Statistical Hypothesis Testing in R

SHT aims at providing a casket of tools for hypothesis testing procedures ranging from classical to modern techniques. We hope it not be used as a primary means of p-hacking.

Installation

SHT released version can be obtained from CRAN with:

install.packages("SHT")

or the up-to-date development version from github:

## install.packages("devtools")
## library(devtools)
devtools::install_github("kisungyou/SHT")

List of Available Tests

We categorized available functions by their object of interest for better navigation.

• Notations x and y refer to samples.
• Authors are referred by last names. See the help page of each function for complete references.
• k-sample means that the test is checking the homogeneity across multiple samples.
• Function naming convention is {type of test.test name}, or {type of test.year authors}, where there are two or three authors, we took their initials as abbreviation or simply the last name of the first author otherwise.
• usek1d and useknd lets a user to apply any k-sample tests for two-sample testings.
• When ℝ^p notation is used, it denotes multivariate procedures.

0. utilities

function name	description
usek1d	apply k-sample test method for two univariate samples
useknd	apply k-sample test method for two multivariate samples

1. tests for univariate mean μ ∈ ℝ

function name	authors	description of H0
mean1.ttest	Student (1908)	μx {≤, =, ≥} μ0 (1-sample)
mean2.ttest	Student (1908) & Welch (1947)	μx {≤, =, ≥} μy (2-sample)
meank.anova	-	μ1 = ⋯ = μk (k-sample)

2. tests for multivariate mean μ ∈ ℝ^p

function name	authors	description of H0
mean1.1931Hotelling	Hotelling (1931)	μx = μ0 (1-sample)
mean1.1958Dempster	Dempster (1958, 1960)	μx = μ0 (1-sample)
mean1.1996BS	Bai and Saranadasa (1996)	μx = μ0 (1-sample)
mean1.2008SD	Srivastava and Du (2008)	μx = μ0 (1-sample)
mean2.1931Hotelling	Hotelling (1931)	μx = μy (2-sample)
mean2.1958Dempster	Dempster (1958, 1960)	μx = μy (2-sample)
mean2.1965Yao	Yao (1965)	μx = μy (2-sample)
mean2.1980Johansen	Johansen (1980)	μx = μy (2-sample)
mean2.1986NVM	Nel and Van der Merwe (1986)	μx = μy (2-sample)
mean2.1996BS	Bai and Saranadasa (1996)	μx = μy (2-sample)
mean2.2004KY	Krishnamoorthy and Yu (2004)	μx = μy (2-sample)
mean2.2008SD	Srivastava and Du (2008)	μx = μy (2-sample)
mean2.2011LJW	Lopes, Jacob, and Wainwright (2011)	μx = μy (2-sample)
mean2.2014CLX	Cai, Liu, and Xia (2014)	μx = μy (2-sample)
mean2.2014Thulin	Thulin (2014)	μx = μy (2-sample)
meank.2007Schott	Schott (2007)	μ1 = ⋯ = μk (k-sample)
meank.2009ZX	Zhang and Xu (2009)	μ1 = ⋯ = μk (k-sample)
meank.2019CPH	Cao, Park, and He (2019)	μ1 = ⋯ = μk (k-sample)

3. tests for variance σ²

function name	authors	description of H0
var1.chisq	-	σx2 {≤, =, ≥} σ02 (1-sample)
var2.F	-	σx2 {≤, =, ≥} σy2 (2-sample)
vark.1937Bartlett	Bartlett (1937)	σ12 = ⋯ = σk2 (k-sample)
vark.1960Levene	Levene (1960)	σ12 = ⋯ = σk2 (k-sample)
vark.1974BF	Brown and Forsythe (1974)	σ12 = ⋯ = σk2 (k-sample)

4. tests for covariance Σ

function name	authors	description of H0
cov1.2012Fisher	Fisher (2012)	Σx = Σ0 (1-sample)
cov1.2015WL	Wu and Li (2015)	Σx = Σ0 (1-sample)
cov2.2012LC	Li and Chen (2012)	Σx = Σy (2-sample)
cov2.2013CLX	Cai, Liu, and Xia (2013)	Σx = Σy (2-sample)
cov2.2015WL	Wu and Li (2015)	Σx = Σy (2-sample)
covk.2001Schott	Schott (2001)	Σ1 = ⋯ = Σk (k-sample)
covk.2007Schott	Schott (2007)	Σ1 = ⋯ = Σk (k-sample)

5. simultaneous tests for mean μ and variance σ² in ℝ¹

function name	authors	description of H0
mvar1.1998AS	Arnold and Shavelle (1998)	μx = μ0,  σx2 = σ02 (1-sample)
mvar1.LRT	-	μx = μ0,  σx2 = σ02 (1-sample)
mvar2.1930PN	Pearson and Neyman (1930)	μx = μy,  σx2 = σy2 (2-sample)
mvar2.1976PL	Perng and Littell (1976)	μx = μy,  σx2 = σy2 (2-sample)
mvar2.1982Muirhead	Muirhead (1982)	μx = μy,  σx2 = σy2 (2-sample)
mvar2.2012ZXC	Zhang, Xu, and Chen (2012)	μx = μy,  σx2 = σy2 (2-sample)
mvar2.LRT	-	μx = μy,  σx2 = σy2 (2-sample)

6. simultaneous tests for mean μ and covariance Σ in ℝ^p

function name	authors	description of H0
sim1.2017Liu	Liu et al. (2017)	μx = μ0,  Σx = Σ0 (1-sample)
sim2.2018HN	Hyodo and Nishiyama (2018)	μx = μy,  Σx = Σy (2-sample)

7. tests for equality of distributions

function name	authors	description of H0
eqdist.2014BG	Biswas and Ghosh (2014)	FX = FY ∈ ℝ1 & ℝp (2-sample)

8. goodness-of-fit tests of normality

function name	authors	description of H0
norm.1965SW	Shapiro and Wilk (1965)	FX = Normal ∈ ℝ1
norm.1972SF	Shapiro and Francia (1972)	FX = Normal ∈ ℝ1
norm.1980JB	Jarque and Bera (1980)	FX = Normal ∈ ℝ1
norm.1996AJB	Urzua (1996)	FX = Normal ∈ ℝ1
norm.2008RJB	Gel and Gastwirth (2008)	FX = Normal ∈ ℝ1

9. goodness-of-fit tests of uniformity

function name	authors	description of H0
unif.2017YMi	Yang and Modarres (2017)	FX = Uniform ∈ ℝp
unif.2017YMq	Yang and Modarres (2017)	FX = Uniform ∈ ℝp