L_corr: Likelihood Support for Correlation

In likelihoodR: Likelihood Analyses for Common Statistical Tests

Likelihood Support for Correlation

Description

This function calculates the support for a correlation from 2 vectors of data. An expected correlation can be specified and the support calculated for this relative to the observed and the null (which is assumed to be 0, but can also be specified) values. A likelihood function is plotted for the obtained correlation with a likelihood interval added and expected correlation, if specified. Conventional p value is also given.

Usage

L_corr(xv, yv, null=0, exp.r=NULL, L.int=2, alpha=.05,
toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)

Arguments

xv	a numeric vector.
yv	a numeric vector the same length as xv.
null	the null value, default = 0.
exp.r	a specified correlation (could be expected value for the study), default = NULL.
L.int	likelihood interval given as support values, e.g. 2 or 3, default = 2.
alpha	the significance level used, 1 - alpha interval calculated, default = 0.05.
toler	the desired accuracy using optimise, default = 0.0001.
logplot	plot vertical axis as log likelihood, default = FALSE
supplot	set minimum likelihood display value in plot, default = -10
verb	show output, default = TRUE.

Value

$obs.r - observed correlation.

$S.0 - support for observed correlation versus the null.

$S.1 - support for the specified correlation versus observed correlation.

$S.10 - support for the specified correlation versus the null value.

$exp.r - the specified correlation.

$N - the sample size.

$p.value - the p value for significance test versus 0.

$like.int - the likelihood interval.

$like.int.spec - the specified likelihood interval in terms of support.

$conf.int - the % confidence interval for the correlation.

$alpha.spec - the specified alpha for the % confidence interval.

References

Cahusac, P.M.B. (2020) Evidence-Based Statistics, Wiley, ISBN : 978-1119549802

Royall, R. M. (1997). Statistical evidence: A likelihood paradigm. London: Chapman & Hall, ISBN : 978-0412044113

Edwards, A.W.F. (1992) Likelihood, Johns Hopkins Press, ISBN : 978-0801844430

Examples

# for heptathlon example, p 104
m200 <- c(22.6,	23.7,	23.1,	23.6,	23.6,	23.6,	25.5,
23.9,	24.5,	23.9,	24.9,	24.8,	24.7,
25.0,	24.6,	24.9,	25.0,	25.6,	24.8,
25.5,	25.7,	24.9,	26.6,	25.2,	26.2)
m800 <- c(128.5,	126.1,	124.2,	132.5,
134.7,	132.5,	138.5,	127.9,	133.7,	132.2,
136.1,	142.8,	125.8, 131.5,	137.1,	134.9,
146.7,	133.9,	146.4,	144.0,	133.4,
138.0,	139.2,	137.3,	163.4)
m=L_corr(m200, m800, null=0, exp.r=.4, L.int=3, alpha=.05,
toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)
m
#Note: the support for observed vs 0 is different from book (5.776 vs 5.700)
#due to differences in calculation of r by Excel and R

likelihoodR documentation built on Oct. 22, 2024, 5:06 p.m.