L_2S_ttest: Likelihood Supports for Independent Samples t Test

In likelihoodR: Likelihood Analyses for Common Statistical Tests

Likelihood Supports for Independent Samples t Test

Description

This function calculates several different supports for independent samples. 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. Finally, the requested likelihood interval is provided. The t, p and observed d values for the test against the null are given. If variances are specified as unequal then uses Welch's test where homogeneity of variance is not required.

Usage

L_2S_ttest(data, group, veq=0, null=0, d=0.5, alt.2=NULL,
L.int=2, toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)

Arguments

data	a (non-empty) numeric vector of data values.
group	an integer vector the same length as data, coding for 2 groups.
veq	whether variances are equal: 1 = Yes, 0 = No, default = 0.
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 as support values, 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.

Value

$obs.diff - the observed difference in means.

$df - degrees of freedom.

$var.eq - if not equal (0) then Welch's test used.

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

$alt.H2 - specified second hypothesis value.

$S_max - maximum support for observed mean difference 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 (from null).

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. (1997) Statistical Evidence: A Likelihood Paradigm, Chapman & Hall, ISBN : 978-0412044113

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

Examples

# using a variation on Gosset's original additional hours of sleep data, p 59
mysample <- c(0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0)
treat <- rep(1:0,each=5)
L_2S_ttest(mysample, treat, veq=0, null=0, d=0.5, alt.2=2, L.int=2,
toler=0.0001, logplot=FALSE, supplot=-10, verb=TRUE)

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