Bland–Altman Agreement Analyzer

Method

Difference mode analyzes A − B against the arithmetic pair mean. Ratio mode analyzes ln(A/B) against the log geometric pair mean, then exponentiates the center and interval endpoints; the reported center is therefore a geometric mean of paired ratios, not a ratio of arithmetic means. Symmetric-percentage mode analyzes 100 ln(A/B) against the log geometric pair mean. On the selected analysis scale, estimated 95% limits of agreement are the sample center plus or minus 1.9599639845 sample SDs. The center interval uses Student's t distribution. Exact individual 95% confidence intervals for the lower and upper limits use noncentral-t normal-percentile pivots and are generally asymmetric. The exact simultaneous two-sided normal 95%/95% tolerance interval uses a separate versioned lookup of exact factors.

Statistical diagnostics

Exploratory diagnostics operate on the selected analysis scale: differences against arithmetic pair means in difference mode, and log ratios or symmetric percentages against log geometric pair means in the alternative modes. They include ordinary least-squares regression, a Breusch–Pagan score based on squared regression residuals, Shapiro–Wilk W and its approximate p-value, adjusted sample skewness, a histogram, and observed confidence-interval widths. These are descriptive aids rather than a validation score.

Assumptions and limitations

• Exactly one independent pair is supplied for each target.
• Both methods measure the same quantity in compatible units.
• The selected difference, log-ratio, or symmetric-percentage values are adequately represented by an independent normal distribution with constant center and spread.
• Ratio and symmetric-percentage modes require every measurement to be strictly positive and are inappropriate where zero is arbitrary or ratios lack scientific meaning.
• Acceptable ratio limits must be positive and oriented as Method A divided by Method B; swapping methods reciprocates and reverses them.
• 100 ln(A/B) is Cole's symmetric percentage difference and must not be interpreted as an ordinary percentage change.
• Regression on pair magnitude can be affected by unequal method variances and does not by itself prove a specific magnitude-dependent bias mechanism.
• Shapiro–Wilk significance depends on sample size; a large p-value does not prove normality, and a small p-value does not automatically make the analysis unusable.
• The Q–Q plot, histogram, heteroscedasticity score, and precision widths require contextual interpretation.
• Repeated, clustered, nested, nonparametric, and multi-method analyses remain outside this release.

Important warnings

Bland–Altman statistics do not by themselves establish clinical interchangeability, regulatory acceptance, device equivalence, validity, or patient benefit. The analysis scale and acceptable limits must be justified from intended use and consequences.

Privacy

Manual, pasted, and uploaded data are processed in browser memory. The app does not intentionally transmit measurements, file names, worksheet names, or column names and does not store them in localStorage or IndexedDB.

Validation status

Version 2.1.0 completed the documented automated benchmarks, independent numerical comparisons, owner review, accessibility checks, responsive-layout review, and production-build checks on 7 August 2026. This documented scope is not a claim of regulatory validation, universal correctness, or suitability for every clinical application.

Current application version: 2.2.0. The interface and reporting refinements retain the statistical calculations. Automated tests, responsive rendering, PDF pagination, production-build checks, and the owner-confirmed browser/Windows Narrator review passed. Version 2.2.0 was accepted as the shared interface reference design on 8 September 2026.

References

1. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1(8476):307–310.
2. Bland JM, Altman DG. Measuring agreement in method comparison studies. Stat Methods Med Res. 1999;8(2):135–160.
3. Cole TJ. Sympercents: symmetric percentage differences on the 100 log(e) scale simplify the presentation of log transformed data. Stat Med. 2000;19(22):3109–3125.
4. Carkeet A. Exact parametric confidence intervals for Bland–Altman limits of agreement. Optom Vis Sci. 2015;92(3):e71–e80.
5. Carkeet A, Goh YT. Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals. Stat Methods Med Res. 2018;27(5):1559–1574.
6. Royston P. Remark AS R94: A remark on Algorithm AS 181: The W-test for normality. Appl Stat. 1995;44(4):547–551.
7. Breusch TS, Pagan AR. A simple test for heteroscedasticity and random coefficient variation. Econometrica. 1979;47(5):1287–1294.
8. Young DS, Cheng K. tolerance: Statistical Tolerance Intervals and Regions. Version 3.0.0.