R: Calculate Mandel's k statistics for replicate observations
mandel.k
R Documentation
Calculate Mandel's k statistics for replicate observations
Description
mandel.k calculates Mandel's k statistics for replicate observations.
Mandel's k an indicator of precision compared to the pooled standard deviation across
all groups.
Usage
mandel.k(x, g = NULL, m = NULL, na.rm = T, rowname = NULL,
method=c("classical", "robust"), n = NA, ...)
## Default S3 method:
mandel.k(x, g = NULL, m = NULL, na.rm = T, rowname = NULL,
method=c("classical", "robust"), n = NA, ...)
## S3 method for class 'ilab'
mandel.k(x, g = NULL, m = NULL, na.rm = T, rowname = NULL,
method=c("classical", "robust"), n = NA, ...)
Arguments
x
An R object (see Details below), which contains replicate observations or,
if g is absent, means or standard deviations.
g
A primary grouping factor, usually corresponding to Laboratory in an
inter-laboratory study. If not present, x is taken as
a set of means or standard deviations (depending on whether
type is "h" or "k".
m
A secondary grouping factor, usually corresponding to test item
or measured quantity. m is ignored if x has
more than one column.
na.rm
A logical value indicating whether 'NA' values should be
stripped before the computation proceeds. Passed to functions
such as mean and sd.
rowname
A single character label for the primary grouping factor
(e.g. "Lab", "Organisation").
method
Character scalar giving the calculation method. "classical" gives the
traditional calculation; "robust" gives a robust variant (see Details).
n
scalar number of observations per group. Required only if x consists of
calculated standard deviations.
...
Additional parameters passed to other methods. Currently not
implemented.
Details
mandel.k is a convenience wrapper for mandel.kh(..., type="k"). It is generic,
with methods for numeric vectors, arrays, data frames, matrices and objects of
class 'ilab'. All parameters are passed to mandel.kh.
Mandel's k is an indicator of relative dispersion for grouped
sets of observations. Given a set of observations x[i,j,l] where i, j, l
denotes observation l, l=1, 2, ... n for measurand or test item j and group
(usually laboratory) i, i=1, 2, ... p, Mandel's k is given by:
k=√{frac{s_{ij}^2}{∑_{i=1}^p{s_{ij}^2/p}}}
where s_{ij} is the standard deviation of values x_{ijk} over k=1, 2, ..., n.
If x is a vector, one-dimensional array or single-column matrix, values are aggregated
by g and, if present, by m. If x is a data frame or matrix, each column
is aggregated by g and m silently ignored if present. In all cases, if g
is NULL or missing, each row (or value, if a vector) in x
is taken as a pre-calculated mean (for Mandel's h) or standard deviation (for Mandel's k).
If x is an object of class 'ilab', g defaults to '$org' and
m to $measurand.
The returned object includes a label ('grouped.by') for the primary grouping factor.
For the 'ilab' method, this is "Organisation". For other methods, If rowname is
non-null, rowname is used. If rowname is NULL, the default is deparse(substitute(g));
if g is also NULL or missing, "Row" is used.
If method="robust", Mandel's k is calculated by replacing the classical pooled standard
deviation with the robust pooled standard deviation calculated by algorithm S (see algS).
Value
mandel.k returns an object of class "mandel.kh", which is a data frame consisting
of the required Mandel's statistics and in which each row corresponds to a level of g
and each column to a level of m or (if x was a matrix or data frame) to the
corresponding column in x. In addition to the class, the object has attributes:
'mandel.type'
"h" or "k"
'grouped.by'
Character scalar giving the label used for the grouping
factor g; see Details above for the defaults.
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).
See Also
mandel.h, mandel.kh;
pmandelh, pmandelk for probabilities, quantiles etc.;
plot.mandel.kh, barplot.mandel.kh for plotting methods.