Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates derSimonian-Laird estimate of location, with standard error, assuming a random-effects model

1 2 3 4 |

`x` |
numeric vector of mean values for groups, or (if |

`s` |
numeric vector of length |

`n` |
integer giving the number of observations in each group. May be a vector
of length |

`groups` |
factor, or vetor which can be coerced to factor, of groups. If
present, |

`na.rm` |
logical: if |

`...` |
Further parameters passed to other methods. |

`dsl`

implements the derSimonian-Laird random-effects estimate of location,
using the implementation described by Jackson (2010).

The estimator assumes a model of the form

*x[i]=mu+b[i]+e[i]*

in which *b[i]* is drawn from *N(0, tau^2)* and
*e[i]* is drawn from *N(0, sigma[i]^2)*.

The estimator forms a direct calculation of *tau*, and uses this to
form revised estimates of standard error *sqrt(s[i]^2+tau^2)*
in `x`

, calculates weights as the inverse of these and in turn calculates a
weighted mean, allowing for any calculated excess variance *tau^2*.

This implementation permits input in the form of:

means

`x`

and standard errors`s`

, in which case neither`n`

nor`groups`

are supplied;means

`x`

, standard deviations`s`

and group size(s)`n`

, standard errors then being calculated as`s/sqrt(n)`

individual observations

`x`

with a groupinf factor`groups`

, in which case standard errors are calculated from the groups using`tapply`

.

A loc.est object; see loc.est for details. In the returned object, individual
values `xi`

are always input means (calculated from groups and `n`

as
necessary); `method.details`

is returned as a list containing:

- mu
The estimated location.

- s
The standard error in the location.

- tau
The excess variance (as a standard deviation).

S L R Ellison s.ellison@lgc.co.uk

Jackson et al. (2010) J Stat Plan Inf 140, 961-970

1 2 3 4 5 6 | ```
#PCB measurements in a sediment from Key Comparison CCQM-K25
#s are reported standard uncertainties
pcb105 <- data.frame(x=c(10.21, 10.9, 10.94, 10.58, 10.81, 9.62, 10.8),
s=c(0.381, 0.250, 0.130, 0.410, 0.445, 0.196, 0.093))
with( pcb105, dsl(x, s) )
``` |

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