R: Robustified t-test

Robustified-t-test

R Documentation

Robustified t-test

Description

Performs robustified one-sample t-test on a vector of data.

Usage

rt.test(x, alternative = c("two.sided", "less", "greater"), 
  mu = 0, test.stat = c("TA", "TB"), conf.level = 0.95)

Arguments

`x`	vector of quantiles.
`alternative`	a character string 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.
`test.stat`	a character string specifying the test statistic.
`conf.level`	confidence level of the interval.

Details

Based on the empirical distributions of the TA statistic (based on median and MAD) and the TB statistic (based on Hodges-Lehmann and Shamos), this function performs one-sample robustified t-test.

Value

A list with class "htest" containing the following components:

`statistic`	the value of the test statistic.
`parameter`	sample size (non-missing observations in the sample).
`p.value`	the p-value for the test.
`conf.int`	a confidence interval for the mean appropriate to the specified alternative hypothesis.
`estimate`	the specified hypothesized value of the median (TA) or the Hodges-Lehmann (TB).
`sample.size`	numeric scalar containing the number of non-missing observations in the sample used for the hypothesis test
`null.value`	the specified hypothesized value of the true mean.
`alternative`	a character string describing the alternative hypothesis.
`method`	a character string indicating which statistic (TA or TB) is used.
`data.name`	a character string giving the name(s) of the data.

Author(s)

Chanseok Park and Min Wang

References

Park, C. and M. Wang (2018). Empirical distributions of the robustified t-test statistics. ArXiv e-prints, 1807.02215. https://arxiv.org/abs/1807.02215

Jeong, R., S. B. Son, H. J. Lee, and H. Kim (2018). On the robustification of the z-test statistic. Presented at KIIE Conference, Gyeongju, Korea. April 6, 2018.

Park, C. (2018). Note on the robustification of the Student t-test statistic using the median and the median absolute deviation. ArXiv e-prints, 1805.12256. https://arxiv.org/abs/1805.12256

Examples

# For robustified t-test (two-sided) using median and MAD (TA).
#    test.stat="TA" (default)
x = rnorm(10) 
rt.test(x)

# For robustified t-test (two-sided) using Hodges-Lehmann and Shamos (TB).
x = rnorm(10)
rt.test(x, test.stat="TB")

# 90% CI (two sides).
x = rnorm(10)
rt.test(x, conf.level=0.9)

# 90% CI (one side).
x = rnorm(10)
rt.test(x, alternative="less", conf.level=0.9)