# ci: Confidence intervals In IsoplotR: Statistical Toolbox for Radiometric Geochronology

 ci R Documentation

## Confidence intervals

### Description

Given a parameter estimate and its standard error, calculate the corresponding 1-sigma, 2-sigma or 100(1-\alpha)\% confidence interval, in absolute or relative units.

### Usage

ci(x = 0, sx, oerr = 3, df = NULL, absolute = FALSE)


### Arguments

 x scalar estimate sx scalar or vector with the standard error of x without and (optionally) with \sqrt{MSWD} overdispersion multiplier. oerr indicates if the confidence intervals should be reported as: 1: 1\sigma absolute uncertainties. 2: 2\sigma absolute uncertainties. 3: absolute (1-\alpha)% confidence intervals, where \alpha equales the value that is stored in settings('alpha'). 4: 1\sigma relative uncertainties (\%). 5: 2\sigma relative uncertainties (\%). 6: relative (1-\alpha)% confidence intervals, where \alpha equales the value that is stored in settings('alpha'). df (optional) number of degrees of freedom. Only used if sx is a vector. absolute logical. Returns absolute uncertainties even if oerr is greater than 3. Used for some internal IsoplotR functions.

### Details

Several of IsoplotR's plotting functions (including isochron, weightedmean, concordia, radialplot and helioplot) return lists of parameters and their standard errors. For ‘model-1’ fits, if the data pass a Chi-square test of homogeneity, then just one estimate for the standard error is reported. This estimate can be converted to a confidence interval by multiplication with the appropriate quantile of a Normal distribution. Datasets that fail the Chi-square test are said to be ‘overdispersed’ with respect to the analytical uncertainties. The simplest way (‘model-1’) to deal with overdispersion is to inflate the standard error with a \sqrt{MSWD} premultiplier. In this case, IsoplotR returns two estimates of the standard error. To convert the second estimate to a confidence interval requires multiplication with the desired quantile of a t-distribution with the appropriate degrees of freedom.

### Value

A scalar or vector of the same size as sx.

### Examples

attach(examples)
fit <- isochron(PbPb,plot=FALSE,exterr=FALSE)
err <- ci(x=fit$age[1],sx=fit$age[-1],oerr=5,df=fit$df) message('age=',signif(fit$age[1],4),'Ma, ',
'2se=',signif(err[1],2),'%, ',
'2se(with dispersion)=',signif(err[2],2),'%')


IsoplotR documentation built on May 29, 2024, 7:57 a.m.