When the differences are related to magnitude, it is best to try to eliminate the
relationship using a transformation. Because it has a clear interpretation, logarithmic
transformation is often used to remove the effect of differences increasing with magnitude.
(The difference between the logarithms of two values is equivalent to the ratio of the two
Other transformations, such as square root or reciprocal, cannot be clearly
interpreted and are best avoided. However, rather than use a logarithmic transformation,
it is usually easier to use the ratio of the measurements or the difference expressed as
a percentage of the mean.
The difference plot shows the ratio of the measurements with the points now forming a
constant-width band across the measuring interval.
(click to enlarge)
The mean ratio estimate is 1.10, which indicates that the Nadler method measures an
average of 10% higher than the Hurley method. The limits of agreement indicate that
the Nadler method may measure between ~6% to ~15% above the Hurley method for 95% of