How to use the bland-altman agreement calculator
- Paste the readings from method A, one per subject, separated by commas, spaces or new lines.
- Paste the readings from method B for the same subjects, in the same order.
- Choose the level of the limits of agreement. The usual choice is 95 percent.
- Read the bias, the standard deviation of the differences, the limits of agreement with their intervals, and the slope of the differences against the means.
Formula
Difference for each subject: d = A - B, and mean m = (A + B) / 2
Bias = the mean of the differences, and s = their standard deviation
Limits of agreement = bias plus or minus z x s, with z = 1.96 for 95 percent
Standard error of the bias = s / sqrt(n), and of each limit = s x sqrt(3 / n); intervals use t for n - 1 degrees of freedom
If the differences are roughly normal, about 95 percent of future differences between the two methods should fall inside the limits.
Differences of 1, 2 and 3
With A = 11, 12, 13 and B = 10, 10, 10, the differences are 1, 2 and 3. The bias is 2 and the standard deviation is 1, so the limits of agreement are 2 plus or minus 1.96 = 0.040036 to 3.95996. The 95 percent interval for the bias is -0.48414 to 4.4841, and the slope of the differences against the means is 2.
For two blood pressure monitors measured on ten people, the bias is 2.5, the standard deviation of the differences is 1.5811 and the limits are -0.59898 to 5.599. Their interval for the lower limit is -2.5581 to 1.3601, and the slope of the differences is 0.1074, which is small.
Agreement is not correlation
Two methods can correlate almost perfectly and still disagree: one may read 20 units higher than the other everywhere. The Bland-Altman approach looks directly at the differences, so it shows both the average gap (the bias) and how much the gap varies from subject to subject. Whether the limits are good enough is a decision about the use of the measurement, made before the study.
For agreement between raters on categories, see the Cohen's kappa calculator. To fit a line between two methods, use the linear regression calculator.
Checking the pattern
A plot of the differences against the means shows whether the gap grows with the size of the measurement. The page gives the slope of that relationship: a slope far from zero means the bias changes with level, and a single bias and set of limits misleads. Differences that are not close to normal also weaken the limits. With few pairs the intervals around the limits are wide, which is why they matter.
For intervals on a mean difference, use the confidence interval calculator.
Assumptions and limits
- Both methods measure the same subjects on the same scale, and the pairs are in the same order.
- The differences are roughly normal, and their spread does not depend on the size of the measurement.
- At least three pairs are needed. More are needed for narrow intervals.
- Whether the limits are acceptable depends on your use and is not decided by this page.
Frequently asked questions
What are limits of agreement?
They are the bias plus or minus 1.96 standard deviations of the differences. Most differences between the two methods should fall between them.
What does the bias mean?
It is the average difference. A positive bias means method A reads higher than method B on average.
Why not just use correlation?
Correlation measures how well one method predicts the other, not whether they give the same values. Methods can correlate well and still differ by a lot.
What does the slope tell me?
It shows whether the difference changes with the size of the measurement. A large slope means the bias is not constant.