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BiostatKit / Agreement / Bland-Altman analysis

Bland-Altman Analysis Calculator

Paste pairs of measurements made by two methods and get the bias, the 95% limits of agreement with their confidence intervals, the Bland-Altman plot, a sentence you can paste into your manuscript, and the R code that reproduces the numbers.

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Your paired measurements

Pick how to express the difference, then paste the pairs.

Use the percentage if the spread of the differences grows with the size of the measurement.
Shown in the results, for example mmHg or g/L.
Paste two columns from Excel or type. Separate the two values with a space, tab or comma. Numbers only, with a decimal point, no headings.

Result

Agreement between two measurement methods.

Sentence for your manuscript

Written in AMA style from your numbers. Check it against your own study design before you submit.

Reporting checklist

  • GRRAS 2011 (reliability and agreement studies): describe the subjects, how the two methods were applied and whether they were blinded to each other, and report the agreement with its confidence interval.
  • Report the bias and the limits of agreement together with their 95% CIs, and show the plot.
  • Say in advance how large a difference would be acceptable in practice and compare the limits of agreement with it. The method itself does not say whether agreement is good enough.

Methods wording. Agreement between the two methods was assessed with BiostatKit [1] using a Bland-Altman analysis [2]: the mean difference and the 95% limits of agreement (mean difference plus or minus 1.96 SD), with 95% CIs from the t distribution.
[1] BiostatKit. Bland-Altman analysis calculator. Accessed [date]. [URL]
[2] Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1(8476):307-310.

Reproduce it in R

The script is filled in with your numbers. Paste it into R or RStudio and compare.

R 4.x · base R only

    
This calculator was checked against Python (SciPy t distribution and linear regression; the bias CI also equals the CI of SciPy's one-sample t test, and the CI of the limits was checked by simulation) on 2 reference cases and matched to 4 significant digits. See the verification log.

  


  

    
How to read a Bland-Altman analysis

    

      

        
What it is

        
For each pair, the difference between the two methods is plotted against the mean of the two. The mean difference (bias) shows a systematic shift between the methods. The 95% limits of agreement are the range expected to contain 95% of the differences between the two methods.

        
How this page computes it

        
With d = A - B (or 100 x (A - B) / mean of the pair) for n pairs, bias = mean of d and SD = SD of d.

        
limits of agreement = bias ± 1.96 x SD

        
The 95% CI of the bias is bias ± t x SD / √n, with t from the t distribution on n - 1 degrees of freedom. The 95% CI of each limit is the limit ± t x SD x √(1/n + 1.96² / (2 (n - 1))), the approximation of Bland and Altman (1999). The trend line is the least-squares regression of d on the mean of the pair, tested with a t test.

      

      

        
Assumptions

        
    
          
  • The differences are roughly normal and their spread does not change with the size of the measurement. Check the plot: if the dots fan out, use the percentage difference.
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  • Each pair comes from a different subject. Repeated pairs on the same subject need a different analysis.
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  • Both methods measure the same quantity on the same scale.
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Common mistakes

        
    
          
  • Claiming agreement from a high correlation or a non-significant paired t test. Neither tells you how far apart single measurements can be.
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  • Reporting the limits without their confidence intervals. With few pairs the limits are imprecise.
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  • Leaving out the clinically acceptable difference. The limits are only useful when compared with it.
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  • Plotting the difference against one method instead of the mean of the two.
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Frequently asked questions

    
What do the limits of agreement mean?
If the differences are roughly normal, about 95% of the differences between the two methods fall between the lower and the upper limit. If that range is narrower than the difference you can accept in practice, the methods can be used interchangeably.

    
How many pairs do I need?
There is no fixed number. The confidence intervals of the limits show the precision: with 20 pairs each limit is uncertain by roughly 0.8 SD either side, with 100 pairs by roughly 0.3 SD.

    
When should I use the percentage difference?
When the scatter of the differences grows with the size of the measurement, for example blood levels that range over several fold. The percentage difference puts the limits on a relative scale.

    
Bland-Altman or ICC?
A Bland-Altman analysis shows how far apart two methods can be in the original unit. The ICC gives one number for reliability. Many method-comparison papers report both.

    
Is my data stored or sent anywhere?
No. All calculations run in your browser tab. Nothing is uploaded, and the page works offline once loaded.

    
Related calculators: Intraclass correlation (ICC) · Cohen's kappa