# duewer.plot: Duewer concordance/apparent precision plot In metRology: Support for Metrological Applications

## Description

Produces a Duewer concordance/apparent precision plot, showing relative precision or uncertainty plotted against (relative) deviation from assigned value.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```dplot(x, ...) duewer.plot(x, ...) ## Default S3 method: duewer.plot(x,s,mu=median(x),sigma=mad(x), s0=median(s), labels=NA, radius=1:3, units=c("z","x"), main, xlab, ylab, xlim, ylim, at.xax=NULL, at.yax=NULL, aspect, col.contours="lightgrey", lty.contours=par("lty"), lwd.contours=par("lwd"), label.contours=T, format.clab="p=%4.3f", cex=par("cex"), cex.label=0.7, pos=3, adj=NULL, pos.clab="bottomright", col.clab=col.contours, cex.axis=par("cex.axis"), pch=par("pch"), las=par("las"), col=par("col"), bg=par("bg"), ...) ```

## Arguments

 `x` Numeric vector of values to be plotted. `s` Numeric vector of standard deviations, standard errors or uncertainties of length `length(x)` associated with x. `mu` A single location against which to compare x. `sigma` A measure of dispersion against which deviations x-mu can be compared. `s0` A typical, expected or reference value for the standard uncertainties s `labels` An optional vector of point labels of length `length(x)`. `labels` are coerced to character on use, so may be character, factor etc.. `radius` A vector of radii for reference lines in the classic Duewer plot. `units` Controls scaling of the plot. If set to `"z"`, a classic Duewer plot of `s/s0` vs. `(x-mu)/sigma` is produced. If `units=="x"`, the plot is drawn without scaling by `sigma` or `s0`. `main` Main title for the plot, passed to `title()`. `xlab, ylab` x- and y-axis labels, passed to `title()`. `xlim, ylim` x- and y-limits for the plot. `at.xax, at.yax` Locations for x- and yaxis tick marks, passed to `axis()` `aspect` The aspect ratio for the plot, passed to `plot.window`. This defaults to 1.0 for `basis=="radius"`, giving semicircular countours, and NA otherwise. `col.contours, lty.contours, lwd.contours` Colour, line type and line width for contour lines. `label.contours` Logical, controlling whether countour lines are labelled with approximate probabilities. `format.clab` format string for contour labels; passed to `sprintf`. `cex` Expansion factor for plotted symbols. `cex.label` Expansion factor for point labels. `pos, adj` Specifies position/adjustment of point labels. Passed to `text`. `pos.clab` Specification for location of contour labels. Options are '"top"', '"topright"', '"right"', '"bottomright"', '"bottom"', '"bottomleft"', '"left"', '"topleft"'. A vector can be provided to give multiple labels. Contour labels for `basis="prob"` are placed approximately at the location indicated and adjusted outward appropriately. For basis="radius", "bottomright" and "bottomleft" are as for "right" and "left" but just below the x-axis, and "bottom" is replaced with c("bottomright", "bottomleft"). `col.clab` Colour for contour labels. `cex.axis` Expansion factor for axis labels. `las` Axis label orientation, passed to `axis`. `pch, col, bg` Graphical parameters passed to `points`. `...` Other parameters passed to plotting functions. Currently unused.

## Details

A Duewer plot is a plot of dispersion against location. Classically, this has been applied to multiple observations from laboratories. Locations `x` are mean results of the form `(x-mu)/s` and and dispersions `s` are the associated sd. The principle has also been applied to multiple results for different measurands per laboratory, by calculating z-scores for all observations relative to the assigned value and dispersion for each measurand and then plotting mean and sd of the scores. More recently the plot has been used to summarise reported values and (usually) standard uncertainties in metrology comparisons to allow quick assessment of anomalies within data sets.

The traditional plot includes visual guides in the form of semicircular contours at multiples of (x-mu)/sigma for the x-axis and s/s0 for the y-axis, s0 being a median or other estimate of the typical standard deviation.

Contours are, by default, labelled with probabilities corresponding to quantiles of the normal distribution.

`dplot` is an alias for `duewer.plot`.

## Value

This function is called for its side effect, which is the production of a plot.

## Author(s)

S Ellison s.ellison@lgc.co.uk

## References

Duewer, D, Probably in Anal. Chem. in about 1990

`axis` for axis control, `points`, `text` for plotting parameters; `sprintf` for contour label format.
`xs.plot` for a plot of location and scale data with probabilistic confidence regions.
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` require(metRology) data(Pb) Pb duewer.plot(Pb\$value, Pb\$u) duewer.plot(Pb\$value, Pb\$u, basis="prob", df=5) #Illustrate contour labelling duewer.plot(Pb\$value, Pb\$u, pos.clab="bottom") ```