Bland–Altman plot

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Bland–Altman plot example

A Bland–Altman plot (Difference plot) in analytical chemistry or biomedicine is a method of data plotting used in analyzing the agreement between two different assays. It is identical to a Tukey mean-difference plot[1], the name by which it is known in other fields, but was popularised in medical statistics by J. Martin Bland and Douglas G. Altman.[2][3]

Agreement vs correlation[edit]


How to construct a Bland–Altman plot[edit]

Consider a set of samples (for example, objects of unknown volume). Both assays (for example, different methods of volume measurement) are performed on each sample, resulting in data points. Each of the samples is then represented on the graph by assigning the mean of the two measurements as the -value, and the difference between the two values as the -value.

The Cartesian coordinates of a given sample with values of and determined by the two assays is


This version of the plot is used in MA plot.


One primary application of the Bland–Altman plot is to compare two clinical measurements each of which produced some error in their measures.[5] It can also be used to compare a new measurement technique or method with a gold standard, as even a gold standard does not—and should not—imply it to be without error.[4] See Analyse-it, MedCalc, NCSS, GraphPad Prism, R, or StatsDirect for software providing Bland–Altman plots.

Bland-Altman plots are extensively used to evaluate the agreement among two different instruments or two measurements techniques. Bland-Altman plots allow identification of any systematic difference between the measurements (i.e., fixed bias) or possible outliers. The mean difference is the estimated bias, and the SD of the differences measures the random fluctuations around this mean. If the mean value of the difference differs significantly from 0 on the basis of a 1-sample t-test, this indicates the presence of fixed bias. If there is a consistent bias, it can be adjusted for by subtracting the mean difference from the new method. It is common to compute 95% limits of agreement for each comparison (average difference ± 1.96 standard deviation of the difference), which tells us how far apart measurements by 2 methods were more likely to be for most individuals. If the differences within mean ± 1.96 SD are not clinically important, the two methods may be used interchangeably. The 95% limits of agreement can be unreliable estimates of the population parameters especially for small sample sizes so, when comparing methods or assessing repeatability, it is important to calculate confidence intervals for 95% limits of agreement. This can be done by Bland and Altman's approximate method [3] or by more precise methods.[6]



A similar method was proposed in 1981 by Eksborg.[7] This method was based on Deming regression—a method introduced by Adcock in 1878.

Bland and Altman's Lancet paper [3] was number 29 in a list of the top 100 most-cited papers of all time with over 23,000 citations.[8]

See also[edit]


  1. ^ Cleveland, William S. (1993). Visualizing data. Murray Hill, N.J.: At & T Bell Laboratories. pp. 22–23. ISBN 978-0963488404. OCLC 29456028.
  2. ^ Altman DG, Bland JM (1983). "Measurement in medicine: the analysis of method comparison studies". The Statistician. 32 (3): 307–317. doi:10.2307/2987937. JSTOR 2987937.
  3. ^ a b c Bland JM, Altman DG (1986). "Statistical methods for assessing agreement between two methods of clinical measurement" (PDF). Lancet. 327 (8476): 307–10. CiteSeerX doi:10.1016/S0140-6736(86)90837-8. PMID 2868172.
  4. ^ a b c Bland JM, Altman DG (1999). "Measuring agreement in method comparison studies". Statistical Methods in Medical Research. 8 (2): 135–60. doi:10.1177/096228029900800204. PMID 10501650.
  5. ^ Hanneman SK (2008). "Design, analysis, and interpretation of method-comparison studies". AACN Advanced Critical Care. 19 (2): 223–234. doi:10.1097/01.AACN.0000318125.41512.a3. PMC 2944826. PMID 18560291.
  6. ^ Carkeet A (2015). "Exact parametric confidence intervals for Bland–Altman Limits of Agreement". Optometry and Vision Science. 92 (3): e71–e80. doi:10.1097/OPX.0000000000000513. PMID 25650900.
  8. ^ Van Noorden, Richard; Maher, Brendan; Nuzzo, Regina (2014). "The top 100 papers". Nature. 514 (7524): 550–553. doi:10.1038/514550a. ISSN 0028-0836. PMID 25355343.