wle.t.test {wle}R Documentation

Weighted Likelihood Student's t-Test

Description

wle.t.test performs one and two sample Weighted Likelihood t-tests on vectors of data. This is a robust version of the classical t-test. It should be used when the majority of the data follows a normal distribution.

Usage

wle.t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),
       mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.95,
       boot=30, group, num.sol=1, raf="HD", smooth=0.003, 
       tol=10^(-6), equal=10^(-3), max.iter=500)

Arguments

x a numeric vector of data values.
y an optional numeric vector data values.
alternative character specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
mu a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
paired a logical indicating whether you want a paired weighted t-test.
var.equal a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch approximation to the degrees of freedom is used.
conf.level confidence level of the interval.
boot the number of starting points based on boostrap subsamples to use in the search of the roots.
group the dimension of the bootstap subsamples. The default value is max(round(size/4),2) where size is the number of observations.
num.sol maximum number of roots to be searched.
raf type of Residual adjustment function to be use:
raf="HD": Hellinger Distance RAF,
raf="NED": Negative Exponential Disparity RAF,
raf="SCHI2": Symmetric Chi-Squared Disparity RAF.
smooth the value of the smoothing parameter.
tol the absolute accuracy to be used to achieve convergence of the algorithm.
equal the absolute value for which two roots are considered the same. (This parameter must be greater than tol).
max.iter maximum number of iterations.

Details

If paired is TRUE then both x and y must be specified and they must be the same length. Missing values are removed (in pairs if paired is TRUE). If var.equal is TRUE then the pooled estimate of the variance is used. By default, if var.equal is FALSE then the variance is estimated separately for both groups and the Welch modification to the degrees of freedom is used.

Value

The function return a list of class "wle.t.test" with the following components:

test A list with two dimensions. Each cell is related with a combination of 'x', 'y' roots. In each cell a list of class "htest" containing the following components:
statistic the value of the t-statistic.
parameters the degrees of freedom for the t-statistic.
p.value the p-value for the test.
conf.int a confidence interval for the mean appropriate to the specified alternative hypothesis.
estimate the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test.
null.value the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.
alternative a character string describing the alternative hypothesis.
method a character string indicating what type of t-test was performed.
data.name a character string giving the name(s) of the data.
x.weights the weights related to the 'x' data.
y.weights the weights related to the 'y' data.
x.root the number of the 'x' root.
y.root the number of the 'y' root.
x.tot.sol the number of solutions for the dataset 'x'.
y.tot.sol the number of solutions for the dataset 'y' or 1.
call the match.call().
paired a logical indicating whether is a paired weighted t-test.
x 'x' data.
y 'y' data or NULL.

Author(s)

Claudio Agostinelli

References

Agostinelli, C., (1998) Inferenza statistica robusta basata sulla funzione di verosimiglianza pesata: alcuni sviluppi, Ph.D Thesis, Department of Statistics, University of Padova (in italian).

Agostinelli, C., (2002) Un approccio alla verifica d'ipotesi robusta basato sulla funzione di verosimiglianza pesata - Robust Testing Hypotheses via Weighted Likelihood function, Statistica, Anno LXII, 1, 87-110.

Agostinelli, C., and Markatou, M., (2001) Test of hypotheses based on the Weighted Likelihood Methodology, Statistica Sinica, vol. 11, n. 2, 499-514.

Examples

library(wle)

set.seed(1234)

x <- rnorm(20,0,1)
y <- rnorm(20,6,1)

t.test(x,y)                # P < 2.2e-16
wle.t.test(x,y,group=5)    # P < 2.2e-16

t.test(x,y=c(y,250))       # P = 0.1419 -- NOT significant anymore
wle.t.test(x,y=c(y,250),group=5) # P < 2.2e-16 -- still significant 
set.seed(1234)

# three roots for 'x' and three roots for 'y'
# with nine t-test value
res <- wle.t.test(x=c(rnorm(40,0,1),rnorm(40,10,1)),
           y=c(rnorm(40,0,1),rnorm(40,10,1)),
           group=4,num.sol=3,boot=100)

print(res) # print ALL the t-test
print(res,x.root=1,y.root=1)   # print the test associated to the 
                               # x.root=1,y.root=1 

root.1.1 <- res$test[[1]][[1]] # access to the object associated 
                               # to the x.root=1,y.root=1 

names(root.1.1)

set.seed(1234)

# one root and NOT significant t-test
wle.t.test(x=c(rnorm(40,0,1),rnorm(40,10,1)),
           y=c(rnorm(40,0,1),rnorm(40,10,1)),
           group=4,num.sol=3,boot=100,paired=TRUE)


[Package wle version 0.9-3 Index]