Bland-Altman Analysis Calculator

Bland-Altman analysis is a statistical method for assessing agreement between two measurement techniques. Developed by Martin Bland and Douglas Altman in 1986, it addresses a critical question in method comparison studies: "Do two instruments, assays, or observers produce measurements that are close enough to be used interchangeably?" Unlike correlation coefficients, which measure association but not agreement, Bland-Altman analysis quantifies bias and the range within which 95% of measurement differences fall.

The method plots the difference between two measurements against their average for each subject. This reveals systematic bias (one method consistently reading higher), proportional bias (the difference growing with the magnitude of measurement), and random scatter. The limits of agreement (mean difference ± 1.96 × SD) define the range where 95% of future differences would be expected to lie, providing a clinically interpretable measure of interchangeability.

This calculator computes all core Bland-Altman statistics: mean bias with 95% confidence intervals, limits of agreement with CIs, coefficient of repeatability, method means and SDs, correlation between differences and means (to detect proportional bias), and the percentage of pairs falling within the limits.

The analysis begins with paired measurements from method 1 and method 2 collected on the same subjects. For each pair, the difference d_i = m1_i − m2_i and the mean a_i = (m1_i + m2_i)/2 are computed.

The key output is the mean bias (d̄) and the 95% limits of agreement. If the bias is close to zero, the methods agree on average. If the limits of agreement are narrow relative to the clinically acceptable difference, the methods can be considered interchangeable.

The coefficient of repeatability (1.96 × s_d) estimates the smallest detectable change using either method. Confidence intervals around the bias and limits of agreement account for sampling uncertainty — wider CIs with small n indicate less precise estimates.

Enter your paired measurements for the Bland-Altman analysis:

1. Method 1 Measurements: Enter comma-separated numeric values from the first measurement technique (e.g., new device, old method, observer A).
2. Method 2 Measurements: Enter the corresponding values from the second technique for the same subjects, in the same order. Both lists must have at least 3 values and be the same length.
3. Read the results: The calculator displays the mean bias with its 95% CI, SD of differences, upper and lower limits of agreement each with their 95% CIs, percentage of pairs within LoA, method means and SDs, coefficient of repeatability, and the correlation between differences and means for proportional bias detection.

Bland-Altman analysis is the gold standard for medical device comparison. When a new blood pressure monitor, glucose meter, or imaging device is introduced, it must be validated against the existing gold standard. Researchers collect paired measurements from the same patients, compute bias and limits of agreement, and judge whether the new device is accurate enough for clinical use based on pre-specified clinically acceptable limits.

In laboratory science, Bland-Altman plots compare assay methods, reagent batches, or lab technicians. If limits of agreement are narrow relative to biological variability, the methods are interchangeable. In exercise physiology, the method compares heart rate monitors, GPS devices, and wearables against reference measurements. In survey methodology, Bland-Altman analysis assesses inter-rater reliability when two coders rate the same set of items on a continuous scale.