Bland-Altman Analysis Calculator

This calculator performs Bland-Altman analysis to assess agreement between two measurement methods. It computes the bias (mean difference) and 95% limits of agreement, which define the range within which most differences between measurements fall.

Enter paired measurements

Enter paired measurements for the same subjects. Each row must correspond to the same subject measured by both methods.

Optional settings
Confidence level for limits of agreement Use log scale For ratio agreement when measurements are multiplicative

Formulas

Bias (Mean Difference)

\( \bar{d} = \frac{1}{n} \sum_{i=1}^{n} (x_{1i} - x_{2i}) \)

95% Limits of Agreement

\( \text{Upper LoA} = \bar{d} + 1.96 \times s_d \)
\( \text{Lower LoA} = \bar{d} - 1.96 \times s_d \)

where \( s_d \) is the standard deviation of the differences.

Understanding Bland-Altman Analysis

Bland-Altman analysis assesses agreement between two measurement methods by examining the differences between paired measurements:

  • Bias — The mean difference indicates systematic error between methods
  • Limits of Agreement — Define the range containing 95% of differences
  • Clinical acceptability — You must decide if the LoA are narrow enough for clinical purposes

When to Use Bland-Altman

Bland-Altman analysis is appropriate when:

  • Comparing a new measurement method to a reference standard
  • Assessing reproducibility of the same method
  • Evaluating inter-observer or intra-observer agreement for continuous measurements

Note: Correlation coefficients are not appropriate for assessing agreement, as two methods can be highly correlated but have poor agreement.

Assumptions & Limitations

  • Assumes differences are normally distributed
  • Assumes no relationship between difference and magnitude (no proportional bias)
  • Requires paired measurements on the same subjects
  • Clinical acceptability of LoA must be determined a priori
  • Does not account for repeated measurements per subject

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