Title: Robustified t-Test
Version: 1.18.7.9
Date: 2018-07-09
Author: Chanseok Park [aut, cre], Min Wang [ctb]
Maintainer: Chanseok Park <statpnu@gmail.com>
Depends: R (≥ 3.2.3)
Description: Performs one-sample t-test based on robustified statistics using median/MAD (TA) and Hodges-Lehmann/Shamos (TB). For more details, see Park and Wang (2018)<doi:10.48550/arXiv.1807.02215>. This work was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. NRF-2017R1A2B4004169).
License: GPL-2 | GPL-3
URL: https://github.com/statpnu/R-package
LazyData: yes
NeedsCompilation: no
Packaged: 2018-07-09 06:11:20 UTC; cp
Repository: CRAN
Date/Publication: 2018-07-10 17:30:03 UTC

Hodges-Lehmann estimate

Description

Calculates the Hodges-Lehmann estimate.

Usage

HL.estimate(x, na.rm = FALSE, IncludeEqual = FALSE)

Arguments

x

vector of observations.

na.rm

a logical value indicating whether NA values should be stripped before the computation proceeds.

IncludeEqual

FALSE (default) calculates median of ([x[i]+x[j])/2) with i<j. TRUE calculates median of ([x[i]+x[j])/2) with i<=j.

Value

If x is not logical (coerced to numeric), numeric (including integer) or complex, NA_real_ is returned, with a warning.

Author(s)

Chanseok Park and Min Wang

References

Hodges, J. L. and E. L. Lehmann (1963). Estimates of location based on rank tests. Annals of Mathematical Statistics, 34, 598–611.

See Also

mean for calculating sample mean.

Examples

x = c(0:10, 50)
HL.estimate(x)

Quantile values of the robustified statistic, TA.

Description

Quantiles of the robustified statistic, TA. They are obtained using the extensive Monte Carlo with 1E08 replicates.

Usage

Quantiles.TA

Format

This data frame contains 97 rows and 500 columns.

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

Quantile values of the robustified statistic, TB.

Description

Quantiles of the robustified statistic, TB. They are obtained using the extensive Monte Carlo with 1E08 replicates.

Usage

Quantiles.TB

Format

This data frame contains 97 rows and 500 columns.

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

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

See Also

t.test for performing the Student t-test.
prop.test for testing the proportion.

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)

Lower quantiles of TA or TB

Description

Calculates the quantiles of the robustified t-test statistic (TA or TB).

Usage

  q.robustified.t(p, n, test.stat=c("TA", "TB"), lower.tail=TRUE)

Arguments

p

vector of probabilities.

n

the sample size

test.stat

a character string specifying the test statistic.

lower.tail

logical; if TRUE (default), probabilities are p=P[X <= x], otherwise, p=P[X > x].

Details

Using the empirical distributions of TA and TB statistics, it calculates the quantile.

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

See Also

qt for obtaining quantile value of Student t-distribution.

Examples

# quantile value of TA (using median and MAD) statistic
q.robustified.t(p=0.01, n=10, test.stat="TA")

# quantile value of TB (using Hodges-Lehmann and Shamos) statistic
q.robustified.t(p=0.01, n=10, test.stat="TB")