qddyy/learnnonparam

Implements various nonparametric tests in chapters 1-5 of the book "An introduction to modern nonparametric statistics" by James J. Higgins.

LearnNonparam

Overview

This package implements some of the non-parametric tests in chapters 1-5 of Higgins (2003).

It depends on R6 for object oriented design and Rcpp for integration of R and C++.

A few examples in the book can be found here.

Installation

# install.packages("pak")
pak::pkg_install("qddyy/LearnNonparam")

Usage

library(LearnNonparam)
options(LearnNonparam.pmt_progress = TRUE)

• Construct a test object

  • from some R6 class directly

  t <- Wilcoxon$new(n_permu = 1e6)

  • using the pmt (permutation test) function (recommended)

  t <- pmt("twosample.wilcoxon", n_permu = 1e6)

• Provide it with samples

  t$test(rnorm(20, 1), rnorm(20, 0))

  

• Check the results

  t$statistic

  

  t$p_value

  

  t$print()

  

  t$plot(style = "ggplot2", binwidth = 1)

  

• Modify some active bindings and see how the results change

  t$type <- "asymp"
  t$p_value

  

See pmts() for tests implemented in this package.

key	class	test
onesample.quantile	Quantile	Quantile Test
onesample.cdf	CDF	Inference on Cumulative Distribution Function
twosample.difference	Difference	Two-Sample Test Based on Mean or Median
twosample.wilcoxon	Wilcoxon	Two-Sample Wilcoxon Test
twosample.scoresum	ScoreSum	Two-Sample Test Based on Sum of Scores
twosample.ansari	AnsariBradley	Ansari-Bradley Test
twosample.siegel	SiegelTukey	Siegel-Tukey Test
twosample.rmd	RatioMeanDeviance	Ratio Mean Deviance Test
twosample.ks	KolmogorovSmirnov	Two-Sample Kolmogorov-Smirnov Test
ksample.f	KSampleF	K-Sample Test Based on F Statistic
ksample.kw	KruskalWallis	Kruskal-Wallis Test
ksample.jt	JonckheereTerpstra	Jonckheere-Terpstra Test
multcomp.studentized	Studentized	Multiple Comparison Based on Studentized Statistic
paired.sign	Sign	Two-Sample Sign Test
paired.difference	PairedDifference	Paired Comparison Based on Differences
rcbd.f	RCBDF	Test for RCBD Based on F Statistic
rcbd.friedman	Friedman	Friedman Test
rcbd.page	Page	Page Test
association.corr	Correlation	Test for Association Between Paired Samples
table.chisq	ChiSquare	Chi-Square Test on Contingency Table

The define_pmt function allows users to define new permutation tests. Take Cramér-von Mises test as an example:

t <- define_pmt(
    # this is a two-sample permutation test
    inherit = "twosample",
    statistic = function(x, y) {
        # pre-calculate certain constants that remain invariant during permutation
        n_x <- length(x)
        n_y <- length(y)
        F_x <- seq_len(n_x) / n_x
        G_y <- seq_len(n_y) / n_y
        # return another function to calculate the test statistic
        function(x, y) {
            x <- sort(x)
            y <- sort(y)
            F <- approxfun(x, F_x, "constant", 0, 1, ties = "ordered")
            G <- approxfun(y, G_y, "constant", 0, 1, ties = "ordered")
            sum(c(F_x - G(x), G_y - F(y))^2)
        }
    },
    # reject the null hypothesis when the test statistic is large
    rejection = "r",
    scoring = "none", n_permu = 1e4,
    name = "Cramér-von Mises Test",
    alternative = "samples are from different distributions"
)

t$test(rnorm(20, 1), rnorm(20, 0))$print()

References

Higgins, James J. 2003. An Introduction to Modern Nonparametric Statistics. Florence, KY: Brooks/Cole.