Sometimes, a transformation does not solve the problem of a relationship between the
differences and magnitude. For example, this could occur when differences are negative for
low values and positive for high values.
To illustrate these concepts, we will use
another example from Bland & Altman’s 1999 paper. In this example, the fat content
of human milk was measured by enzymic procedures for the determination of triglycerides
and using the standard Gerber method.
The difference plot shows the average bias estimated using a linear regression. The
limits of agreement are estimated using the residual standard deviation from the
(click to enlarge)
The p-value of the slope term is significant (p < 0.05) and confirms that the
average difference is related to the magnitude.
If we suspect that the variability of the differences is also related to the mean, we
could model the SD using the residuals from the fit.