Bland-Altman plot

In analytical chemistry and biostatistics, a Bland-Altman plot is a method of data plotting used in comparing two different assays (each assay is a procedure to determine how much of a component part is in a mixture) or tests. It is identical to a Tukey mean-difference plot, which is what it is still known as in other fields, but was popularized in medical statistics by Bland and Altman.

Consider a set of n samples (for example, objects of unknown volume). Both assays (for example, different methods of volume measurement) are performed on each sample, resulting in 2n data points. Each of the n samples is then represented on the graph by assigning the mean of the two measurements as the abscissa (x-axis) value, and the difference between the two values as the ordinate (y-axis) value.

Hence, the Cartesian coordinates of a given sample S with values of $$S_1$$ and $$S_2$$ determined by the two assays is

$$ S(x,y)=\left( \frac{S_1+S_2}{2},(S_1-S_2) \right) $$

One common application of the Bland-Altman plot is to compare a new measurement technique or method with a gold standard. See Analyse-it or MedCalc for software providing Bland-Altman plots.