What Is a Bland-Altman Plot?
A Bland-Altman plot (also called a difference plot or Tukey mean-difference plot) is a graphical method for comparing two measurement techniques. Introduced by J. Martin Bland and Douglas G. Altman in their landmark 1986 *Lancet* paper, it has become the standard method for assessing agreement between two quantitative methods of measurement.
Unlike correlation or regression analysis, the Bland-Altman method directly visualizes and quantifies the differences between two methods across the range of measurements. Two methods can be highly correlated (r = 0.99) yet disagree by a clinically significant amount.
How it works: For each paired measurement, the plot displays the mean of the two methods on the x-axis and the difference between them on the y-axis. Three horizontal reference lines mark the mean difference (bias) and the limits of agreement.
How to Interpret Bland-Altman Results
Mean Difference (Bias): The average difference between Method 1 and Method 2. A bias near zero indicates no systematic tendency for one method to read higher or lower.
Limits of Agreement (LoA): The range within which 95% of differences are expected to fall. Whether acceptable depends on clinical context.
Confidence Intervals on LoA: CI bands show the uncertainty in the LoA estimates.
Proportional Bias: If the regression slope is significantly non-zero (p < 0.05), disagreement changes with measurement magnitude.
Sample Size: At least 40 pairs recommended; 100+ for narrow CIs.
When to Use Bland-Altman Analysis
Use Bland-Altman analysis when:
- Validating a new method against a reference method
- Comparing two instruments measuring the same quantity
- Assessing inter-rater or intra-rater agreement
- Evaluating point-of-care devices against lab standards
- FDA 510(k) submissions or IVD validation
Do NOT use when: Comparing different quantities, data are categorical, or measurements are not paired.
Common applications: Clinical chemistry, diagnostics, medical imaging, respiratory medicine, cardiology, and sports science.
Difference, Ratio, and Percentage Modes
Difference Mode (default): d = Method 1 − Method 2. Use when variability is constant across the range.
Ratio Mode: r = Method 1 / Method 2. Use for data spanning several orders of magnitude.
Percentage Difference Mode: %d = (d / mean) × 100. Use when absolute difference scales proportionally with magnitude.
How to choose: If the Breusch-Pagan test is significant in Difference mode, try Ratio or Percentage mode.
Statistical Methodology
Core method: Bland JM, Altman DG. "Statistical methods for assessing agreement between two methods of clinical measurement." *The Lancet*, 1986;327(8476):307-310. PMID: 2868172.
Confidence intervals: SE = √(3s²/n) for LoA, with t-distribution critical values.
Proportional bias: Linear regression of differences on means with t-test for slope.
Normality: Shapiro-Wilk test on differences.
Heteroscedasticity: Breusch-Pagan test on squared residuals.
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