Radial Plot

The radial plot is a graphical method for displaying and comparing observations that have differing precisions. Standardized observations are plotted against the precisions, where precision is defined as the reciprocal of the standard error. The original observations are given by slopes of lines through the origin. A scale of slopes is sometimes drawn explicitly.

Suppose, for example, that data are available on the degree classes obtained by students graduating from a university and that we wish to compare, for different major subjects, the proportions of students who achieved upper second-class honors or higher. Typically, different numbers of students graduate in different subjects. A radial plot will display the data as proportions so that they may be compared easily, allowing for the different sample sizes. Similarly, a radial plot can be used to compare other summary statistics (such as means, regression coefficients, odds ratios) observed for different sized groups, or event rates observed for differing time periods.

Sometimes, particularly in the natural and physical sciences, measurements intrinsically have differing precisions because of natural variation in the source material and experimental procedure. For example, archaeological and geochronological dating methods usually produce an age estimate and its standard error for each of several crystal grains or rock samples, and the standard errors differ substantially. In this case, the age estimates may be displayed and compared using a radial plot in order to examine whether they agree or how they differ. A third type of application is in meta-analysis, such as in medicine, to compare estimated treatment effects from different studies. Here the precisions of the estimates can vary greatly because of the differing study sizes and designs. In this context the graph is often called a Galbraith plot. In general, a radial plot is applicable when one wants to compare a number of estimates of some parameter of interest, for which the estimates have different standard errors.

A basic question is, Do the estimates agree (within statistical variation) with a common value? If so, what value? A radial plot provides a visual assessment of the answer. Also, like many graphs, it allows other features of the data to be seen, such as whether the estimates differ systematically in some way, perhaps due to an underlying factor or mixture of populations, or whether there are anomalous values that need explanation. It is inherently not straightforward to compare individual estimates, either numerically or graphically, when their precisions vary. In particular, simply plotting estimates with error bars does not allow such questions to be assessed.

The term radial plot is also used for a display of directional data, such as wind directions and velocities or quantities observed at different times of day, via radial lines of different lengths emanating from a central point. This type of display is not discussed in this entry.