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.