Repeatability
Closeness among results under stated same-condition measurements.
Unit Converters
Concentration Precision Calculator
Preserve every repeat, normalize its unit, quantify repeatability, and keep accuracy evidence separate through an optional reference concentration.
Analytical repeatability
Separate concentration precision from accuracy
Analyze same-condition concentration repeats after unit normalization. The page calculates sample standard deviation, relative standard deviation, range, and Type A uncertainty of the mean; an optional assigned reference adds bias and recovery without redefining repeatability.
Repeat count—
Mean concentration—
Sample standard deviation—
Relative standard deviation—
Type A uncertainty of mean—
Recovery versus reference—
Repeat-by-repeat analytical ledgerUnrounded values drive calculations and decisions
| Run | Reported result | Normalized result | Deviation from mean | Deviation from reference |
|---|
How to use
Separate concentration precision from accuracy
Analyze same-condition concentration repeats after unit normalization. The page calculates sample standard deviation, relative standard deviation, range, and Type A uncertainty of the mean; an optional assigned reference adds bias and recovery without redefining repeatability.
- Enter results produced under one declared repeatability condition.
- Choose the unit used by the instrument or analytical report.
- Choose the unit needed for the review.
- Enter an assigned reference only when it is traceable and condition matched.
- Read precision statistics separately from bias and recovery.
Repeatability, bias, and uncertainty quantities
Sample standard deviation
Spread estimate using n − 1 degrees of freedom.
RSD
Sample standard deviation divided by the mean.
Type A uncertainty
Standard uncertainty of the repeat mean estimated as s/√n.
Recovery
Mean divided by an assigned reference; it addresses accuracy evidence, not precision.
Result interpretation
Read precision separately from recovery
A narrow strip and low RSD show that these runs agree with each other. They do not prove that the agreed value is correct. Recovery and bias appear only when a defensible reference is entered, so the page cannot turn repeated agreement into an unsupported accuracy claim.
Calculation method
Normalize repeats before calculating analytical spread
Convert every record through kg/m³, calculate the arithmetic mean from unrounded normalized values, then calculate sample standard deviation with n − 1. Divide the standard deviation by the mean for RSD and by √n for Type A uncertainty. If a reference is present, calculate mean minus reference and mean divided by reference.
Evidence controls
Control the repeatability evidence before reporting precision
One measurand and matrix
Do not combine different analytes, chemical forms, matrices, methods, dilutions, or reporting bases in one repeat set.
Independence of repeats
Repeated reads of one unchanged instrument cell may omit sampling and preparation variation. Describe what was actually repeated.
Order reveals drift
Preserve acquisition order so warm-up, carryover, evaporation, reaction, or calibration drift remains visible.
Reference commutability
A certified solution or spike must behave adequately like the samples before recovery supports accuracy.
Non-detects and censoring
Do not replace less-than values with arbitrary numbers merely to obtain a standard deviation. Follow the analytical method.
Outlier governance
Apply only a pre-authorized outlier rule, retain excluded observations, and report both the rule and reason.
Uncertainty budget
Type A is one component; calibration, preparation, standards, recovery, resolution, and environmental effects may also matter.
Visual explanation
Ordered repeatability strip with mean and one-standard-deviation band
Each point remains in run order. The mean line identifies the calculated center, while the blue band spans one sample standard deviation. The pattern can reveal drift or clustering that a single RSD card would hide.
Detailed calculation process
Recalculate Separate concentration precision from accuracy from current inputs
c̄ = Σci/n; s = √[Σ(ci − c̄)²/(n − 1)]; RSD = 100s/c̄; uA = s/√n; recovery = 100c̄/cref
| Symbol | Meaning | Required unit |
|---|---|---|
| ci | normalized concentration for run i | selected target unit |
| n | number of valid repeats | count |
| c̄ | repeat mean | target unit |
| s | sample standard deviation | target unit |
| uA | Type A standard uncertainty of mean | target unit |
| cref | optional assigned reference concentration | target unit |
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Reconciliation:Waiting for current inputs.
Defaults and assumptions
Separate concentration precision from accuracy starting assumptions
The six starting values are one demonstration repeat series centered near 25 mg/L. They are not five alternative answers and not a regulatory dataset. Replace the complete series with actual same-condition repeats.
| Check | Current value A | Current value B | Decision role |
|---|
Decision analysis
Decide whether the repeat set supports the intended review
Compare RSD or standard deviation with a method-specific precision criterion, then assess recovery or bias under a separate accuracy criterion. If either criterion is absent, report the statistic without inventing a pass/fail decision.
Investigate ordered residuals before trusting the summary. A monotonic rise may indicate drift, alternating values may reflect resolution, and one isolated result may reflect preparation or transcription. Verify dilution factors and calibration status before increasing repeats. More observations reduce Type A uncertainty of the mean only when the measurements are representative and sufficiently independent. For compliance work, name whether the decision concerns an individual result, a batch mean, or method performance; those are different measurands and require different uncertainty and acceptance rules.
Verification workflow
Build the concentration precision evidence chain
Design the repeat series before collecting it
Define whether the study repeats instrument reads, vial injections, aliquots, preparations, analysts, days, or laboratories. Those designs estimate different variance components. Use enough observations for the governing precision study and record their order before looking at results. Keep the sample stable, or document its changing state as part of the measurand. If an instrument automatically averages scans, distinguish those internal scans from independent reported repeats. A credible precision statement names the conditions held constant and those intentionally varied.
Review residual shape, not only its width
Plot signed deviations in acquisition order and look for monotonic drift, steps after recalibration, alternating resolution patterns, clusters, and dependence on concentration. The sample standard deviation summarizes spread but does not explain structure. A trend can make the nominal degrees of freedom optimistic, while two clusters may mean that incompatible conditions were combined. When the response variance grows with concentration, compare RSD across levels or use the method’s concentration-dependent precision function rather than one universal absolute limit.
Separate accuracy evidence cleanly
An assigned reference should have identity, value, uncertainty, matrix relevance, expiry, preparation history, and traceability appropriate to the analytical question. Recovery from a spike is not identical to bias against a certified matrix material, and neither automatically transfers to routine samples. Report bias in concentration units and recovery in percent, then apply the criterion specified by the method. Never alter the repeat values to force recovery to 100% unless a documented correction model requires that operation.
Build the broader uncertainty record
Type A uncertainty of the repeat mean is only the statistical component shown here. Add justified components for reference preparation, volumetric glassware, pipettes, calibration function, blank, recovery, instrument resolution, environmental influence, and sample preparation. Consider correlation when the same stock solution or calibration is shared across repeats. State whether the final uncertainty applies to an individual result or the reported mean, and state the coverage method before comparing it with a tolerance.
Close the review with reproducible evidence
Archive the exact numeric series rather than a screenshot of summary cards. Link it to sample identifiers, raw responses, calculations, excluded results, units, software revision, and reviewer disposition. Recalculate the mean and signed-deviation sum independently for critical work. When the precision requirement fails, investigate cause before simply increasing n: more repeats can narrow uncertainty of a biased or unstable process without making the method suitable. Record corrective action and the new study as separate evidence.
Evidence and data lineage
Records required for Separate concentration precision from accuracy
Retain analyte identity, matrix, method revision, instrument, calibration, standards, preparation batch, operator, timestamps, dilution history, raw response, reported unit, temperature where relevant, reference certificate, recovery criterion, and any excluded result.
Limits and exclusions
Boundaries of Separate concentration precision from accuracy
The model does not estimate trueness without a reference, correct matrix effects, choose an outlier test, establish detection capability, model autocorrelation, pool reproducibility data, or construct a complete uncertainty budget.
Reference framework
Authority for Separate concentration precision from accuracy
Use the International Vocabulary of Metrology to keep precision, repeatability, trueness, bias, and uncertainty distinct. The JCGM Guide to the Expression of Uncertainty in Measurement supports evaluating Type A components statistically while requiring other justified components to remain in the uncertainty model. NIST Special Publication 811 provides SI quantity and unit conventions for mass concentration. The calculator implements those distinctions, but it does not claim that one repeat design satisfies a particular laboratory accreditation, pharmacopeial, environmental, or product method. Cite the governing analytical standard alongside the exported record and preserve its acceptance limits, significant-digit rules, and required control design.
Separate concentration precision from accuracy terminology
AnalyteChemical entity reported by the method.
RepeatOne result included in the same-condition series.
BiasMean minus assigned reference.
RecoveryMeasured mean as a percentage of assigned reference.
Degrees of freedomn − 1 for this sample spread estimate.
Type AUncertainty evaluated from statistical observations.
Matrix effectSample-composition effect on measurement response.
CommutabilityReference behavior sufficiently like routine samples.
Worked decision cases
Separate concentration precision from accuracy decisions in practice
Instrument repeat check
Six reads of one prepared standard quantify short-term instrumental repeatability but not preparation variation.
Independent sample preparations
Replicate extractions include more of the routine method and commonly produce a larger, more representative spread.
Important note
Before relying on Separate concentration precision from accuracy
Precision is agreement, not truth. Never use a low RSD to excuse an unacceptable recovery or an unverified reference.
Separate concentration precision from accuracy FAQ
Why are several numbers entered?
Each number is a separate repeat of the same concentration measurement. The statistics describe the group, not one selected row.
Which result is the final result?
The mean is the group center; SD, RSD, range, and Type A describe its spread. Every row remains evidence.
Can I enter one result?
No. Sample standard deviation requires at least two observations.
Why use n − 1?
The mean is estimated from the same sample, leaving n − 1 degrees of freedom.
Is RSD always appropriate?
No. It becomes unstable near zero and may not match a method whose repeatability is specified in concentration units.
Does more data remove bias?
No. Repeating a biased process can estimate its biased mean more precisely.
Can I mix units?
Use one source unit per series. Convert externally documented exceptions before entry.
Should I sort the values?
No. Order can expose drift, carryover, or instability.
Can recovery exceed 100%?
Yes; it can indicate positive bias, matrix enhancement, contamination, or reference uncertainty.
Is Type A expanded uncertainty?
No. It is a standard uncertainty component, not automatically a coverage-expanded uncertainty.