wle.t.test: 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

a numeric vector of data values.

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.

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.

Value

The function return a list of class "wle.t.test" with the following components:
testA 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.solthe number of solutions for the dataset 'x'.
y.tot.solthe number of solutions for the dataset 'y' or 1.
callthe match.call().
paireda logical indicating whether is a paired weighted t-test.
x'x' data.
y'y' data or NULL.

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.

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., (1998). Un approccio robusto alla verifica d'ipotesi basato sulla funzione di verosimiglianza pesata - Robust Testing Hypotheses via Weighted Likelihood function, submitted to {Statistica, revised february 2000 (in italian).

Agostinelli, C., Markatou, M. (2001) Test of hypotheses based on the Weighted Likelihood Methodology, in print {Statistica Sinica probably vol. 11, n. 2, Aprile 2001.

}

[object Object]

library(wle) library(ctest)

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)

robust htest