Diagnostics › Method comparison

Bland–Altman plot

A Bland-Altman plot assesses agreement between two measurement methods by plotting each pair's difference against its mean, with 95% limits of agreement.

What is Bland–Altman plot?

Bland-Altman dethroned correlation as the method-comparison standard in the 1980s. The argument: correlation tells you whether two methods rank subjects the same way (concordance), but two methods can be perfectly correlated and yet differ by a constant or proportional bias that matters clinically. The mean-difference plot makes both visible.

Bias is the mean of the differences (B − A). LoA is bias ± 1.96·SD_diff — the range within which 95% of differences should fall under approximate normality. If the LoA is narrow enough that you'd be willing to use the methods interchangeably for clinical decisions, the methods agree; if not, they don't, regardless of correlation.

Look for two patterns in the plot: a non-zero mean line (constant bias) and a sloping trend or fanning (proportional bias / heteroscedasticity). The first means one method is biased high or low; the second means the bias depends on the magnitude.

When should I use Bland–Altman plot?

  • Comparing a new measurement method against a reference (gold standard or established assay).
  • Comparing two interchangeable devices on the same samples.
  • Reporting agreement after a calibration step.

What data does it need?

Two numeric columns, row-paired (one measurement per subject per method).

What does it report?

Bias, SD of differences, 95% LoA + CI on each LoA. Optional percentage-difference mode for proportional-bias data. Proportional-bias regression of difference on mean with CI band.

What does it assume?

  • Independent paired observations.
  • Differences are approximately normal (CLT covers moderate n).
  • Constant variance of differences across the measurement range — if violated, switch to percentage difference.

Formula

LoA = mean(diff) ± 1.96 · SD(diff); SE(LoA) = SD(diff) · √(1/n + 1.96² / (2(n − 1)))

How do I interpret the result?

The LoA is the *predictive* range — where you expect a new pair of measurements to differ. The CI on the LoA itself shows how precisely the LoA is estimated.

A proportional-bias slope significantly different from 0 ⇒ the methods don't agree the same way at low vs high magnitudes ⇒ report percentage difference or model the bias.

See also

References

  • Bland & Altman (1986). Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 327(8476).