# radialplot: Visualise point-counting data on a radial plot In provenance: Statistical Toolbox for Sedimentary Provenance Analysis

## Description

Implementation of a graphical device developed by Rex Galbraith to display several estimates of the same quantity that have different standard errors.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```radialplot( x, num = 1, den = 2, from = NA, to = NA, t0 = NA, sigdig = 2, show.numbers = FALSE, pch = 21, levels = NA, clabel = "", bg = c("white", "red"), title = TRUE, ... ) ```

## Arguments

 `x` an object of class `counts` `num` index or name of the numerator variable `den` index or name of the denominator variable `from` minimum limit of the radial scale `to` maximum limit of the radial scale `t0` central value `sigdig` the number of significant digits of the numerical values reported in the title of the graphical output. `show.numbers` boolean flag (`TRUE` to show sample numbers) `pch` plot character (default is a filled circle) `levels` a vector with additional values to be displayed as different background colours of the plot symbols. `clabel` label of the colour legend `bg` a vector of two background colours for the plot symbols. If `levels=NA`, then only the first colour is used. If `levels` is a vector of numbers, then `bg` is used to construct a colour ramp. `title` add a title to the plot? `...` additional arguments to the generic `points` function

## Details

The radial plot (Galbraith, 1988, 1990) is a graphical device that was specifically designed to display heteroscedastic data, and is constructed as follows. Consider a set of dates \{t_1,...,t_i,...,t_n\} and uncertainties \{s[t_1],...,s[t_i],...,s[t_n]\}. Define z_i = z[t_i] to be a transformation of t_i (e.g., z_i = log[t_i]), and let s[z_i] be its propagated analytical uncertainty (i.e., s[z_i] = s[t_i]/t_i in the case of a logarithmic transformation). Create a scatterplot of (x_i,y_i) values, where x_i = 1/s[z_i] and y_i = (z_i-z_\circ)/s[z_i], where z_\circ is some reference value such as the mean. The slope of a line connecting the origin of this scatterplot with any of the (x_i,y_i)s is proportional to z_i and, hence, the date t_i. These dates can be more easily visualised by drawing a radial scale at some convenient distance from the origin and annotating it with labelled ticks at the appropriate angles. While the angular position of each data point represents the date, its horizontal distance from the origin is proportional to the precision. Imprecise measurements plot on the left hand side of the radial plot, whereas precise age determinations are found further towards the right. Thus, radial plots allow the observer to assess both the magnitude and the precision of quantitative data in one glance.

## References

Galbraith, R.F., 1988. Graphical display of estimates having differing standard errors. Technometrics, 30(3), pp.271-281.

Galbraith, R.F., 1990. The radial plot: graphical assessment of spread in ages. International Journal of Radiation Applications and Instrumentation. Part D. Nuclear Tracks and Radiation Measurements, 17(3), pp.207-214.

Galbraith, R.F. and Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks and Radiation Measurements, 21(4), pp.459-470.

## Examples

 ```1 2``` ```data(Namib) radialplot(Namib\$PT,components=c('Q','P')) ```

provenance documentation built on May 5, 2021, 1:06 a.m.