. The lean is invisible in the reported scatter because the unstable
participants are absent from it. Recomputing the consensus with a model for dropout, or from all
partial data, and comparing the two values, quantifies the selection.
Unit trap
H2912. An uncertainty quoted in parts per million of full scale and one quoted in parts
per million of reading coincide at exactly one point of the range, and an instrument specified
the first way has a relative uncertainty that grows without bound as the reading falls. A budget
that imports the full-scale figure at a low reading therefore understates relative uncertainty
by the range ratio. Sweeping the range with a stable divider and plotting relative error against
reading shows the divergence and where it starts.
Derived quantity
H2913. The sensitivity coefficient printed beside each influence in a budget is a
property of the model, not of the instrument, and two laboratories measuring the same thing can
legitimately report coefficients differing by a factor when their models parameterize the
influence differently. Because the product of coefficient and standard uncertainty is what
enters the total, a compensating change in the uncertainty hides the difference. Exchanging the
two models and recomputing each budget from the other's inputs shows whether the totals agree
for the right reason.
Misattribution
H2914. Slow offset drift in a nanovoltmeter is often booked as amplifier drift when it is
the thermal EMF of the input connections, which reverses when the connections are swapped and
follows the room's temperature, while amplifier drift does neither. A copper-to-copper reversal
at constant ambient, followed by a deliberate ambient step, separates a reversing thermal term
from a non-reversing electronic one.
Hidden term
H2915. Two-wire resistance measurement carries lead and contact resistance as an additive
term stable enough to be mistaken for the resistor's own value, and the error is largest where
the resistor is smallest. Four-wire sensing removes it only if the potential leads attach inside
the current path. Measuring one resistor both ways, and again with a deliberately lengthened
current lead, gives the lead term as a slope rather than an assumption.
Identity
H2916. Gain error and linearity of a digital multimeter are the same parameter at the
zero point, so a specification quoting them separately names one physical effect twice and a
calibration correcting only one leaves a residue with the other's shape. The residue is
proportional to reading in both cases. Fitting measured error against reading across several
ranges and testing whether the intercept differs from zero shows whether the two names describe
distinguishable behaviour.
Non-identifiability
H2917. Separating a comparator's scale error from a common scale error in the artefact
set is impossible from the comparison alone, and only an absolute realization of the unit breaks
the symmetry. A report that quotes both a comparator correction and an artefact correction has
silently fixed one of them. Reversing the roles, treating the artefacts as reference and the
comparator as unknown, and checking whether the corrections transform consistently, exposes the
choice.
Bound
H2918. Two traceability routes to one quantity cannot confirm each other below the
smaller of their uncertainties, and agreement much better than that points to a shared term
rather than to independent confirmation. The shared term is usually a constant, a reference
artefact, or a correction assumption common to both. Auditing the routes for shared inputs and
re-deriving the expected agreement from the shared fraction alone tests whether the observed
agreement is explainable without independent evidence.
Threshold
H2919. Wringing of gauge blocks holds only above a contact pressure at which the adsorbed
film is displaced; below it the blocks appear to wring yet separate under the comparator's
probe, and the measured length is short by roughly the film thickness, of order tens of
nanometres (estimate). Measuring a stack at several wringing loads and looking for a step in
length against load locates the threshold without needing the film's properties.
Reversal
H2920. The sign of the temperature correction in a comparison depends on whether the
artefact expands more or less than the comparator's scale, so a correction validated on steel
blocks reverses on ceramic blocks of the same nominal length. Applying the steel-derived
correction to ceramic doubles the error instead of removing it. Measuring a mixed set at two
temperatures and checking the sign of each material's slope detects the reversal.
Closure
H2921. Distributing a ring's closure error equally among its artefacts assumes they are
exchangeable, and when one artefact has a heavier use history the equal split places most of the
closure in the wrong members. The error surfaces later as a re-calibration shift in the
least-used blocks. Weighting the split by each artefact's measured drift history, then
re-testing closure after one cycle, distinguishes exchangeable from unequal closure.
Lag
H2922. A disseminated value lags the artefact's actual state by one calibration interval,
so a comparison against it uses a past state and the resulting correction is systematically
stale. The lag is not random and does not average away over repeated comparisons. Comparing a
standard against a freshly calibrated transfer at the start and the end of an interval, and
testing whether the endpoint difference exceeds the drift predicted for the interval, measures
the lag.
Reference materials
Misattribution
H2923. Batch inhomogeneity in a powdered reference material is frequently reported as
instability, because the stability study and the homogeneity study use one analytical sequence
and cannot be separated after the fact. In the records the two are indistinguishable.
Randomizing the measurement order across vials and across time, so that time and vial are not
confounded, lets the two variance components be estimated separately.
Hidden term
H2924. Every hygroscopic reference material carries a water term set by the humidity of
the weighing room rather than by the certified value, moving the mass fraction without moving
the amount fraction, and since certificates usually state one while users need the other, the
discrepancy is absorbed into the user's budget as unexplained bias. Weighing one vial at two
humidities, with the balance enclosed, gives the water term as a slope against humidity.
Identity
H2925. Commutability and matrix match are one property described at two levels: a
material is commutable exactly when its matrix behaves like the routine samples' matrix in the
measuring system, so a matrix-match claim that is not a commutation test is empty. The confusion
arises because matrix match is a statement about composition and commutation a statement about
response. Running candidate and native samples through two methods and checking whether the
candidate's method-to-method difference falls inside the natives' range is the direct test.
Bound
H2926. A homogeneity study cannot resolve inhomogeneity smaller than the repeatability of
the method used, so a material certified as homogeneous is often certified only as homogeneous
relative to one method's noise, and the bound moves with the method rather than with the
material. Splitting each vial into replicate determinations and comparing within-vial to
between-vial variance, with the analytical variance taken from replicate determinations on one
homogenized portion, gives the material's contribution free of that floor.
Threshold
H2927. Homogeneity of a powder fails below a minimum sample intake set by the largest
particle's mass relative to the test portion rather than by the certified concentration, so two
materials at the same concentration but different particle sizes have different intakes and a
method validated at one fails quietly at a smaller one. Measuring one material across a series
of intakes and finding where between-unit variance rises above within-unit variance locates the
threshold.
Reversal
H2928. Grinding a material finer to improve homogeneity can make it worse for a component
that segregates by density or by surface energy, because finer particles amplify per-particle
compositional differences and multiply the contacts. The turn happens where the component's size
distribution is much finer than the matrix's. Preparing one batch at three grinding energies and
measuring both the mean and the between-unit variance shows whether variance falls monotonically
or turns.
Count
H2929. The number of independent certified values a material can carry is bounded by the
number of independent realization methods available, not by the number of analytes listed, since
values from one primary method share its bias. A certificate listing fifteen values from two
methods carries two independent claims and thirteen correlated ones. Measuring a subset of
analytes by a wholly independent method and checking whether the listed values move together
shows how many claims are actually supported.
Artefact mimics effect
H2930. An expiry date on a certificate can mimic ageing: material is discarded at the
date, the instability that justified the date is never re-tested, and the date becomes
self-confirming, leaving real stability beyond it unknown. Re-testing a retained batch well past
its stated expiry against a freshly prepared comparison separates a measured shelf life from a
stated one.
Scale argument
H2931. Demonstrating homogeneity at a one-gram intake says nothing about a one-milligram
intake, because between-unit variance for a powder scales inversely with the number of particles
in the portion and that count scales with the cube of the portion's linear size. A material can
be acceptable for macro analysis and hopeless for speciation work on the same batch. Measuring
variance at four intakes spanning three decades and checking whether it follows the predicted
inverse-count law tests the scaling directly.
Inversion
H2932. Freeze-drying, used to stabilize a biological reference material, creates
heterogeneity of its own through solute concentration at the drying front, so the material can
be more variable after stabilization than before. The variability is spatially structured,
highest near the vial's outer surface. Sectioning one vial and measuring concentric fractions,
or comparing cores against shells, separates drying-front structure from bulk inhomogeneity.
Selection effect
H2933. Stability studies are often run on the portion of a batch that was easiest to
homogenize, so the reported stability describes a selected part of production rather than the
material as distributed. The selection is invisible because the rejected portions never enter
the study. Retaining a sample from every lot, including lots that were nearly rejected, and
comparing stability slopes across them tests whether the studied material is representative.
Unit trap
H2934. A certified mass fraction in milligrams per kilogram and an amount fraction in
micromoles per mole are related by both the analyte's molar mass and the mixture's, and a
conversion that uses only one of the two is wrong by the other. For a light analyte in a heavy
matrix the omitted factor can be several (estimate). Preparing a gravimetric standard of the
pure analyte and comparing both conversions against it measures the factor instead of assuming
it.
Derived quantity
H2935. Purity by difference, one hundred per cent minus the sum of measured impurities,
is a derived quantity whose uncertainty is dominated by the impurities the method cannot see,
while its stated uncertainty is computed only from the ones it can. The unmeasured fraction is
bounded by detection limits rather than by zero, and that bound can exceed the measured
impurities combined. Adding a deliberate, quantified impurity of a class the method misses, then
checking whether the by-difference purity responds, tests whether the mass balance is closed or
merely asserted.
Misattribution
H2936. Disagreement in a titrimetric assay is often charged to sample inhomogeneity when
it is the titrant's standardization temperature that differs between laboratories, since the
titrant's volume expands and its concentration is defined at one temperature. The two causes
produce the same scatter. Circulating one titrant to all laboratories at a common temperature,
or standardizing each laboratory's titrant against a common primary standard on one day,
separates the standardization term from the sample term.
Hidden term
H2937. Gravimetric preparation carries an air-buoyancy term for every mass, proportional
to the difference between the density of the weights and the density of the object, so it
cancels only where the two densities match, and weighings of water and of a solid differ in its
sign and size. Weighing a solid of known density in air and in a liquid of known density, or
using two weight sets of different density, yields the correction as a measured difference.
Identity
H2938. A certified value and a consensus value are the same number whenever one method
supplies all the data, and the distinction between them is then documentary; a certificate's
authority can rest on one laboratory's one method without the certificate saying so. The tell is
that the expanded uncertainty equals that method's own budget. Comparing the certified
uncertainty against the method's published budget, and against the spread of any second method,
shows whether a consensus exists at all.
Threshold
H2939. Vial-to-vial variation in a liquid reference material appears only above a fill
volume at which the headspace becomes large enough to allow evaporation and re-condensation
during transport. Below it the vials behave as one pool; above it each vial's history matters.
Filling at several volumes, subjecting all to the same transport simulation, and plotting
between-vial variance against headspace volume locates the threshold.
Reversal
H2940. Extending a stability study can increase rather than decrease the uncertainty
assigned to a material's value, because a longer study resolves a small trend that a shorter one
averaged away, and extrapolating that trend carries more uncertainty than the noise it replaced.
Assigned uncertainty therefore rises with study duration past the point where the trend becomes
resolvable. Re-analyzing one stability dataset truncated at several end points, and plotting
assigned uncertainty against duration, shows the turn if it exists.
Misplaced transfer
H2941. A quality-control material validated in one matrix is routinely used to monitor a
method applied to another, on the assumption that a control is a control whatever the matrix,
but where the matrices differ in extraction efficiency the control's result tracks the matrix
rather than the method. Running the control alongside both matrices in one batch, alternated,
and checking whether its result shifts with its neighbour, tests the assumption.
Count
H2942. Significant figures in a certified value should not exceed what its budget
supports, and the usual failure is a value at four figures with an uncertainty that makes the
last two meaningless. Rewriting a value at the precision its uncertainty allows changes the
reported conformity of borderline samples. Recomputing every user's decision after rounding the
certified value and its uncertainty to the supported figures counts how many decisions were
being made on digits the certificate could not defend.
Conservation
H2943. A mass balance that closes within its stated uncertainty can still be wrong when
closure is reached by adjusting one unmeasured component, usually water or an unlisted
remainder, so closure certifies arithmetic rather than composition. Perturbing the assumed water
content and observing whether closure survives, or measuring water independently, tests whether
the balance is a measurement or a residual.
Aliasing
H2944. A scoop of fixed volume dipped into a stratified powder draws from a layer set by
the scoop's depth rather than by the material's bulk composition, so a series of scoops at fixed
depth aliases vertical stratification into an apparent batch variability. The alias has a period
set by scoop depth and layer thickness. Sampling the same material with scoops of two depths and
checking whether the variance changes with depth exposes the aliasing.
Interlaboratory comparison
Misattribution
H2945. Between-laboratory scatter is usually read as a measure of laboratory competence,
but a large part of it is method-dependent bias that no amount of care removes while the method
stays fixed. Because the assigned value comes from one method family, laboratories using another
are scored against a centre that is not theirs. Splitting the scatter by method and testing
whether within-method scatter is smaller than the between-method offset shows how much of a
score is method rather than laboratory.
Hidden term
H2946. The denominator of a z-score omits the uncertainty of the assigned value, so
participants are scored as though the reference were exact; when few laboratories contribute,
that omission can halve the effective denominator. Consequently scores near a decision threshold
are overstated in small comparisons. Recomputing every score with the assigned value's
uncertainty added in quadrature, and counting the verdicts that change, measures the omission
without any new measurement.
Identity
H2947. A z-score and an En number are one ratio with different denominators, so a single
result can look excellent on one scale and poor on the other, and the two coincide only where
the participant's uncertainty equals the comparison's scale. Plotting both across one
comparison's results collapses them onto a curve whose shape identifies whose uncertainties are
inflated.
Bound
H2948. No comparison can detect a bias shared by all participants, at any number of
laboratories, because a common bias moves the assigned value along with the results. The limit
is structural rather than statistical and does not shrink with participation. Including one
laboratory traceable by a different physical route, and comparing its departure from the
consensus against its own budget, gives the only available check on the common term.
Threshold
H2949. Robust scale estimators need a minimum number of participants before their
breakdown behaviour means anything, and below that the estimator's own variability exceeds the
differences it is asked to judge; the common estimators stabilize somewhere above ten
participants (estimate). Small comparisons therefore report scores at finer resolution than
their reliability. Resampling a large comparison down to a small one many times, and plotting
the estimator's spread against participant count, locates the threshold.
Reversal
H2950. Removing outliers can increase the reported spread, because an outlier inflates
the scale the remaining values are judged against and dropping it lowers the denominator faster
than the numerator; the reversal appears when outliers are a sizeable fraction of a small group.
Recomputing the comparison with and without each suspect value, in both orders, shows whether
the spread rises or falls and which decision is doing the work.
Count
H2951. Among n participants at most n-1 independent statements about bias can be
supported, and a table of pairwise equivalences is a re-expression of those, so a report
presenting every pair as independent overstates what the data carry. The redundancy is invisible
because each pair is computed from its own two results. Counting the rank of the difference
matrix, or checking whether the reported pairs satisfy a consistency relation, establishes how
many independent statements exist.
Artefact mimics effect
H2952. A mislabelled or mis-shipped sample in one round produces a pattern
indistinguishable from a laboratory bias, and the pattern is self-consistent enough to survive a
re-check of that laboratory's own data. What identifies it is that the anomaly follows the
sample rather than the laboratory. Re-scoring after exchanging the suspect sample's identity
with another participant's, and seeing whether the anomaly moves with it, separates the two.
Scale argument
H2953. Over a narrow range a proportional bias is undetectable, because a proportional
bias is a rotation and a short segment cannot distinguish a rotation from an offset, so a
comparison's power against bias depends on the span covered rather than on the number of
samples. Including one sample far outside the usual range, at the cost of some within-range
replication, converts an unmeasurable rotation into a measurable one.
Inversion of standard practice
H2954. Giving the reference value to the most experienced laboratory assumes that
experience protects the reference, yet it also makes that laboratory's method the de facto
definition of the measurand, against which everyone else is scored. Assigning the reference role
to a laboratory using a different method, or rotating it between rounds, tests whether the value
is method-free. Comparing the two rounds' consensus values on the same samples shows how much of
the value was the assigner.
Selection effect
H2955. Where participation is self-selected, laboratories tend to enter rounds for
quantities they expect to measure well, so the reported score distribution is truncated in a way
correlated with the score. The mean then looks optimistic and the spread looks small. Comparing
the scores of first-time entrants against repeat entrants, or against a round recruited without
self-selection, estimates the effect without knowing who declined.
Unit trap
H2956. Results reported on a dry-mass basis and results reported as received differ by
the sample's moisture, which is not measured in the comparison and is therefore absorbed into
between-laboratory scatter, where for hygroscopic samples it can dominate and be misread as
method bias. Circulating a paired sample with and without a specified drying step, and comparing
the two scatters, separates moisture from method.
Derived quantity
H2957. The consensus value of a comparison is a derived quantity whose definition changes
with the estimator chosen, so two coordinators can publish different assigned values from
identical data and both defend them. Participants are then scored against a choice rather than a
measurement. Computing the assigned value by three estimators on one dataset and checking
whether any participant's verdict changes identifies how much of the outcome is
estimator-dependent.
Hysteresis
H2958. A laboratory's result can depend on what it measured immediately before, through
carry-over in the instrument or the operator's expectation, and being small per sample the
dependence appears as scatter rather than as a trend. Re-measuring a subset in reverse order,
and comparing each sample's two results against its position in the run, exposes the carry-over.
Non-identifiability
H2959. In a nested design where each laboratory measures each sample once, laboratory
bias and sample inhomogeneity are formally confounded, because both appear as a
laboratory-by-sample interaction with no replication. A report that attributes that interaction
to inhomogeneity has made an assumption it cannot test. Replicating one sample per laboratory,
even as a single duplicate, breaks the confounding for that sample and measures how much of the
interaction is inhomogeneity.
Composition error
H2960. The uncertainty of a difference between two laboratories is not the sum of their
uncertainties when both used the same reference material or the same calibration service,
because the shared term cancels in the difference while it adds in each individual budget.
Summing therefore overstates the difference's uncertainty and understates the significance of a
disagreement. Identifying shared inputs and recomputing with the shared term removed changes
which disagreements are significant, and that list is the test.
Convergence trap
H2961. Iterative schemes that assign a consensus and re-score until stable do converge,
but on the dominant method's value, because the dominant method contributes most of the data and
therefore most of each iteration's reference. Stability of the iteration is not evidence that
the value is method-free. Seeding the iteration from each method family in turn and checking
whether the converged value depends on the seed measures the pull of the dominant method.
Rounding artefact
H2962. Reporting results to too few digits creates ties that rank-based scoring resolves
arbitrarily, and the ties are not random with respect to the quantity, since a result near a
rounding boundary is also near a decision boundary. Re-scoring with raw values, or with a
tie-aware statistic, and counting the verdict changes, gives the cost of the reporting
precision.
Asymmetry
H2963. The information in a comparison is asymmetric: the coordinator holds all results
while each participant holds only its own before publication, so a participant cannot
distinguish its own bias from an error in the reference, and the coordinator can. Any scheme
that lets participants self-correct before publication therefore moves the reference toward the
participants rather than the reverse. Withholding the assigned value until all results are
locked, in one round and not in another, and comparing the shifts, tests whether pre-publication
feedback changes the outcome.
Order dependence
H2964. Sample order within a round matters when samples are run in packing order rather
than randomized, because packing order usually follows concentration and instrument response
drifts monotonically. The drift then appears as a smooth trend across concentration, easily read
as non-linearity. Re-running the same samples in reverse packing order and checking whether the
apparent non-linearity reverses separates drift from response.
Interference
H2965. Two participants sharing a transfer standard, a calibration service, or a shipping
container are not independent, so their agreement is partly the shared artefact's value rather
than evidence about the measurand, and the correlation is invisible in the scores while
inflating apparent consensus. Mapping which participants shared which artefact, and comparing
within-cluster agreement to between-cluster agreement, estimates the shared fraction.
Saturation
H2966. Past some number of participants the assigned value stops improving while its
reported uncertainty keeps falling as the inverse square root of the count, so the uncertainty
claim outruns the information. The reason is that added participants share the same systematic
terms, which do not average. Comparing the assigned value's uncertainty under an independence
assumption against the observed between-cluster variation locates the point where the shrinkage
stops being real.
Uncertainty budgets
Misattribution
H2967. Repeatability measured on a fixture is usually entered as the instrument's own
repeatability, but on a compliant fixture most of it is the fixture's resonance and the
mounting's creep. The figure is then a property of one bench and will not transfer to a user
with a different mount. Measuring the same instrument on two mounts of different stiffness, and
checking whether repeatability scales with the mount's compliance, assigns the term correctly.
Hidden term
H2968. Budgets are assembled as though their inputs were independent, and an omitted
correlation is invisible because a budget has no place to record what was left out. When two
inputs share a thermometer, a supply, or a calibration, their errors are partly common and the
combined uncertainty is overstated or understated depending on the signs of the sensitivity
coefficients. Measuring both inputs' errors over time and computing their covariance, then
recomputing the total, shows the sign and size of the omission.
Identity
H2969. Type A and Type B evaluations are one operation applied to data of different
provenance, and the label carries no information about the resulting number's trustworthiness. A
Type B value distilled from one specification and a Type A value from three readings are both
estimates, each with its own uncertainty about the uncertainty. Replacing every Type B entry
with the corresponding Type A estimate where data exist, and comparing the two budgets, tests
whether the labels were doing any work.
Bound
H2970. No combined uncertainty can be smaller than the calibration uncertainty of the
reference behind its largest contributor, because that reference's error is common to every
later use; a budget reporting a total below that figure has either omitted a term or
double-counted a cancellation. Comparing each budget's total against the calibration uncertainty
of its dominant input flags the impossible ones without any new measurement.
Threshold
H2971. Instrument non-linearity is negligible below a curvature threshold set by the
ratio of second derivative to resolution, and above it the term grows with the square of the
range used. A budget validated over a narrow range therefore understates the term when the
instrument is used across its full span. Comparing residuals from a linear fit at two range
spans, and checking whether residual grows as the square of span, tests the threshold.
Reversal
H2972. Adding an influence to a budget can reduce the expanded uncertainty when the new
term's sensitivity coefficient is opposite in sign to an existing one and the two are
correlated, because the correlation turns a sum into a difference. The reduction is a
cancellation rather than an improvement and vanishes when the correlation does. Measuring the
two influences' joint variation over time, rather than separately, and recomputing the budget
with and without the covariance term, shows whether the reduction is supported.
Count
H2973. In most budgets three or four terms carry nearly all the variance, and the
remainder can be lumped into one entry without changing the expanded uncertainty at the reported
precision (estimate), so a budget with thirty terms describes its author's thoroughness rather
than the measurement. Truncating a set of budgets to their largest terms and comparing totals
shows how many terms the reporting precision actually supports.
Artefact mimics effect
H2974. Components that combine to a suspiciously round total invite the reading that the
total was the target and one entry was adjusted until it matched, which is invisible because
every individual term remains plausible. Disagreement with the same instrument's earlier budget,
in a term whose method did not change, is the residual evidence. Comparing term by term across
two independent budgets for one instrument, and flagging entries that moved without a
methodological reason, tests the reading.
Scale argument
H2975. Whether a term is negligible depends on the value being measured rather than on
the instrument, because absolute terms hold fixed while relative terms scale, so resolution
dominates at small values and calibration at large ones. A budget stated as one set of numbers
therefore misdescribes the instrument across its range. Measuring a standard at three points
spanning a decade and computing the budget at each from the same terms shows the crossover and
where the single-number budget fails.
Inversion
H2976. After a logarithmic or ratio transformation the smallest term in a budget can
become the largest, because a small additive term is a large relative term near zero, so budgets
for quantities expressed in decibels or in ratios need re-derivation rather than rescaling.
Transforming a complete budget term by term, and comparing the result against an uncertainty
measured directly in the transformed domain, shows whether rescaling was adequate or whether the
ordering changed.
Selection effect
H2977. Budgets are often back-fitted to past comparisons so that they reproduce the
observed scatter, and the comparisons used are those in which the laboratory's results were
already acceptable. The fitted budget then describes a selected history. Constructing a budget
from first principles, without reference to past scores, and comparing its predicted scatter
against a fresh comparison, tests whether the fit was to physics or to the selection.
Unit trap
H2978. The standard deviation of the mean and the standard deviation of a single
observation differ by the square root of the count, so a budget mixing them under one symbol
produces an uncertainty that changes whenever the protocol changes, for reasons unrelated to the
measurement; the confusion bites hardest in Type A entries, where both numbers come from the
same data. Recomputing a published budget with the two conventions exchanged, and seeing which
version reproduces an independently observed scatter, identifies which convention was used.
Composition error
H2979. Two entries arising from one physical source are frequently entered twice under
different names, once as resolution and again as noise, or once as drift and again as stability,
so the combined uncertainty overstates that source by about the square root of two. Duplication
is hard to see because the names differ. Grouping entries by physical source rather than by name
and recomputing changes the total by a factor that reveals whether duplication is present.
Non-monotonicity
H2980. Averaging more readings lowers the noise term and raises the drift term, since the
averaging window lengthens while the drift continues, so combined uncertainty has a minimum at
an averaging time set by the ratio of white noise to drift rate. The optimum belongs to the
instrument's noise spectrum, not to the protocol. Measuring the variance of one instrument
across averaging times, in the manner of an Allan plot, locates the minimum and shows on which
side the protocol sits.
Closure
H2981. Reproducing a validation set's observed scatter exactly is evidence of fitting
rather than of completeness, and a genuinely complete budget usually disagrees with validation
scatter by a factor of order one (estimate). The disagreement is expected because the validation
set samples only the conditions it happened to include. Predicting the validation scatter from a
first-principles budget before seeing the validation data, and only then comparing, is the one
version of the test that is not circular.
Observability
H2982. A term whose influence was never varied cannot be estimated from the data at hand,
however many measurements were made, so a small value claimed for a term held constant claims
knowledge the data do not contain, and its contribution is bounded only by the range over which
it was held. Deliberately varying the neglected influence, at some cost, and measuring the
change, supplies an empirical bound where the budget previously had an assumption.
Conformity and decision rules
Degeneracy
H2983. Influences whose sensitivity coefficients stay in fixed proportion across the
whole operating range are one influence as far as the data are concerned, and a budget assigning
them separate uncertainties partitions an unobservable split. The split matters only if
something outside the data distinguishes them. Perturbing one influence while holding the other,
where the apparatus allows it, or comparing two instruments in which the ratio differs, breaks
the degeneracy and shows whether the split was meaningful.
Lag
H2984. Every budget silently describes the instrument at its calibration, while the
quantity that matters in use is the uncertainty under the conditions of use, and the difference
is a term growing with the interval since calibration, so a budget without a reference date is
incomplete rather than conservative. Recomputing the budget at two intervals since calibration
and comparing its drift prediction against a re-calibration measures the missing term directly.
Misattribution
H2985. A failed conformity decision is usually attributed to the instrument's accuracy
when it is the decision rule's position relative to the tolerance that failed, and the same
measurement would pass under a rule with a different guard band. The attribution is invisible
because a test report states the measurement and the verdict, not the rule. Recomputing the
verdict from the same measurement under two rules, and counting the cases that change, separates
the instrument's contribution from the rule's.
Hidden term
H2986. The guard band itself has an uncertainty, being derived from an estimated
uncertainty which is itself an estimate, and that second-order term is almost never carried into
the conformity statement; where the underlying estimate is poor the guard band is effectively
random within a range and the decision inherits the randomness. Recomputing the pass rate with
the guard band drawn from its own distribution rather than fixed at its central value shows how
much of the decision is rule-noise.
Identity
H2987. Choosing a guard band fixes the split of risk between producer and consumer, and
stating a split fixes the guard band, so the two are one parameter seen from two sides.
Documents presenting them as separate choices describe one choice twice. Deriving the guard band
from a stated risk split, and comparing it with the guard band in use, shows whether the two
descriptions agree.
Bound
H2988. No decision rule can hold both the consumer's and the producer's risk below a
floor set by the ratio of measurement uncertainty to tolerance width, because the two risks are
two tails of one distribution and shrinking both requires a narrower distribution rather than a
better rule. When that ratio exceeds roughly one third the floor climbs steeply (estimate).
Computing both risks across a range of ratios for a fixed rule, and finding where their sum
exceeds a stated level, gives the floor empirically.
Threshold
H2989. Conformity testing approaches a coin flip as measurement uncertainty approaches
the tolerance half-width, and the transition is sharp enough to locate: for an item truly at the
limit the pass probability falls from near certainty to near chance over a factor of about two
in that ratio (estimate). Below the threshold more testing helps; above it more testing only
sharpens the coin. Simulating pass probability against the ratio, or measuring it with a
calibrated artefact set at the limit, locates the transition.
Reversal
H2990. Tightening an acceptance limit to protect the consumer can loosen effective
control once measurement uncertainty dominates, because more truly conforming items fail and are
re-measured until they pass, and re-measurement selects the favourable error. The delivered
population then holds a higher fraction of items whose true value sits near the limit. Comparing
the true-value distribution of accepted items under two limits, using a calibrated reference
set, shows the reversal.
Count
H2991. Among tolerance width, measurement uncertainty, and the two risks, at most two are
free: fixing tolerance and uncertainty determines both risks, and fixing a risk and a tolerance
determines the greatest permissible uncertainty. A specification stating all four independently
is over-determined and at least one statement is redundant. Checking a specification's four
numbers against the relation that should connect them shows which one is decorative.
Artefact mimics effect
H2992. A bimodal distribution of results near a tolerance limit can be produced by the
rule itself, because failed items are re-measured and only passing re-measurements are recorded,
leaving a pile-up just inside the limit and a gap just outside that resembles genuine
manufacturing bimodality. Recording all measurements including repeats, and checking whether the
gap closes when repeats are admitted, distinguishes the rule's artefact from real population
structure.
Scale argument
H2993. One uncertainty-to-tolerance ratio is benign for a wide tolerance and fatal for a
narrow one, so a laboratory's conformity performance cannot be characterized by its uncertainty
alone; the ratio is needed, and the ratio changes with the product. A laboratory competent on
one product line can be incompetent on another with identical instruments. Recomputing the pass
rate for the same measurements against tolerance widths spanning a decade maps where the
verdicts stop carrying information.
Inversion
H2994. Accepting a lot on the mean of a sample can accept a lot that would fail item by
item, and rejecting on the mean can reject a lot whose items mostly conform, so the statistic
chosen decides the outcome more than the measurement does. The inversion is largest when lot
spread is comparable to the tolerance. Comparing the two rules on the same measured sample, and
on a lot whose true distribution is known from a reference set, quantifies the difference.
Selection effect
H2995. Conformity samples come from the accessible part of a lot, the top layer of a drum
or the outside of a coil, while the inaccessible part differs systematically because it has had
different handling, so the sample's conformity says little about the lot's. The bias is not
random and does not shrink with more samples from the same region. Sampling deliberately from
the least accessible region, at a cost, and comparing it with the accessible region, measures
the stratification that routine sampling cannot see.
Unit trap
H2996. A tolerance quoted as a plus-or-minus number without a stated coverage is
ambiguous by about a factor of two, because one reader takes it as a standard uncertainty and
another as an expanded uncertainty at ninety-five per cent, and both readings are defensible
while yielding different verdicts on the same measurement. Recomputing a batch of verdicts under
both readings, and counting disagreements, gives the cost of the missing word.
Derived quantity
H2997. A measurement capability index, tolerance width divided by expanded uncertainty,
is a ratio whose denominator is an estimate with substantial uncertainty of its own, so the
index's apparent precision is spurious and two laboratories of indistinguishable capability can
report indices differing by a third. The ratio also moves if the uncertainty is recomputed at a
different coverage. Propagating the denominator's uncertainty into the index, and comparing the
resulting interval against a decision threshold, shows how often the index decides something it
cannot support.
Non-identifiability
H2998. From pass or fail data alone the true distribution of the measurand and the
measurement uncertainty cannot both be recovered, because a wide true distribution with small
uncertainty and a narrow one with large uncertainty give the same acceptance rate. A conformity
dataset therefore cannot validate an uncertainty claim without an independent measurement.
Observing two acceptance limits yields two rates and two equations, making the problem
identifiable, and checking that the two-limit fit reproduces the single-limit rate tests the
model.
Hysteresis
H2999. A conformity decision made near a boundary depends on the previous decision for
the same item, because failure triggers re-measurement and the re-measurement's error is not
independent of the first, so the process has a memory no single-measurement model represents,
and the memory shows up as reduced variance among accepted items. Comparing the variance of
accepted items against the variance a memoryless model predicts, using items measured twice
regardless of outcome, exposes the dependence.
Closure
H3000. The disagreement between two independent traceability routes to one quantity
estimates their combined uncertainty better than either route's own budget, because each budget
omits terms its author could not see and the disagreement includes them. It should therefore
exceed the combined budget by a factor greater than one, and a factor near one suggests shared
terms rather than two complete routes. Computing the ratio of observed disagreement to combined
budget across many pairs of routes, and testing whether the ratios scatter above one, is the
test.
Status
100 of 1,000. Forms were tracked deliberately so that repetition would be visible rather than invisible; where a form appears twice the second instance had to earn its place with a different mechanism. Every entry is a claim about measurement, not about institutions.
Several of these are cheap to test with equipment most metrology laboratories already own: a comparator, two mounts, a thermometer, one afternoon. That is the point of writing them this way. None has been tested; a hypothesis list is worth the ideas in it, and a test is worth something else.
If one is worth an experiment, it is H3000 — that two traceability routes disagree by more than their combined budget predicts, systematically and by a factor above one. It needs only two routes to the same quantity and the willingness to publish both budgets before the comparison.
Incoprea Research · hand-considered hypotheses 2901–3000 · 3 November 2026 · ~/Desktop/Nov3/