Bland-Altman Analysis Calculator

Use Bland-Altman analysis when you need to determine whether two measurement methods can be used interchangeably. For example, can a new, cheaper blood pressure device replace the gold standard? Simply showing that two methods are correlated isn't enough—this analysis reveals whether the actual differences between methods are small enough to be clinically or practically acceptable.

What Is Bland-Altman Analysis?

Bland-Altman analysis assesses agreement between two measurement methods. It plots the difference between methods against their mean, revealing systematic bias and limits of agreement.

Question answered: "Do these two methods give sufficiently similar results to be used interchangeably?"

Note: Correlation is NOT appropriate for method comparison—high correlation doesn't mean good agreement.

Why Correlation Fails

The Problem

Two methods can be highly correlated but have:

• Systematic bias (one always reads higher)
• Poor agreement (large differences between readings)

Example:

Correlation: r = 1.00 (perfect!) But Method B always reads 10 units higher—not interchangeable.

Bland-Altman Shows This

The plot would show all points at +10 difference, clearly revealing the bias.

The Bland-Altman Plot

Axes

• X-axis: Mean of two methods: $(A + B) / 2$
• Y-axis: Difference between methods: $A - B$

Key Features

• Mean difference (bias): Average of all differences
• Limits of agreement: Mean ± 1.96 × SD of differences
• Pattern inspection: Look for trends, proportional bias, outliers

Calculation Steps

Data: Two methods measuring the same quantity

Step 1: Calculate mean difference (bias)

$\bar{d} = \frac{\sum(A_i - B_i)}{n} = \frac{2-5+3+4-5}{5} = -0.2$

Step 2: Calculate SD of differences

$SD_d = \sqrt{\frac{\sum(d_i - \bar{d})^2}{n-1}} = 4.32$

Step 3: Calculate limits of agreement

• Upper limit: $\bar{d} + 1.96 \times SD_d = -0.2 + 8.47 = 8.27$
• Lower limit: $\bar{d} - 1.96 \times SD_d = -0.2 - 8.47 = -8.67$

Interpretation: 95% of differences fall between -8.67 and +8.27.

Interpreting the Plot

Mean Difference (Bias)

• Near zero: No systematic difference
• Positive: Method A tends to read higher
• Negative: Method B tends to read higher

Limits of Agreement

Ask: "Are these limits clinically acceptable?"

If limits are ±10 units and clinical tolerance is ±5, methods are NOT interchangeable.

Patterns to Look For

Proportional bias: Differences increase/decrease with mean value

• Indicates: Bias depends on measurement magnitude
• Solution: Consider ratio or percentage difference

Funnel pattern: Spread increases with mean

• Indicates: Variability proportional to magnitude
• Solution: Log-transform data, or use percentage differences

Outliers: Points far from limits

• Indicates: Measurement errors or special cases
• Action: Investigate; consider excluding with justification

Confidence Intervals

CI for Mean Difference

$\bar{d} \pm t_{n-1, 0.975} \times \frac{SD_d}{\sqrt{n}}$

CI for Limits of Agreement

$\text{Limit} \pm t_{n-1, 0.975} \times \sqrt{\frac{3 \times SD_d^2}{n}}$

With small samples, these CIs can be wide—report them.

Regression-Based Approach

When proportional bias exists, fit a regression:

$d_i = \alpha + \beta \times \text{mean}_i + \epsilon_i$

• Test if β = 0 (no proportional bias)
• Limits of agreement become prediction intervals

Percentage Differences

When proportional bias exists, use:

$\text{Difference} \% = \frac{A - B}{(A + B)/2} \times 100$

This normalizes differences for magnitude.

Repeated Measures

When subjects are measured multiple times:

• Account for within-subject correlation
• Use mixed-effects models
• Calculate separate components of variance

Applications

Medical Devices

Validating new measurement device against gold standard.

Laboratory Methods

Comparing assay techniques.

Clinical Assessment

Agreement between clinicians or assessment tools.

Research Validation

Verifying that methods produce comparable results.

Clinical Acceptability

Pre-Define Criteria

Before analysis, specify acceptable limits:

• "Methods are interchangeable if 95% of differences are within ±5 units"

Compare to Criteria

If observed limits of agreement fall within acceptable limits, methods agree sufficiently.

Consider the Application

Narrow limits needed for:

• Drug dosing
• Diagnostic thresholds
• High-stakes decisions

Wider limits may be acceptable for:

• Screening
• General monitoring
• Research purposes

Reporting Results

Minimal report:

"Bland-Altman analysis showed a mean difference of -0.2 units (95% CI: -4.5, 4.1) with limits of agreement from -8.7 to 8.3."

Complete report:

"Agreement between Method A and Method B was assessed using Bland-Altman analysis. The mean difference (bias) was -0.2 units (95% CI: -4.5 to 4.1), indicating no significant systematic bias. The 95% limits of agreement were -8.7 to 8.3 units, meaning 95% of differences between methods fall within this range. Visual inspection of the Bland-Altman plot showed no proportional bias (regression slope = 0.02, p = .87) or heteroscedasticity. Given our pre-specified clinical acceptability threshold of ±10 units, the two methods can be considered interchangeable for clinical use."

Common Mistakes

Using Correlation

Correlation measures association, not agreement. High r doesn't mean methods agree.

Not Pre-Specifying Limits

Define acceptable limits before analysis to avoid post-hoc rationalization.

Ignoring the Plot

Look at the actual plot—statistics alone may miss patterns.

Small Sample Size

Limits of agreement are imprecise with n < 30. Report wide confidence intervals.

Non-Constant Variance

If spread varies with magnitude, use percentage differences or log transformation.

Alternatives and Extensions

Regression Analysis

For proportional bias modeling.

Total Deviation Index (TDI)

Probability-based criterion for agreement.

Coverage Probability (CP)

Proportion of differences within specified limits.

Concordance Correlation Coefficient (CCC)

Single summary measure of agreement (combines precision and accuracy).

Historical Context

J. Martin Bland and Douglas Altman introduced this method in 1983 and 1986, revolutionizing method comparison studies. Their critique of correlation for agreement assessment fundamentally changed practice in clinical chemistry and medical research.

The method remains the standard for assessing measurement agreement.

Related Calculations

• Pearson Correlation — NOT for agreement
• ICC Calculator — Reliability assessment
• Mean Calculator — Bias estimation
• Standard Deviation Calculator — Variability

Summary

Bland-Altman analysis compares two measurement methods by plotting differences against means. The mean difference shows systematic bias; limits of agreement (mean ± 1.96×SD) show the range containing 95% of differences. Pre-specify clinically acceptable limits before analysis. Look for proportional bias (trend in plot) and heteroscedasticity (funnel shape). Don't use correlation for method comparison—it measures association, not agreement. Report mean difference, limits of agreement, confidence intervals, and whether the observed limits fall within acceptable clinical bounds.