Bland-Altman Calculator
Bland–Altman method comparison — mean difference (bias), SD of differences, 95% limits of agreement with confidence intervals and the points outside the limits.
How it works
dᵢ = Aᵢ − Bᵢ (or 100·(Aᵢ − Bᵢ) ÷ mean); bias = d̄; LoA = d̄ ± 1.96·s_d; CI of bias = d̄ ± t(0.975, n−1)·s_d/√n; CI of each limit = LoA ± t(0.975, n−1)·√(3s_d²/n)
Bland and Altman (1986) showed that a correlation coefficient cannot tell you whether two measurement methods agree. Instead, plot the difference of each pair against its mean: the average difference is the systematic bias, and the 95% limits of agreement show the range within which most differences between the methods fall. Whether the limits are narrow enough is a clinical or engineering judgement, not a statistical one. The confidence intervals use the approximate standard error √(3s²/n) for the limits (Bland & Altman, 1999).
Worked example
Twelve paired readings give a bias of 2.92 with an SD of 3.09, so the 95% limits of agreement run from −3.14 to 8.97; the bias CI is 0.95 to 4.88 and no point falls outside the limits.
Sources: Bland & Altman (1986), Statistical methods for assessing agreement between two methods of clinical measurement, The Lancet · Bland & Altman (1999), Measuring agreement in method comparison studies
Frequently asked questions
Why not just use correlation?
Two methods can be perfectly correlated yet disagree by a constant or a proportional amount. Bland–Altman measures agreement directly, in the units of measurement.
When should I use percentage differences?
When the spread of the differences grows with the size of the measurement (a funnel shape on the plot). Expressing differences as a percentage of the mean usually makes the spread constant.
What counts as acceptable agreement?
Decide before the study how big a difference would matter in practice; the methods agree if the limits of agreement (and ideally their confidence intervals) lie inside that range.
Does the test assume normality?
The ±1.96 SD limits assume the differences are roughly normal. Check this with a histogram or a Shapiro–Wilk test on the differences.
Related calculators
Educational tool: check the test’s assumptions (sample size, independence, distribution) before relying on a result for a real decision.