weightedmean  R Documentation 
Averages heteroscedastic data either using the ordinary weighted mean, or using a random effects model with two sources of variance. Computes the MSWD of a normal fit without overdispersion. Implements a modified Chauvenet criterion to detect and reject outliers. Only propagates the systematic uncertainty associated with decay constants and calibration factors after computing the weighted mean isotopic composition. Does not propagate the uncertainty of any initial daughter correction, because this is neither a purely random or purely systematic uncertainty.
weightedmean(x, ...)
## Default S3 method:
weightedmean(
x,
from = NA,
to = NA,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'other'
weightedmean(
x,
from = NA,
to = NA,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'UPb'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
type = 4,
cutoff.76 = 1100,
oerr = 3,
cutoff.disc = discfilter(),
exterr = FALSE,
ranked = FALSE,
common.Pb = 0,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'PbPb'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
common.Pb = 2,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'ThU'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
ranked = FALSE,
Th0i = 0,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'ArAr'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
ranked = FALSE,
i2i = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'KCa'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
ranked = FALSE,
i2i = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'ThPb'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
ranked = FALSE,
i2i = TRUE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'ReOs'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
ranked = FALSE,
i2i = TRUE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'SmNd'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
ranked = FALSE,
i2i = TRUE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'RbSr'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
i2i = TRUE,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'LuHf'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
i2i = TRUE,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'UThHe'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
## S3 method for class 'fissiontracks'
weightedmean(
x,
random.effects = FALSE,
detect.outliers = TRUE,
plot = TRUE,
from = NA,
to = NA,
levels = NA,
clabel = "",
rect.col = c("#00FF0080", "#FF000080"),
outlier.col = "#00FFFF80",
sigdig = 2,
oerr = 3,
exterr = FALSE,
ranked = FALSE,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
x 
a two column matrix of values (first column) and their
standard errors (second column) OR an object of class

... 
optional arguments 
from 
minimum yaxis limit. Setting 
to 
maximum yaxis limit. Setting 
random.effects 
if if 
detect.outliers 
logical flag indicating whether outliers should be detected and rejected using Chauvenet's Criterion. 
plot 
logical flag indicating whether the function should produce graphical output or return numerical values to the user. 
levels 
a vector with additional values to be displayed as different background colours of the plot symbols. 
clabel 
label of the colour legend 
rect.col 
Fill colour for the measurements or age estimates. This can
either be a single colour or multiple colours to form a colour
ramp (to be used if a single colour: multiple colours: a colour palette: a reversed palette: For empty boxes, set 
outlier.col 
if 
sigdig 
the number of significant digits of the numerical values reported in the title of the graphical output. 
oerr 
indicates whether the analytical uncertainties of the output are reported in the plot title as:

ranked 
plot the aliquots in order of increasing age? 
hide 
vector with indices of aliquots that should be removed from the weighted mean plot. 
omit 
vector with indices of aliquots that should be plotted but omitted from the weighted mean calculation. 
omit.col 
colour that should be used for the omitted aliquots. 
type 
scalar indicating whether to plot the

cutoff.76 
the age (in Ma) below which the

cutoff.disc 
discordance cutoff filter. This is an object of
class 
exterr 
propagate decay constant uncertainties? 
common.Pb 
common lead correction:

Th0i 
initial

i2i 
‘isochron to intercept’: calculates the initial
(aka ‘inherited’, ‘excess’, or ‘common’) Note that choosing this option introduces a degree of circularity in the weighted age calculation. In this case the weighted mean plot just serves as a way to visualise the residuals of the data around the isochron, and one should be careful not to overinterpret the numerical output. 
Let \{t_1, ..., t_n\}
be a set of n age estimates
determined on different aliquots of the same sample, and let
\{s[t_1], ..., s[t_n]\}
be their analytical
uncertainties. IsoplotR
then calculates the weighted mean of
these data using one of two methods:
The ordinary errorweighted mean:
\mu = \sum(t_i/s[t_i]^2)/\sum(1/s[t_i]^2)
A random effects model with two sources of variance:
\log[t_i] \sim N(\log[\mu], \sigma^2 = (s[t_i]/t_i)^2 + \omega^2 )
where \mu
is the mean, \sigma^2
is the total variance
and \omega
is the 'overdispersion'. This equation can be
solved for \mu
and \omega
by the method of maximum
likelihood.
IsoplotR uses a modified version of Chauvenet's criterion for outlier detection:
Compute the errorweighted mean (\mu
) of the n
age determinations t_i
using their analytical uncertainties
s[t_i]
For each t_i
, compute the probability p_i
that
that t\mu>t_i\mu
for t \sim N(\mu, s[t_i]^2 MSWD)
(ordinary weighted mean) or \log[t] \sim
N(\log[\mu],s[t_i]^2+\omega^2)
(random effects model)
Let p_j \equiv \min(p_1, ..., p_n)
. If
p_j<0.05/n
, then reject the j^{th}
date, reduce n
by one (i.e., n \rightarrow n1
) and repeat steps 1 through 3
until the surviving dates pass the third step.
If the analytical uncertainties are small compared to the scatter
between the dates (i.e. if \omega \gg s[t]
for all i
),
then this generalised algorithm reduces to the conventional
Chauvenet criterion. If the analytical uncertainties are large and
the data do not exhibit any overdispersion, then the heuristic
outlier detection method is equivalent to Ludwig (2003)'s ‘2sigma’
method.
The uncertainty budget of the weighted mean does not include the uncertainty of the initial daughter correction (if any). This uncertainty is neither a purely systematic nor a purely random uncertainty and cannot easily be propagated with conventional geochronological data processing algorithms. This caveat is especially pertinent to chronometers whose initial daughter composition is determined by isochron regression. You may note that the uncertainties of the weighted mean are usually much smaller than those of the isochron. In this case the isochron errors are more meaningful, and the weighted mean plot should just be used to inspect the residuals of the data around the isochron.
Returns a list with the following items:
a two or three element vector with:
t
: the weighted mean. An asterisk is added to the plot title
if the initial daughter correction is based on an isochron
regression, to mark the circularity of using an isochron to compute
a weighted mean.
s[t]
: the standard error of the weighted mean, excluding the
uncertainty of the initial daughter correction. This is because
this uncertainty is neither purely random nor purely systematic.
a twoelement vector with the (over)dispersion and its standard error.
the Mean Square of the Weighted Deviates (a.k.a. ‘reduced Chisquare’ statistic)
the number of degrees of freedom of the Chisquare test
for homogeneity (df=n1
, where n
is the number of
samples).
the pvalue of a Chisquare test with df
degrees of freedom, testing the null hypothesis that the underlying
population is not overdispersed.
vector of logical flags indicating which steps are included into the weighted mean calculation
list of plot parameters for the weighted mean
diagram, including mean
(the mean value), ci
(a grey
rectangle with the (1 s.e., 2 s.e. or 100[1\alpha
]%,
depending on the value of oerr
) confidence interval ignoring
systematic errors), ci.exterr
(a grey rectangle with the
confidence interval including systematic errors), dash1
and
dash2
(lines marking the confidence interval augmented by
\sqrt{mswd}
overdispersion if random.effects=FALSE
),
and marking the confidence limits of a normal distribution whose
standard deviation equals the overdispersion parameter if
random.effects=TRUE
).
central
ages < c(251.9,251.59,251.47,251.35,251.1,251.04,250.79,250.73,251.22,228.43)
errs < c(0.28,0.28,0.63,0.34,0.28,0.63,0.28,0.4,0.28,0.33)
weightedmean(cbind(ages,errs))
attach(examples)
weightedmean(LudwigMean)
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