likelihoodR (version 1.1.5)

L_corr: 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)

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.

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.

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