Bland-Altman Analysis: Visual Guide to Method Comparison Studies

Bland-Altman analysis, also called the limits of agreement method, is the internationally accepted statistical standard for evaluating whether two measurement methods can be used interchangeably in clinical practice. First described by Martin Bland and Douglas Altman in their landmark 1986 Lancet paper, the method has been cited more than 40,000 times and remains the cornerstone of method comparison studies in medicine, physiology, and quality control.

This guide explains exactly how the Bland-Altman analysis works, how to construct and read a Bland-Altman plot, what the limits of agreement and bias mean in practice, and how to avoid the most common interpretation mistakes. Whether you are validating a new pulse oximeter, comparing two laboratory assays, or designing a device study for regulatory submission, this article gives you the foundation to do it correctly.

Written by the Editverse Medical Writing Team | Reviewed by the Editverse Editorial Board | Last updated: June 2026

Why Correlation and Regression Are Not Enough for Method Comparison

A fundamental error in clinical research is using Pearson’s r or simple linear regression to decide whether two measurement methods agree. Researchers publishing regression vs correlation analyses often assume that a high r (e.g., r = 0.95) means the methods are interchangeable — but this is wrong, and the reason is subtle.

Correlation measures the strength of a linear relationship, not the closeness of agreement. Two methods could have perfect correlation (r = 1.0) but still disagree systematically by a constant amount. If your new thermometer reads exactly 2°C higher than the reference device for every patient, the r value is 1.0, but the methods clearly do not agree. Similarly, regression models fit a line through the data but do not quantify how far individual pairs of measurements deviate from each other.

Bland and Altman demonstrated this problem empirically in 1986. The solution they proposed (plotting differences against averages) directly visualises both systematic bias and random variability without the misleading optimism of high correlation coefficients.

Core Principles of Bland-Altman Analysis

The Mean Difference (Bias)

The mean difference (d̄) is the arithmetic mean of all pairwise differences (Method B minus Method A) across your study sample. A value close to zero indicates no systematic bias between methods. A positive value means Method B consistently reads higher; a negative value means it reads lower. The magnitude is interpreted in clinical units, not as a percentage, so whether d̄ = 3 mmHg is acceptable depends entirely on clinical context.

The Limits of Agreement

The limits of agreement (LOA) are calculated as:

These limits define the range within which 95% of individual measurement differences are expected to fall, assuming the differences are normally distributed. A method comparison study is judged acceptable if both LOA fall within a pre-specified maximum allowable difference (MAD), a clinical threshold decided before data collection, not after. This pre-specification requirement is non-negotiable; setting the MAD after seeing the data is circular reasoning.

A 2020 review by Gerke published in Diagnostics (PMC7278016) examined reporting standards across hundreds of Bland-Altman agreement studies and found that pre-specification of the acceptable limits was absent in the majority of published papers, a significant methodological gap that reviewers now flag at major journals.

Confidence Intervals Around the Limits

The LOA are sample estimates, not population parameters. They carry uncertainty. For small samples (n < 60), these confidence intervals can be wide enough to make the analysis uninformative. Sample size planning for agreement studies is therefore essential. Gerke et al. (2022) in the Journal of Clinical Monitoring and Computing (PMID 35438365) provide dedicated sample size formulas for LOA studies — a reference that every researcher designing a method comparison study should consult.

Preparing Data for Bland-Altman Analysis

Data Requirements

Valid Bland-Altman analysis requires the following:

• Paired measurements: Each subject must be measured by both methods, ideally simultaneously or within a clinically acceptable time window.
• Continuous variables: The method applies to quantitative measurements (blood pressure, glucose concentration, lung volume). It is not appropriate for ordinal or categorical data.
• Adequate sample size: A minimum of 40–50 pairs is widely recommended; some authors suggest at least 100 pairs for stable LOA estimates.
• Independence: Each pair should represent a different individual. Repeated measurements on the same individual require modified versions of the analysis (see below).
• Normally distributed differences: The LOA formula assumes normality of differences, not of the raw measurements. A Shapiro-Wilk test or Q-Q plot of the differences should be used to verify this assumption before proceeding.

When the Normality Assumption Fails

If differences are skewed or show proportional error (variance increasing with measurement magnitude), two approaches are available. First, a log transformation of the raw data before computing differences often stabilises variance. Back-transformation gives ratio LOA rather than difference LOA. These are interpreted as the factor by which one method exceeds the other, not an additive difference. Second, non-parametric LOA using the 2.5th and 97.5th percentiles of the raw difference distribution can be used, though this requires larger samples.

Constructing a Bland-Altman Plot: Step by Step

The following steps walk through creating a Bland-Altman plot from raw data:

1. Compute the difference: For each subject i, calculate d_i = B_i − A_i. The sign convention (B minus A or A minus B) should be stated and maintained consistently throughout the paper.
2. Compute the average: For each subject, calculate avg_i = (A_i + B_i) / 2.
3. Calculate the mean difference: d̄ = mean of all d_i values.
4. Calculate the SD of differences: SD = standard deviation of all d_i values.
5. Calculate the LOA: Upper = d̄ + 1.96 × SD; Lower = d̄ − 1.96 × SD.
6. Plot: X-axis = avg_i for each pair; Y-axis = d_i for each pair. Add three horizontal reference lines for the mean difference and both LOA. Add 95% confidence interval bands around each line.
7. Assess visually: Check for non-random patterns (see Interpretation section).

Software Implementation

All major statistical platforms support Bland-Altman plots. In R, the blandr package (CRAN) automates all steps including CI bands. In Python, the pyCompare library produces publication-ready plots. SPSS users can use the Bland-Altman macro available from MedCalc. GraphPad Prism and MedCalc have native Bland-Altman functions. For a quick web-based analysis, the free Bland-Altman calculator on Editverse and the BA-plotteR Shiny app both handle standard and repeated-measures designs without any programming knowledge.

Limits of Agreement, Bias, and the Difference Plot: Interpretation Guide

The three structural elements of a Bland-Altman analysis (bias, limits of agreement, and the scatter plot) each answer a different clinical question.

Reading Visual Patterns in the Plot

A random horizontal scatter around the mean difference line is the ideal pattern, meaning the discrepancy between methods is constant and unpredictable, with no systematic features. The following patterns indicate problems:

• Funnel shape (proportional error): If the scatter widens as the average increases, the methods disagree more at higher values. This violates the normality assumption and typically requires logarithmic transformation before proceeding.
• Slope trend: A visible upward or downward trend across the X-axis suggests a proportional bias — one method reads proportionally higher or lower at different measurement levels. Passing-Bablok regression quantifies this more precisely.
• Outliers beyond the LOA: Approximately 5% of points are expected outside the LOA by definition. More than 5%, or a cluster of outliers, warrants investigation. Check for data entry errors, patient-specific confounders, or protocol deviations.
• Non-random clustering: Groups of points at specific measurement ranges may indicate subpopulation effects (e.g., the methods agree in normotensive but not hypertensive patients).

Advanced Topics: Repeated Measures and the Modified Bland-Altman

The standard Bland-Altman analysis assumes one pair of measurements per subject. In practice, researchers often have multiple measurements per subject — for example, three readings by each method on the same day. Applying the standard analysis to repeated measurements violates the independence assumption and produces artificially narrow LOA because within-subject measurements are correlated.

The correct approach for repeated measures is the Bland-Altman with random effects (also called the mixed-effects Bland-Altman), which partitions the variance into within-subject and between-subject components. The blandr R package supports this extension, as does the MedCalc repeated measures module. Taffe (2023) in Statistical Methods in Medical Research (PMID 36352556) provides further extensions using clinical tolerance limits that are directly applicable to regulatory submissions.

Comparing Bland-Altman with Passing-Bablok Regression

Passing-Bablok regression is the other major method for comparing two quantitative measurement methods. It is a non-parametric technique that estimates a regression line between the two methods without assuming that either method is error-free or that errors are normally distributed. It is particularly useful in clinical chemistry for detecting constant and proportional bias simultaneously.

The two methods are complementary, not competing. Bland-Altman analysis quantifies the clinical range of disagreement in original measurement units. Passing-Bablok regression identifies whether the relationship between methods is linear and whether a calibration correction could eliminate the discrepancy. Used together, as recommended by the Clinical and Laboratory Standards Institute (CLSI), they give a complete picture of method agreement.

Applications Across Clinical and Research Settings

Medical Device Validation

Regulatory bodies including the FDA and ISO TC 215 require method comparison data when a new diagnostic device is submitted for approval. ISO 5725 and CLSI EP09, the two dominant guidelines for measurement comparison, both endorse Bland-Altman LOA analysis as a primary endpoint. For wearable health technology (continuous glucose monitors, wrist-based blood pressure devices, pulse oximeters), Bland-Altman analysis is mandatory before any clinical claim can be made about measurement accuracy.

Clinical Laboratory Medicine

When a hospital switches from one analyser platform to another (for example, changing the immunoassay system for troponin measurement), a Bland-Altman study is performed to confirm that patient results will remain clinically equivalent. Fang et al. (2024) in Clinical Chemistry and Laboratory Medicine (PMID 38742665) demonstrated that a Bland-Altman plot-based harmonisation algorithm significantly improved assay equivalence across IVD-MD platforms, a finding directly applicable to laboratory accreditation workflows.

Physiological and Cardiorespiratory Research

Cardiac output monitoring studies almost universally use Bland-Altman analysis to compare new, less invasive techniques (pulse contour analysis, thoracic bioimpedance) against the thermodilution reference standard. The mean difference and LOA, not r, determine whether the new device can replace the invasive reference in clinical practice. The study design choices made before data collection directly affect the validity of these comparisons.

Industrial Quality Control

In manufacturing, Bland-Altman analysis is used in measurement system analysis (MSA) to evaluate whether two instruments, two operators, or two measurement sites produce equivalent results. The ISO 5725 standard for accuracy and precision of measurement methods explicitly incorporates LOA-type analyses for inter-laboratory and inter-method comparisons.

Advantages and Limitations

Advantages

• Expressed in clinically meaningful units, so clinicians can directly judge whether the LOA are acceptable for their specific application
• Detects both systematic bias (mean difference) and random error (LOA width) simultaneously
• Graphical output is interpretable by non-statisticians
• Visual patterns (funnel, slope, outliers) reveal problems that summary statistics alone would miss
• Extensions available for repeated measures, proportional error, and non-normal data

Limitations and Common Errors

• Missing pre-specification: The most common error. LOA without a pre-specified MAD cannot confirm acceptable agreement. They can only describe disagreement.
• Normality assumption: Violated in skewed biological variables; requires transformation or non-parametric alternatives.
• Does not account for measurement error in the reference: The analysis treats Method A as error-free, which is rarely true in practice.
• Sample size underestimation: Many published studies use fewer than 40 pairs, producing LOA with very wide confidence intervals that are uninformative.
• Ignoring the reference range: The LOA should always be compared against the natural biological variation in the measured quantity, not just the clinical tolerance threshold.

Reporting Standards for Bland-Altman Studies

Gerke’s 2020 review (PMID 32456091) in Diagnostics identified the minimum reporting requirements for Bland-Altman agreement studies. A properly reported study should include: the study population and number of measurement pairs; the pre-specified maximum allowable difference (MAD) and its clinical justification; the mean difference (bias) with 95% CI; both LOA with 95% CI; the Bland-Altman plot with all three reference lines and CI bands; confirmation that normality of differences was assessed; and a statement of whether the LOA fall within the pre-specified MAD.

Researchers preparing method comparison studies for journal submission should also consult the STARD reporting guidelines, which include Bland-Altman elements for diagnostic agreement studies.

Related Statistical Methods: Choosing the Right Tool

Bland-Altman analysis sits within a broader family of agreement and reliability methods. The table below maps each scenario to the correct approach.

For a broader discussion of when to choose regression versus correlation approaches, see the Editverse guide on regression vs correlation in clinical research. For studies involving observational confounding, propensity score matching is often used alongside Bland-Altman analysis to control for patient-level covariates. If your study involves a systematic review component, refer to Systematic Review vs Meta-Analysis: Key Differences Explained.

Conclusion

The Bland-Altman analysis, built around the limits of agreement, the mean difference (bias), and the difference plot, remains the most transparent and clinically useful method for determining whether two measurement techniques can be used interchangeably. Its strength is that it speaks in the same units as the measurement itself, allowing clinicians and researchers to judge agreement against their own pre-defined standards of acceptability.

The most important principles to carry forward: always pre-specify the maximum allowable difference before analysing data; ensure your differences are normally distributed before applying the standard formula; calculate and report 95% confidence intervals around all three reference lines; and use the visual scatter to detect proportional errors and outliers that summary statistics alone would miss. For regulatory submissions, follow ISO 5725 and CLSI EP09, both of which centre on LOA.

Reviewers regularly challenge how agreement limits were calculated and whether the sample size supported them. If it is easier to discuss the analysis in Mandarin, our statisticians working in Simplified Chinese can review the method comparison before submission.

Key References

• Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;327(8476):307–310. doi:10.1016/S0140-6736(86)90837-8
• Gerke O. Reporting Standards for a Bland-Altman Agreement Analysis: A Review of Methodological Reviews. Diagnostics. 2020;10(5):334. PMID: 32456091
• Gerke O, Pedersen AK, Debrabant B, et al. Sample size determination in method comparison and observer variability studies. J Clin Monit Comput. 2022. PMID: 35438365
• Taffe P. Use of clinical tolerance limits for assessing agreement. Stat Methods Med Res. 2023;32(3):589–606. PMID: 36352556
• Fang H, Yang R, Guo J, et al. Using Bland-Altman plot-based harmonization algorithm to optimize harmonization for immunoassays. Clin Chem Lab Med. 2024. PMID: 38742665
• Giavarina D. Understanding Bland Altman analysis. Biochem Med (Zagreb). 2015;25(2):141–151. PMC4470095