Bland-Altman Plot Calculator

A Bland-Altman plot (also called a difference plot) is a graphical method used to compare two measurement techniques. It plots the difference between two paired measurements on the Y-axis against their mean on the X-axis, helping visualize systematic bias and the spread of agreement between methods.

The limits of agreement define the range within which 95% of differences between the two methods are expected to fall. They are calculated as the mean difference ± 1.96 times the standard deviation of the differences. Narrower limits indicate better agreement between methods.

The mean difference, or bias, represents a systematic offset between the two measurement methods. A bias close to zero suggests the methods produce similar readings on average. A consistently positive or negative bias indicates that one method tends to measure higher or lower than the other.

Two methods are considered in agreement when the limits of agreement fall within a pre-defined maximum allowed difference (Δ). Specifically, the upper LoA must be less than Δ and the lower LoA must be greater than −Δ. This threshold should be set based on clinical or practical relevance before collecting data.

A minimum of 30 to 40 paired observations is generally recommended to produce reliable estimates of bias and limits of agreement. Larger sample sizes narrow the confidence intervals around the limits of agreement, giving more certainty about method agreement.

The 95% confidence interval (CI) of the LoA accounts for sampling variability. To be 95% certain that two methods do not disagree, the allowed difference Δ must exceed the upper CI of the upper LoA, and −Δ must be less than the lower CI of the lower LoA. This calculator computes these CIs automatically.

If the differences between methods increase or decrease with the magnitude of measurements (proportional bias), a standard Bland-Altman plot may not be ideal. In that case, a ratio-based or log-transformed Bland-Altman analysis is more appropriate. You can detect proportional bias by looking for a trend in the scatter of points on the plot.

The standard and most widely used confidence level is 95%, which corresponds to a multiplier of 1.96. This means the LoA capture approximately 95% of differences under a normal distribution assumption. You can select 90% or 99% depending on the stringency required by your study protocol.