Radial Plots

with z_j a transformation of some data and s(z_j) the corresponding measurement uncertainty. For example, if z_j = log(t_j) then σ(z_j) = σ(t_j)/t_j. z₀ is a convenient central value such as the weighted mean. The slope of a line connecting the origin (x=0,y=0) of a radial plot with a data point (x_j,y_j) equals z_j, and the horizontal distance along x-axis is a measure if its precision. Thus, the radial plot simultaneously visualises a measurement's value and precision. No other graphical method achieves this goal with the same elegance. This makes the radial plot the method of choice for visualising heteroscedastic data, i.e. data with (large and) variable measurement uncertainties. Traditional applications in the Earth Sciences are fission track and luminescence dating, which are governed by Poisson processes (e.g., Galbraith, 1988, 1990; Galbraith et al., 1999). In principle, however, radial plots can be used for any kind of data.