Bland-Altman Analysis

Bland-Altman assesses agreement between two measurement methods that are supposed to measure the same thing. Answers whether methods agree closely enough to be used interchangeably — not merely whether they correlate.


Step 1 — Provide paired measurements

Two columns of same length:

  • Method 1 measurements
  • Method 2 measurements

Row i = same subject measured by both methods.

Supports Excel Import, Manual Entry, and Sample Data.


Step 2 — Results

  • Mean difference (bias) with 95% CI
  • SD of differences
  • Upper Limit of Agreement with 95% CI
  • Lower Limit of Agreement with 95% CI
  • Percentage within LoA (should be ~95%)
  • Proportional bias test — regression of differences on means

Bland-Altman plot — mean of methods (x) vs difference (y), with bias and LoA lines.

A UniversalChatBot is available for discussion.


Statistical methods used

Core quantities

  • Difference: d_i = method1_i - method2_i
  • Mean: m_i = (method1_i + method2_i) / 2
  • Bias: d_bar = mean(d_i)
  • SD: s_d = SD(d_i)

Limits of Agreement

Upper LoA = d_bar + 1.96 * s_d
Lower LoA = d_bar - 1.96 * s_d

If clinically acceptable, methods are interchangeable.

CI for LoA

SE(LoA) = sqrt((1/n + 1.96^2 / (2*(n-1))) * s_d^2)

Proportional bias

Regression: d_i = beta0 + beta1 * m_i. If slope != 0, disagreement changes with magnitude.

H0: slope = 0 (no proportional bias). alpha = 0.05.

Why not correlation? High correlation does not mean agreement — methods can correlate perfectly yet differ by a constant. Bland-Altman quantifies actual disagreement.