# plot.mandel.kh: Classical plots of Mandel's statistics. In metRology: Support for Metrological Applications

## Description

`plot.mandel.kh` produces classic plots of Mandel's statistics, suitably grouped and with appropriate indicator lines for unusual values.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ``` ## S3 method for class 'mandel.kh' plot(x, probs = c(0.95, 0.99), main, xlab = attr(x, "grouped.by"), ylab = attr(x, "mandel.type"), ylim = NULL, las = 1, axes = TRUE, cex.axis = 1, frame.plot = axes, lwd = 1, lty = 1, col = par("col"), col.ind = 1, lty.ind = c(2, 1), lwd.ind = 1, separators = TRUE, col.sep = "lightgrey", lwd.sep = 1, lty.sep = 1, zero.line = TRUE, lwd.zero = 1, col.zero = 1, lty.zero = 1, p.adjust = "none", ...) ```

## Arguments

 `x` An object of class `'mandel.kh'` `probs` Indicator lines are drawn for these probabilities. Note that `probs` is interpreted as specifying two-tailed probabilities for Mandel's h and one-sided (upper tail) probabilities for Mandel's k. `main` a main title for the plot. If missing, the default is ``` paste(deparse(substitute(x)), " - Mandel's", attr(x, "mandel.type"), if(attr(x, "mandel.method") == "robust") "(Robust variant)")``` `xlab` a label for the x axis; defaults to the `grouped.by` attribute for `x`. `ylab` a label for the x axis; defaults to the `mandel.type` attribute for `x`. `ylim` the y limits of the plot. For Mandel's k, the default lower limit is zero. `las` the style of the axis labels; see `par` for details. `axes` a logical value indicating whether axes should be drawn on the plot. `cex.axis` The magnification to be used for axis annotation relative to the current setting of 'cex'. `frame.plot` Logical; If `TRUE` a box is drawn around the plot. `lwd, lty, col` Graphical parameters used for the plotted vertical lines corresponding to each value of Mandel's statistics (the plot is of type "h"). All are recycled across the prinmary grouping factor, allowing different measurands/test items to be identified more clearly. `col.ind, lty.ind, lwd.ind` Graphical parameters used for the indicator lines, recyckled to `length(probs)`. For `attr(x, "mandel.type")=="h"` the graphical parameters are applied to negative as well as positive indicator lines, applied outwards from zero. `separators` Logical; if `TRUE`, separator lines are drawn between groups of values. `col.sep, lwd.sep, lty.sep` Graphical parameters used for the separator lines. `zero.line` logical; if `TRUE` a horizontal line is drawn at zero. `lwd.zero, col.zero, lty.zero` Graphical parameters used for the zero line. `p.adjust` Correction method for probabilities. If not `"none"`, passed to `p.adjust` prior to calculating indicator lines. Usually, indicator lines are drawn without correction (that is, with `p.adjust="none"`); specifying a p-value correction effectively turns the Mandel's statistics into single outlier tests. `...` Other (usually graphical) parameters passed to `plot`.

## Details

Mandel's statistics are traditionally plotted for inter-laboratory study data, grouped by laboratory, to give a rapid graphical view of laboratory bias and relative precision. The traditional plot is a plot of type `"h"`, that is, simple vertical lines from the x-axis.

For classical Mandel statistics, indicator lines are drawn based on `qmandelh` or `qmandelk` as appropriate. For robust variants, indicator lines use `qnorm` for the h statistic and `qf(probs, n, Inf)` for the k statistic. Note that this corresponds to taking the robust estimates of location and scale as true values, so will be somewhat anticonservative.

`plot.mandel.kh` uses `gplot` for the main plot.

## Value

plot.mandel.kh returns a numeric vector of mid-points of the groups along the x-axis.

## Author(s)

S Ellison s.ellison@lgc.co.uk

## References

Accuracy (trueness and precision) of measurement methods and results – Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. ISO, Geneva (1994).

`mandel.h`, `mandel.k`, `mandel.kh`, `pmandelh`, `pmandelk` for probabilities, quantiles etc.
See `barplot.mandel.kh` for an alternative plotting method. `gplot` for the underlying plotting function.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` data(RMstudy) h <- with(RMstudy, mandel.h(RMstudy[2:9], g=Lab)) plot(h, las=2) # Lab 4 shows consistent low bias; # Lab 23 several extreme values. #Use colours to identify particular measurands: plot(h, las=2, col=1:8) legend("bottomleft", legend=names(h), col=1:8, lty=1, cex=0.7, bg="white") #Example of Mandel's k: k <- with(RMstudy, mandel.k(RMstudy[2:9], g=Lab)) plot(k, las=2) # Lab 8 looks unusually variable; # Lab 14 unusually precise ```