Confidence Interval Interface - Common Arguments — ConfidenceIntervals • DescToolsX

Arguments shared by the confidence interval functions in this package, documented once. Individual functions describe only which values they accept and refer here for what the values mean.

Arguments

conf.level: confidence level of the interval. If set to NA (the default), only the point estimate is returned.
sides: character string specifying the sidedness of the confidence interval. Must be one of "two.sided" (default), "left" or "right". For a one-sided interval, the value names the side with the finite bound. The initial letter is sufficient.
method: character string specifying the interval method. The available methods and the default differ between functions; see the individual help page for the choices.
...: additional arguments for the bootstrap, such as the number of resamples R and the interval type type.

Details

Return value

With conf.level = NA the functions return the point estimate as an unnamed scalar. With a confidence level they return a named numeric vector with the elements est, lci and uci, in that order. Reading the result by name rather than by position is the safer habit, since some functions return further elements.

One-sided intervals

sides names the side carrying the finite bound:

"left": the lower bound is finite, the upper one is open.
"right": the upper bound is finite, the lower one is open.

Thus sides = "left" corresponds to alternative = "greater" in stats::t.test(), and sides = "right" to alternative = "less". This is also the convention used by the corresponding functions in DescTools.

The open side is reported at the boundary of the parameter space, not at infinity - most of the statistics here are bounded, so this is the ordinary case rather than an exception. A correlation opens to \(\pm 1\), an association measure in \([0, 1]\) to 0 or 1, Cramer's \(V\) to 1, Pearson's \(C\) to \(\sqrt{(m-1)/m}\). Where the parameter really is unbounded, \(\pm\infty\) is reported: a relative risk opens upwards to Inf but downwards only to 0, a location estimator opens to -Inf and Inf, Cronbach's \(\alpha\) to -Inf and 1. An interval never claims a value the statistic cannot take.

A one-sided bound at level \(\gamma\) is the corresponding end of the two-sided interval at level \(2\gamma - 1\): a 95\ lower end of the two-sided 90\ interval requires conf.level above 0.5 and is refused below it, where the adjusted level would not be positive.

Choice of method

The available options depend on the statistic and on what is known about its distribution. Classical intervals rely on asymptotic normality or on an analytic variance formula, and are fast and deterministic where such a formula exists. Bootstrap intervals, requested with "boot", need no closed-form variance and are therefore available for statistics that have none - at the price of being random and slower.

Bootstrap intervals are partly computed with the boot package (see boot::boot() and boot::boot.ci()). The number of resamples R and the interval type - "perc", "bca" and others - are passed through \dots.

"bca" corrects for bias and skewness and is the better choice for a smooth statistic whose parameter lies well inside its range. It is the weaker choice near a boundary: both of its ingredients degrade where the parameter sits at the edge of the parameter space, which for an association measure under independence is the ordinary situation rather than a pathology. "perc" is the more robust default there.

Random number generation

Requesting a bootstrap confidence interval draws a seed from R's global random number generator and therefore advances it. Call base::set.seed() beforehand for reproducible intervals. This applies to the bootstrap methods only; classical intervals are deterministic.

Confidence Interval Interface - Common Arguments