Calculation checks

For every study type, the values, confidence intervals and Met, Not met and Undecided outcomes are checked against answers worked out independently, against published examples, or both.

On the Results stage, Methods and sources shows the method and published sources behind each calculation, and Study reference lists them for every study type.

A separate program recalculated 86 studies covering all 21 study types, 16 of them published laboratory studies. It implements the documented formulas and published methods separately from the application’s calculation engine. All 1,904 values, 605 decisions and 114 limit-boundary checks matched the application’s result.

Each value and decision is compared with the result field that shows it. Values must agree within a relative tolerance of 1e-9 or an absolute tolerance of 1e-9, whichever is larger. Decisions (a Met, Not met or Undecided outcome, a zone, a grade or a chosen method) must match exactly. Boundary checks set a limit at the recalculated value, then just above and below it, and check the decision against exact arithmetic.

The QC targets (QC export) workup (24 values) and the allowable-error candidates (9 values) were recalculated and compared the same way. The engine methods covered are listed under Study reference.

Download the evaluation package (ZIP, 11.4 MB, source a5759c64c412; ZIP SHA-256 4b0d288e0f5f4dceb133629a912590de0da79e3c68411ca88dcae07a7a9538e6). Inside is one study of each type with its input data, settings, limits, expected values and rendered report, plus a manifest and instructions for the evaluator.

Of these studies, 16 use the data of 6 published laboratory sources, and the 90 values those sources print are compared with the recalculated result. A match means agreement within half a unit of the last printed digit.

Checked against the NIST mean, sample SD and Student t interval formulas, calculated independently.

Inputs 2, 4, 6, 8 and 10 give mean 6, sample variance 10 and SD √10. Intervals are checked at 90%, 95% and 99% confidence. The checks also cover 0,125 typed in a decimal-point study, which would otherwise read as 125.

Descriptive summary calculations and sources.

Checked against the NIST sample SD, CV and Student t mean-interval formulas.

A 20-result example gives mean 100.17, SD 0.936 and CV 0.935%. The mean limit is met, a CV limit of 0.8% is not, and the excluded result stays out of the calculation.

Repeatability calculations and sources.

Checked against independent nested variance-component calculations and the Chakravarthy 2019 and Wilkes 2018 precision datasets.

The checks cover repeatability, between-run and between-day components, and within-laboratory SD and CV, including components estimated at zero. Manufacturer-claim checks use independently calculated chi-square verification limits and effective degrees of freedom for balanced and unequal designs; they remain separate from direct laboratory limits.

Multi-day precision calculations and sources.

Checked against independent bias, recovery and combined-uncertainty calculations, the NIST Student t formulas, the Wilkes 2018 assigned-target dataset and the Chakravarthy 2019 daily means.

Results 2, 4, 6, 8 and 10 against an assigned value of 5 give bias +1, percent bias +20% and recovery 120%.

Correcting an assigned value from 100 to 110 makes a limit set on 100 read Undecided until you review it. For mean 100, the corrected 8%-or-6-unit allowance is 8.8 units, and a difference of 10 fails.

Bias against an assigned value calculations and sources.

Checked against the Giavarina 2015 example, the Giachino 2024 point-of-care device dataset and independent OLS, Deming, weighted Deming and Passing–Bablok calculations. Weighted Deming is checked against independently calculated values for the Linnet (1990) method.

Specimen acceptance is checked by exact counting. Twenty differences alternating −10 and +10 have mean 0 but none within ±5, so the limit is not met. With the greater of 6 mg/dL or 8%, comparative results 50, 75, 100, 200 and 300 get limits 6, 6, 8, 16 and 24. A difference exactly on a limit passes. Specimens with missing results are counted the same way under the comparison and lot rules.

Method comparison calculations and sources.

Checked against independent paired-difference calculations and the NIST Student t formulas.

Differences 4, 5 and 6 give mean bias 5 and SD 1. The checks also cover changing the reference instrument, replicate averaging, missing results and limit boundaries. With 24 specimens on three analyzers, a short sample excluded on analyzer C leaves C deciding on 23 of 23 specimens, while an unentered result on analyzer B keeps B Undecided. The specimen limit uses the same counts as method comparison.

Instrument comparison calculations and sources.

Checked against exact specimen differences and concentration-dependent allowable error, with replicates averaged for each specimen.

At previous-lot result 100 and a 10% limit, new result 89.9 fails (−10.1%), and results 90 and 110 pass at the limits. With the greater of 6 units or 8%, previous results 50, 75, 100 and 200 get limits 6, 6, 8 and 16. Missing pairs, uncovered limits and incomplete plans are never Met.

Supporting mean differences, intervals and imprecision are checked with independent Student t and chi-square calculations.

Reagent lot comparison calculations and sources.

Checked against independent least-squares calculations and the Xiao and Chambliss 2023 LDH dataset.

Slope, intercept, deviations and recovery match separately solved normal equations. Three levels prepared at only two distinct concentrations can't be calculated.

Linearity calculations and sources.

Checked against independently calculated dilution factors, corrected concentrations and recovery decisions.

Volumes of 100 + 400 give factor 5, and a measured 100 gives corrected concentration 500 and recovery 100%. Serial factors 5 × 2 give factor 10. The checks also cover mismatched factors, results outside the measuring interval and range endpoints.

Dilution verification calculations and sources.

Checked by independent counting of subject results and exact calculation of staged decision rules, including blood-donor albumin results from the UCI HCV data against the Hoffmann 2024 limits.

Against limits 70–100, results 69.9, 70, 85, 100 and 100.1 give 1 below, 3 within and 1 above. The checks also cover repeat subjects, separate partitions, one-sided limits and staged decisions.

Reference interval verification calculations and sources.

Checked against independent Hyndman–Fan type-6 quantile and binomial-rank calculations, normal-theory examples and independent calculations of log-normal intervals.

The checks cover one-sided and two-sided reference limits and their confidence intervals. Log-normal limits are compared with independent calculations at 90%, 95% and 99% confidence.

Reference interval establishment calculations and sources.

Checked against the FDA 2007 diagnostic-test guidance and independent agreement, Wilson-interval, kappa and McNemar calculations. Further interval checks use Fleiss–Cohen–Everitt and Newcombe examples and independent calculations. A nonreportable first result keeps an agreement limit from being Met.

Qualitative agreement calculations and sources.

Checked against independent Wilson intervals, probit fits and Fieller confidence limits.

A separate Fisher-scoring calculation gives the expected C5, C50 and C95. The checks cover hit-rate counts, confidence limits, failed fits and concentrations outside the measured range. A nonreportable replicate keeps a fitted-cutoff limit from being Met.

Near-cutoff precision calculations and sources.

Checked against independent Armbruster and Pry 2008 LoB and LoD calculations, percentile calculations and LoQ examples.

LoB checks cover normal-theory and rank-position percentile estimates with independent binomial-rank intervals. LoD checks recalculate the pooled low-level SD and LoB + c_β × SD. LoQ checks confirm the lowest tested concentration that meets the quantitation goal, and the resulting decision.

Detection limits calculations and sources.

Checked against the pSMILE 21-position calculation, with independently derived low-after-low SD, low-after-high means and decisions.

The checks cover all 21 positions, the signed mean difference and the rule that carryover must be below the error limit.

Carryover calculations and sources.

Checked against independent test-minus-control differences and the NIST Welch–Satterthwaite interval formulas.

The checks cover matched controls, absolute and percentage limits, intervals crossing a limit and missing controls. A test aliquot without a matched control stays in the result as undecided.

Interference calculations and sources.

Checked against independent paired-change and NIST Welch–Satterthwaite calculations, with separately derived Student t limits.

The checks cover paired and independent designs, a baseline for each condition, material counts, absolute and percentage changes, and the supported duration.

Stability calculations and sources.

Checked against independent examples of the Westgard, Bayat and Westgard 2019 sigma formula, Equation 5.

At concentration 100, TEa 6, absolute bias 1.5 and SD 0.9 give sigma 5. The checks also cover absolute and percentage inputs, unit conversions and zero imprecision.

Sigma metric calculations and sources.

Checked against independent assigned-concentration arithmetic, NIST Student t and chi-square intervals, and exact decisions at the laboratory's limits.

The checks cover material ranges, calculated assignments from independent preparation values, mean and individual-result accuracy, claimed-range coverage and the optional precision index. A mean within its allowance does not hide an individual result outside its allowance.

Calibration verification calculations and sources.

Checked against the WHO mean normal PT and INR equations, independent geometric-mean calculations and exact decisions using the entered INR precision.

The checks cover normal-interval endpoints, the programming-check rounding rule, separate parameters for each reagent lot and specimen-count acceptance with a complete lot plan.

PT and INR calculations and sources.

Checked against the published Clarke definitions and Parkes boundary coordinates, with independently assigned points in each zone.

The checks cover boundary decisions, equivalent mg/dL and mmol/L pairs, a pair exactly 20% apart in mmol/L, meter readings of 70 mg/dL against a low reference, the separate count of usable percentage differences and optional zone-percentage limits. The saved geometry supplies both zone classification and the plotted grid with its zone letters.

Glucose meter error grids calculations and sources.

Checked against independent bias and SDI arithmetic using the Eurachem proficiency-testing definitions.

The checks keep peer and all-method results separate, retain an event's bias when its group SD is missing, and compare local allowances directly. A provider's grade does not change the laboratory's own limit decision.

Proficiency tracking calculations and sources.

Checked against the Nordtest TR 537 fourth-edition component example and independent calculations for multiple assigned materials and one material measured across independent runs.

The checks cover assigned uncertainties and coverage factors, combined and expanded uncertainty, and exact equality at an expanded-uncertainty limit.

Measurement uncertainty calculations and sources.

Checked against independent decimal-arithmetic examples using the sample SD and CV definitions.

Results 139.0, 140.0 and 141.0 give mean 140, sample SD 1 and CV 5/7%. The checks cover grouping by instrument, lot, analyte and level, decimal rounding, baseline dates, exclusions and nonnumeric results.

QC targets (QC export) calculations and sources.

The report checks cover calculated results, sign-off and PDF output for every study type. Separate workflow examples exercise file import, corrections and reopening earlier signed reports. Published-study checks compare saved calculations with the frozen expected values, verify the saved report records and inspect PDF page structure.

Each check has fixed inputs, independently worked expected values and stated tolerances. A change that can alter a value or a decision you see gets a new Method ID, recorded with every saved result. See Study reference and About records and history.