Bland-Altman Analysis Calculator

Compare two measurement methods with a Bland-Altman analysis: the bias, limits of agreement, confidence intervals for each, a trend check and the difference plot.

Result

Deterministic calculation

Bias (A − B)

1 (95% CI −2.461 to 4.461)

Standard deviation of the differences: 4.14
Lower limit of agreement: −7.115 (95% CI −13.3 to −0.9278)
Upper limit of agreement: 9.115 (95% CI 2.928 to 15.3)
Does the difference change with the size?: r = 0.55, p = 0.16
Pairs: 8

Pairs

Note

Bland-Altman analysis describes agreement: how far apart two methods' results for the same sample are likely to be. It does not say whether the agreement is good enough; that is a judgement about the clinical or scientific use, made before the analysis.

Note

It assumes the differences are roughly normal and that their spread does not depend on the size of the measurement. If the points fan out as the mean increases, or the trend test above is small, consider analysing ratios or logarithms instead. The repeated measures, if any, should not be treated as independent pairs.

Note

The p-value is the probability, if the null hypothesis and every assumption of the test were true, of a result at least as extreme as the one observed. It is not the probability that the hypothesis is true, and it says nothing about how large or important an effect is. Judge the effect size and its interval, the design and the assumptions along with it, and do not treat a p-value on one side of 0.05 as proof of an effect or of its absence.

Note

With fewer than about thirty pairs the limits of agreement are imprecise, as the confidence intervals show.

Significant figuresScientific notation

Calculation

differences dᵢ = A − B; bias = mean(d) = 1; SD(d) = 4.14
limits of agreement = bias ± 1.96 SD(d), which should contain about 95% of differences
standard error of a limit = SD √(1/n + 1.96² / (2(n − 1))) (Bland and Altman 1999); intervals use t with n − 1 degrees of freedom
the plotted values run from 96.5 to 127

Formula

\text{bias} = \overline{A - B}

\text{limits of agreement} = \text{bias} \pm 1.96\,s_{A-B}

\mathrm{SE}_{\text{limit}} = s\sqrt{\dfrac{1}{n} + \dfrac{1.96^2}{2(n - 1)}}

$\text{bias}$: the average difference between the methods
$\text{limits of agreement}$: the range expected to contain about 95% of differences

How it works

Two methods that measure the same thing will not agree exactly. A Bland-Altman analysis describes the disagreement: it plots the difference between the methods for each sample against the mean of the two, and summarises it by the bias (the mean difference) and the limits of agreement (the mean plus and minus 1.96 standard deviations), which should contain about 95% of the differences.

Correlation is not a measure of agreement, since two methods can be perfectly correlated and still differ by a constant or proportional amount. The limits are estimates, and the page gives confidence intervals for each. Whether the agreement is good enough is a scientific or clinical judgement, made in advance, not something the calculation decides. If the spread of differences grows with the size of the measurement, the analysis should use ratios or logarithms.

Worked example

Eight samples measured by two methods.

The differences have mean (bias) 1.0 and SD 4.14.
Limits of agreement: −7.12 to +9.12; the 95% CI of the bias is −2.46 to 4.46.
The trend of difference against mean has r = 0.55, p = 0.16.

Method A reads 1.0 higher on average, and for a given sample the two methods are expected to differ by between −7.1 and +9.1.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

Each pair is one sample measured once by each method.
The differences are roughly normal, with a spread that does not change with the size of the measurement.
Independent samples; repeated measures need a different analysis.

Common mistakes

Using the correlation coefficient or a paired t-test as a measure of agreement.
Ignoring a trend in the differences with the mean.
Judging agreement from a handful of pairs, where the intervals are wide.

Paired t-Test CalculatorPaired t-test on before-and-after or matched measurementsOpen calculator Correlation Calculator (Pearson and Spearman)Pearson r or Spearman ρ with a confidence interval and p-valueOpen calculator Linear Regression CalculatorSlope, intercept, R², standard errors, intervals, residuals and predictionOpen calculator Percent Error CalculatorPercent error of a measured value against an accepted oneOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.

Bland-Altman Analysis Calculator

Result

Calculation

Formula

How it works

Worked example

Assumptions

Common mistakes

Related tools

Related equipment

Result

Calculation