A validated method is not a better method. It is a method whose behavior has been measured, so that a number coming out of it can be held to a stated meaning. Validation does not make a result correct. It establishes the conditions under which the result is allowed to be believed, and the boundaries past which it is not. That distinction is the whole subject: an unvalidated measurement is not a measurement with wide error bars, it is a measurement whose error bars are unknown, and those are different situations. One can be reported with a caveat. The other cannot be reported at all without inventing the caveat.
This guide covers the parameters that carry most of the weight on a method report or a certificate: specificity, linearity, the limit of detection and the limit of quantification. It is about what each one actually demonstrates, how the detection and quantification limits are derived, and why the derivations disagree with each other by amounts large enough to matter.
Validation answers a question that has to be asked first
"Validated" is an incomplete sentence. A procedure is validated against requirements, and the requirements have to exist before the validation does. The analytical target profile formalizes this: it prospectively summarizes what a measurement on a given quality attribute has to deliver, and its criteria are framed as the maximum uncertainty in the reportable result that still supports acceptable confidence in the decision being made from that result [1]. One consequence of framing it that way is that more than one procedure can satisfy the same target profile [1]. The converse also follows from that framing, though the authors do not state it: a procedure that satisfies one target profile may be unfit for another.
So the useful question on a document is never "is this method validated" but "validated to what". A purity method validated to distinguish 98% material from 95% material is not thereby capable of resolving 99.5% from 99.0%. Nothing in the word "validated" tells you which one you are holding.
Specificity: the claim that the signal is only the analyte
Specificity is the assertion that the response being integrated or measured comes from the intended analyte and nothing else. It is the parameter on which every other parameter depends. A calibration curve built on a peak that secretly contains two species is a precise, linear, reproducible curve for the wrong quantity, and none of the precision statistics will notice.
The standard demonstration is forced degradation: stress the material deliberately, then show that the method still resolves the analyte from whatever the stress produced. In one published impurity method for a small-molecule drug substance, samples were subjected to hydrolysis, oxidation and heat as forced-degradation conditions, and the method was reported as stability indicating [2]. A stability-indicating method for a two-component mixture made the same argument and added two things: resolution of each analyte from its own forced-degradation peaks, and a diode-array detector used to check peak identity and purity; the authors also showed separation of both analytes from about thirteen other compounds [3].
What a peak-purity check can and cannot establish
A diode-array purity assessment compares the ultraviolet spectrum recorded across the width of a peak and flags the peak as impure when the spectra diverge. It can therefore only detect a co-eluting species whose spectrum differs from the analyte's, and only when that species contributes enough signal to move the comparison. Two structurally similar species — a peptide and a single-residue variant of the same peptide, for example — may have nearly indistinguishable spectra. We are not aware of a primary study that establishes a general detection threshold for spectral purity checking across peptide chemistries, and a "peak purity passed" statement should be read as evidence that one specific failure mode was looked for, not as proof that the peak is one compound.
Specificity also degrades when the sample matrix changes. Recommendations drawn from a systematic review of calibration practice in clinical mass spectrometry hold that matrix-matched calibrators and stable isotope-labeled internal standards help mitigate the impact of matrix effects [4]. Where a peptide is measured in a biological matrix rather than in clean solvent, the difficulty is attributed to both the complexity of the matrix and the analytical characteristics of the molecules themselves [5]. In one validated LC-MS/MS procedure for a peptide, recovery (84 ± 3%) and ion suppression (86 ± 4% of remaining intensity) were determined from calibration curves prepared specifically for that purpose [6] — that is, the suppression was measured rather than assumed away.
Linearity is a property of the residuals, not of r²
Linearity is the demonstration that response is proportional to concentration across the working range, within a stated tolerance. The correlation coefficient is a poor test of it. A coefficient very close to one is compatible with systematic curvature, because the statistic is dominated by the spread of the concentrations rather than by the fit at any particular point. The recommendation from the calibration review cited above is to assess linearity using the actual experimental data and appropriate statistics, and to consider both the analytical response and the measurand concentrations when constructing the curve [4].
What matters at the bench is the relative error at each level, and the denominator is the true value, not the measured one. If a calibrator prepared at 0.50 µg/mL reads back as 0.60 µg/mL, the error is (0.60 − 0.50) / 0.50 = 0.10 / 0.50 = 20% high. This is the arithmetic that gets reversed most often. A result of 5.00 against a true value of 4.10 is (5.00 − 4.10) / 4.10 = 0.90 / 4.10 = 22.0% high — not 18%. The 18% figure is what appears when the measured value is used as the denominator, which answers a different question than the one being asked.
Weighting, and why the top standard dominates an unweighted fit
Chromatographic and mass-spectrometric calibration data are frequently heteroscedastic: the absolute scatter in the response grows with concentration. Ordinary least squares minimizes the sum of squared absolute residuals, so the high standards take over the fit. Take a curve whose response is about 21,000 area counts per µg/mL and whose relative scatter is 2% at every level. At 1 µg/mL the response standard deviation is 0.02 × 21,000 = 420 counts; at 10 µg/mL it is 0.02 × 210,000 = 4,200 counts. In an unweighted fit those two points enter the objective function through their squared deviations, so the top standard's expected squared deviation is (4,200 / 420)² = 10² = 100 times the bottom standard's, and it dominates the sum being minimized by that factor. The curve is then fitted to the region where the analyst least needs accuracy, and the low end — where the detection and quantification limits live — is where the resulting bias lands.
The remedy is weighting, and the review of calibration practice recommends investigating heteroscedasticity and applying appropriate weighting [4]. Choosing the weights is itself contested. The "quality coefficient" long used in bioanalytical work to select a weighting formula has been shown to be statistically flawed for that purpose, because it is computed in a form that predisposes it to favor whichever error structure matches its own definition — absolute-difference versions favor homoscedastic data, relative-difference versions favor data with constant coefficient of variation [7]. The author's conclusion was that even a modified version combining both tests, while more reliable than either alone, is not recommended when statistically sound alternatives exist [7].
The range is anchored at the quantification limit
Range is not a separate discovery; it is the interval over which specificity, linearity and accuracy have all been shown to hold simultaneously. In practice its lower bound is the LOQ. The impurity method mentioned above established linearity from the LOQ to a concentration level of 200% and accuracy from the LOQ to 150% [2]. A result below the lower bound is outside the validated range whether or not the software prints a number for it.
LOD and LOQ: several derivations, and they do not agree
The detection limit is the lowest concentration at which the analyte can be reliably distinguished from nothing. The quantification limit is the lowest concentration at which a number can be assigned with acceptable precision and accuracy. They are different claims, and the gap between them is where most misreporting happens.
There is no single derivation. A tutorial reviewing the most frequently reported criteria for computing LOD and LOQ in univariate calibration concluded that the criteria rest on diverse theoretical and/or empirical assumptions, require different amounts of experimental data, and that alternative forms of the calculation frequently lead to dissimilar results — a scenario the authors say might worsen in the case of complex analytical systems [8]. A review of detection-limit estimation for one trace element by ICP-MS reached a compatible practical recommendation: apply several estimation methods and test a large number of replicates, because, in those authors' words, the differences and equivalency of the various estimation approaches could be overcome by an experimental comparison [9].
From the calibration statistics
The most common approach derives both limits from the regression: a multiple of the standard deviation of the response divided by the slope. With the conventional coefficients of 3.3 for the detection limit and 10 for the quantification limit, a method with a residual response standard deviation of 420 area counts and a slope of 21,000 counts per µg/mL gives LOD = 3.3 × 420 / 21,000 = 1,386 / 21,000 = 0.066 µg/mL and LOQ = 10 × 420 / 21,000 = 4,200 / 21,000 = 0.20 µg/mL. Note that the ratio between them is fixed by the coefficients at 10 / 3.3 = 3.0, regardless of the instrument. An LOD and LOQ pair reported at a ratio of about three is consistent with having been produced this way, and in that case the pair carries one piece of information rather than two.
From signal-to-noise, and from the blank
The alternatives measure the low end directly: signal-to-noise ratios at a low standard, or the standard deviation of blank measurements. These do not track the regression-based values, and they do not track one another either: which derivation returns the larger limit depends on which pair is being compared and on the study. Applying several official recommendations to the same impurity determination by HPLC with UV detection, one group found that the visual and signal-to-noise approaches produced the smallest detection and quantification limits — values that fell outside the method's linear range — and judged the approach based on the analytical curve parameters the most statistically reliable of those tested [10]. In gas chromatography with flame-ionization detection, another group compared the signal-to-noise concept against a different reference point — the standard deviation of the blank — and there the signal-to-noise values were the larger ones: limits determined by the signal-to-noise concept were about three times higher than those estimated from the standard deviation of the blank, for both the one-dimensional and comprehensive two-dimensional configurations they examined, and the values also shifted with data acquisition frequency [11].
A third family of approaches builds the limit from tolerance intervals rather than from the regression. Comparing an uncertainty-profile approach, an accuracy-profile approach and the classical calibration-parameter calculation on a single HPLC dataset, one group reported that the classical strategy gave underestimated LOD and LOQ values while the two graphical approaches agreed with each other to the same order of magnitude [12].
The practical reading is that an LOD or LOQ quoted without its derivation is not a comparable quantity. Two vendors quoting different limits for the same assay may be reporting the same instrument performance through different arithmetic.
What a result between the LOD and the LOQ means
Using the worked example above, a sample returning 0.12 µg/mL sits above the detection limit of 0.066 and below the quantification limit of 0.20. The correct statement is that the analyte was detected and not quantified. It is not "0.12 µg/mL". It is also not "not detected", and reporting it as zero is the more damaging of the two errors, because it converts a real observation into a false negative that no downstream analysis can recover.
Why an unvalidated number is uninterpretable rather than merely uncertain
An uncertain number has a known distribution around a value. You can propagate it, average it, and decide whether it is fit to act on. An unvalidated number has none of that structure. Without a specificity demonstration, you do not know that it refers to the intended compound. Without linearity across the relevant interval, you do not know that the response-to-concentration mapping used to compute it applies at the concentration observed. Without an LOQ, you do not know whether it is above the level at which the method can assign a value at all. Each missing parameter removes a premise the number depends on, and a conclusion with a missing premise is not a weaker conclusion — it is a different kind of object.
This is why "the method is probably fine" does not rescue the result. Probably fine is a statement about the method. The reportable number needs a statement about itself.
What remains unsettled, and what is convention
Considerable parts of this territory are convention with thin primary literature underneath. The coefficients 3.3 and 10, and the signal-to-noise thresholds of 3 and 10, are inherited conventions rather than results derived for any particular chemistry; the literature cited above is largely a record of what happens when the different conventions are applied to the same data, not of one being shown correct. The tutorial and review literature approaches the choice of derivation by experimental comparison across criteria rather than by a settled rule, and recommends applying more than one [8, 9]. Reporting which one was used is our own reading of what follows from that, not a recommendation we found stated as such.
For peptides specifically, assigning a value is its own unresolved problem, separate from getting a clean separation. In a multi-laboratory collaborative study comparing an HPLC assay, quantitative NMR and amino acid analysis for one nonapeptide, the HPLC assay run against the same bulk material as its standard showed the lowest inter-laboratory variability — with the caveat, stated by the authors, that this coefficient of variation excluded the uncertainty attached to the mass-balance purity assignment of that standard [13]. Peptide adsorption and degradation are recognized as issues of particular concern for this class in quantitative bioanalysis [5], which means a validation performed on freshly prepared solutions does not automatically transfer to the same method run on stored ones. That is a limitation of scope, not a defect, provided the scope is stated.