Bland–Altman Plot
A scatter plot showing the difference between two measurement methods against their mean — revealing systematic bias and limits of agreement at a glance.
// 01 — The chart
What it looks like
A Bland–Altman plot comparing two blood pressure devices. The solid line shows mean bias (+3.2 mmHg), dashed lines show 95% limits of agreement. Most points fall within the limits, indicating acceptable agreement.
// 02 — Definition
What is a Bland–Altman plot?
A Bland–Altman plot (also called a difference plot or Tukey mean-difference plot) is a scatter plot that evaluates the agreement between two quantitative measurement methods. Instead of simply correlating the two measurements, it plots the difference between them on the y-axis against their mean on the x-axis.
Three horizontal reference lines define the plot’s structure: a center line at the mean difference (the bias) and two outer lines at the limits of agreement (mean ± 1.96 × SD). If the two methods agree perfectly, all points would lie on the zero line with no scatter.
The key insight this plot reveals is whether the difference between methods is consistent across the measurement range. A correlation coefficient alone can be misleadingly high even when two methods disagree substantially — the Bland–Altman approach exposes both systematic bias and proportional error that correlation hides.
Origin: The plot was introduced by J. Martin Bland and Douglas G. Altman in their landmark 1986 paper in The Lancet, “Statistical methods for assessing agreement between two methods of clinical measurement.” It remains one of the most cited papers in medical statistics.
// 03 — Anatomy
Parts of a Bland–Altman plot
// 04 — Usage
When to use it — and when not to
- You need to assess agreement (not just correlation) between two measurement methods
- You want to visualize systematic bias and its consistency across the measurement range
- Validating a new clinical instrument against an established reference method
- Checking whether measurement error is proportional to the magnitude being measured
- Reporting limits of agreement to define clinically acceptable tolerances
- You have paired continuous data from two methods measuring the same quantity
- You only want to show correlation — a scatter plot with regression line is simpler
- Your data is categorical or ordinal rather than continuous
- You have more than two methods to compare simultaneously — consider a matrix approach
- Your measurements are not paired (different subjects for each method)
- Sample size is very small (< 10 pairs) — limits of agreement become unreliable
- You need to predict one method from another — use regression instead
// 05 — Reading guide
How to read a Bland–Altman plot
Follow these steps whenever you encounter a Bland–Altman plot in the wild.
Locate the mean bias line
The solid horizontal line shows the average difference between the two methods. If it sits at zero, there is no systematic bias. If it is above or below zero, one method consistently reads higher or lower than the other.
Check the limits of agreement
The two dashed horizontal lines (mean ± 1.96 SD) define the range within which 95% of differences are expected to fall. Narrow limits mean the methods agree closely; wide limits mean large random variation between methods.
Look for points outside the limits
Any points beyond the limits of agreement are outliers — individual cases where the two methods disagreed more than expected. Investigate whether these are measurement errors or genuine discrepancies.
Check for proportional bias
If the scatter of points fans out (wider spread at higher mean values) or slopes upward/downward, the difference depends on the magnitude. This proportional bias means a simple additive correction won’t work.
Decide clinical significance
Narrow statistical limits don’t always mean clinical acceptability. Compare the limits of agreement against a pre-defined clinically acceptable difference. If the limits exceed this threshold, the methods are not interchangeable.
// 06 — Pitfalls
Common mistakes
Using correlation instead of agreement
A high r-value does not mean two methods agree — it only means they are linearly related. Two methods can be perfectly correlated yet differ by a large constant offset. Always use a Bland–Altman plot for agreement analysis.
Plotting difference vs. one method
Plotting the difference against Method A (instead of the mean of both) introduces a spurious correlation because Method A appears on both axes. Always use the mean of the two methods on the x-axis.
Ignoring proportional bias
If the scatter widens or the bias line slopes as the mean increases, the standard limits of agreement are invalid. Use a log transformation or percentage-difference approach to stabilize variance.
Too few subjects
With fewer than about 40–50 paired observations, the confidence intervals around the limits of agreement become very wide. Report confidence intervals for the bias and limits so readers can judge precision.
Ignoring repeated measures
If each subject is measured multiple times, standard Bland–Altman analysis assumes independence and underestimates variability. Use a modified version that accounts for within-subject variance.
// 07 — In practice
Real-world examples
Medical device validation
Comparing a new wearable pulse oximeter against an arterial blood gas analyzer. If limits of agreement are within ±2% SpO₂, the wearable is considered clinically acceptable.
Laboratory method comparison
Validating a rapid point-of-care glucose meter against the gold-standard laboratory assay. Bland–Altman analysis reveals whether bias is constant or proportional to glucose level.
Sports science
Comparing GPS-derived sprint distances against radar tracking. A Bland–Altman plot shows whether GPS overestimates at higher speeds, indicating proportional bias.
Radiology imaging
Assessing inter-observer agreement when two radiologists measure tumor diameter on CT scans. Limits of agreement define how much measurements can differ between observers.
// 08 — Quick reference
Key facts
| Also known as | Difference plot, Tukey mean-difference plot |
| Invented | 1986 by J. Martin Bland and Douglas G. Altman |
| X-axis | Mean of the two measurements |
| Y-axis | Difference between the two measurements |
| Key lines | Bias (mean difference) and ±1.96 SD limits |
| Ideal outcome | Bias near zero, narrow limits, no proportional trend |
| Minimum sample | ~40–50 paired observations for reliable limits |
| Common fields | Clinical medicine, laboratory science, sports science |
// 09 — Variations
Variations and extensions
Percentage difference
Plots percentage difference instead of absolute difference. Useful when variance increases with magnitude (proportional bias).
Regression-based limits
Fits a regression line to the differences and computes limits that vary with the mean. Handles non-constant bias and heteroscedasticity.
Repeated measures
Modified for subjects measured multiple times. Accounts for within-subject variance so limits of agreement are not artificially narrow.
// 10 — FAQs
Frequently asked questions
What is a bland–altman plot?+
A Bland–Altman plot (also called a difference plot or Tukey mean-difference plot) is a scatter plot that evaluates the agreement between two quantitative measurement methods. Instead of simply correlating the two measurements, it plots the difference between them on the y-axis against their mean on the x-axis.
When should you use a bland–altman plot?+
Use a Bland–Altman plot when you need to assess agreement (not just correlation) between two measurement methods. It also works well when you want to visualize systematic bias and its consistency across the measurement range, and when validating a new clinical instrument against an established reference method.
When should you avoid a bland–altman plot?+
Avoid a Bland–Altman plot when you only want to show correlation — a scatter plot with regression line is simpler. It is also a poor fit when your data is categorical or ordinal rather than continuous, or when you have more than two methods to compare simultaneously — consider a matrix approach.
Is a bland–altman plot suitable for dashboards?+
Yes — a Bland–Altman plot can work well in dashboards as long as the panel is large enough for readers to perceive the encoded values, has a clear title, and includes the legend or axis labels needed to interpret it.
What category of chart is a bland–altman plot?+
Bland–Altman Plot belongs to the Statistical family of charts. Charts in that family are designed to answer the same kind of question, so they often work as alternatives when one doesn't quite fit your data.
How do you read a bland–altman plot?+
Start with the axis labels and legend, then look at the overall shape before zooming into individual marks. Compare prominent features against the rest of the data, and verify any conclusion against the underlying numbers when precision matters.