metRology (version 0.9-29-2)

msd : Median scaled difference

Description

Generates median of scaled differences from each point in a data set to all other points..

Usage

msd(x, s=mad , ...)

Value

An object of class "MSD", consisting of a vector of length length(x) of median scaled absolute deviations for each observation, with attributes:

names

character vector of names, taken from x

x

values supplied as x

s

values supplied as s

Print and plotting methods are currently provided for the "MSD" class; see MSD-class.

Arguments

x

Vector of observations

s

Either a function returning an estimate of scale for x or a vector of length length(x) of standard errors or standard uncertainties in x.

...

Parameters passed to s if s is a function.

Author

S. L. R. Ellison

Details

For each observation x[i], msd calculates the median of |x[i]-x[j]|/sqrt(s[i]^2+s[j]^2), j!=i, that is, the median of differences divided by the estimated uncertainties of the distance.

If s is a function, it is applied to x and replicated to length length(x); if a scalar, it is replicated to length length(x).

The median scaled difference is a measure of how ‘far’ an individual observation is from the majority of the other values in the data set. As a rule of thumb, values above 2 are indicative of a suspect (x[i], s[i]) data pair; that is, a value x[i] that is remote from a large fraction of the remaining data given its associated standard error or standard uncertainty s[i].

References

Ellison, S. L. R. (2018) An outlier-resistant indicator of anomalies among inter-laboratory comparison data with associated uncertainty. _Metrologia_ (accepted 4 October 2018)

See Also

pmsd, qmsd, MSD-class.

Examples

  data(Pb)
  msd(Pb$value)  # Uses mad(Pb$value) as scale estimate
  msd(Pb$value, Pb$u)  # Scales differences using standard uncertainties