likelihoodR (version 1.1.5)

L_ttest: Likelihood Supports for the One Sample and Related Samples t Test

Description

This function calculates several different supports. Effect size (Cohen's d) and a second alternative hypothesis value can be specified. The maximum support is the support for the observed mean versus the null value. The support for the specified d versus the null is also calculated. If a second hypothesis value is specified (in units of the original measurements) then two further supports are calculated: d versus 2nd alternative hypothesis, and 2nd alternative hypothesis versus the null. The likelihood curve graphic with MLE and specified hypothesis values is produced. The requested likelihood interval is provided and displayed on likelihood curve. The t and p values for the test against the null value are given.

Usage

L_ttest(data1, data2, null=0, d=0.5, alt.2=NULL,
L.int=2, toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)

Value

$obs.mean - the observed mean or difference in mean for related samples.

$df - degrees of freedom.

$alt.H1 - mean value according to specified d.

$alt.H2 - specified second hypothesis value.

$S_max - maximum support for observed mean against the null.

$S_10 - support for d versus null.

$S_12 - support for d versus specified second hypothesis.

$S_20 - support for second hypothesis versus the null.

$like.int - likelihood interval.

$L.int.spec - specified likelihood interval in units of support.

$null.value - null value.

$t.val - t value for test against null.

$p.val - p value for test against null.

$d.obs - observed effect size.

Arguments

data1

a (non-empty) numeric vector of data values.

data2

a (non-empty) numeric vector of data values for related sample, default = NULL.

null

value for the null hypothesis, default = 0.

d

Cohen's effect size, default = 0.5.

alt.2

value for an alternative hypothesis, in units used for data, default = NULL.

L.int

likelihood interval given for a given support value, e.g. 2 or 3, default = 2.

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

Baguley, T. (2012) Serious Stats, Palgrave Macmillan, ISBN: 978-0230577183

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

Royall, R. M. (2000). On the probability of observing misleading statistical evidence. Journal of the American Statistical Association, 95, 760.

Examples

# one sample Gosset's original additional hours of sleep data, p 29
mysample <- c(0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0)
L_ttest(mysample, d=.5, alt.2=2, L.int=2)

# related samples, p 56
mysample2 <- c(1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4)
L_ttest(mysample, mysample2, d=1, alt.2=2, L.int=2,
toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)