How this calculation works
Two methods can correlate strongly while disagreeing by an amount that matters. Bland–Altman analysis looks directly at paired differences and their spread instead of treating association as interchangeability. This page reports mean A-minus-B bias and estimated limits of agreement, with a plot of difference against pair mean. The sign convention remains visible in both the result and the worked table.
Difference = A−B; bias = mean difference; agreement limits = bias ± multiplier × sample SD of differencesA worked example
For method A values ten, twenty and thirty and method B values nine, eighteen and twenty-seven, differences are one, two and three. Mean bias is two and sample standard deviation of differences is one. With multiplier 1.96 the limits are 0.04 and 3.96 in the original measurement units. Those numbers alone do not say whether either method can replace the other.
Good to know
One independent pair per subject and a suitable distribution of differences are assumed. Repeated readings, clustered subjects and heteroscedastic differences need more complete treatment. No clinical or engineering acceptance margin is selected. The user must define what disagreement is tolerable before interpreting the estimated limits as acceptable or unacceptable.
Reference: Bland and Altman — limits of agreement (opens in a new tab) ↗
What this calculation answers
Two methods can correlate strongly while disagreeing by an amount that matters. Bland–Altman analysis looks directly at paired differences and their spread instead of treating association as interchangeability.
This page reports mean A-minus-B bias and estimated limits of agreement, with a plot of difference against pair mean. The sign convention remains visible in both the result and the worked table.
The Deming regression with entered measurement error ratio calculator fits a line when both measurement coordinates have error. A close fitted relationship still does not establish small individual differences.
Use the right input conventions
Enter measurements in corresponding subject order using the same units. Both lists must have equal lengths. Sorting them independently would destroy pairing and answer a different question.
The multiplier is entered explicitly. A value of 1.96 is commonly associated with approximately normal differences, but it does not automatically provide valid coverage for every distribution or study design.
Interpret the result
Limits of agreement describe the spread of individual paired differences under the assumed model. They are not a confidence interval for the mean bias. Increasing sample size does not make the individual-difference spread vanish.
A pattern in the difference-versus-mean plot can suggest that constant bias and constant variance are inadequate. This descriptive page does not fit a proportional-bias correction or silently transform the data.
Work through the example
For method A values ten, twenty and thirty and method B values nine, eighteen and twenty-seven, differences are one, two and three. Mean bias is two and sample standard deviation of differences is one.
With multiplier 1.96 the limits are 0.04 and 3.96 in the original measurement units. Those numbers alone do not say whether either method can replace the other.
Where the model stops
One independent pair per subject and a suitable distribution of differences are assumed. Repeated readings, clustered subjects and heteroscedastic differences need more complete treatment.
No clinical or engineering acceptance margin is selected. The user must define what disagreement is tolerable before interpreting the estimated limits as acceptable or unacceptable.
A few questions, answered
Are agreement limits a confidence interval for average bias?
No. They describe modeled individual differences, while uncertainty in the average bias is a separate calculation.
What changes in the comparison?
Widen the descriptive SD multiplier while leaving the paired measurements unchanged.