confIntFisherTrafo: Confidence interval for correlation coefficient using...

In biostatUZH: Misc Tools of the Department of Biostatistics, EBPI, University of Zurich

Description

Compute a confidence interval for a correlation coefficient r using the variance-stabilizing transformation

z = \tanh^{-1}(r) = 0.5 \log((1 + r) / (1 - r)),

known as Fisher's z-transformation. By means of this transformation, r is approximately normally distributed with variance (n-3)^{-1} independent of the true correlation ρ, enabling construction of a Wald-type confidence interval. Back-transformation yields a confidence interval for the correlation coefficient. An advantage of this approach is that the limits of the confidence interval are contained in (-1, 1).

Usage

confIntFisherTrafo(var1, var2, pp = c(0.025, 0.975), meth = 
    "spearman", type = "t")

Arguments

var1	Vector containing first variable.
var2	Vector containing first variable.
pp	Vector in R^2 that contains α / 2 and 1 - α/2, where alpha is the confidence level of the confidence interval.
meth	Correlation coefficient to be used: pearson or spearman.
type	Quantile to be used: z or t.

Value

Yields a list with entries:

estimate	Value of correlation coefficient.
ci	Computed confidence interval.
p.value	p-value for a test on ρ = 0 based on the transformation.
n	Number of observations.
p2	p-value based on the R function cor.est.

Author(s)

Kaspar Rufibach
[e-mail]

Examples

n <- 40
x <- runif(n)
y <- 2 * x + 0.5 * rnorm(n)
plot(x, y)
confIntFisherTrafo(x, y, pp = c(0.025, 0.975), meth = "spearman", type = "t")

biostatUZH documentation built on May 2, 2019, 6:06 p.m.