MultNonParam

Description

A collection of nonparametric methods.

Author(s)

Maintainer: John E. Kolassa kolassa@stat.rutgers.edu

Authors:

• Stephane Jankowski

One-way ANOVA using permutation tests

Description

aov.P uses permutation tests instead of classic theory tests to run a one-way or two-way ANOVA.

Usage

aov.P(dattab, treatment = NULL, be = NULL)

Arguments

Details

The function calls a Fortran code to perform the permutation tests and the ANOVA. The function has to be applied directly on a cross-table of two variables.

Value

A list with fields pv, the p-value obtained with the permutation tests, and tot, the total number of permutations.

Permutation test of assication

Description

Calculate the p-value for the test of association between two variables using the permutation method.

Usage

betatest(x, y)

Arguments

Value

p-value

Examples

#Example using data from plant Qn1 from the CO2 data set.^M
betatest(CO2[CO2$Plant=="Qn1",4],CO2[CO2$Plant=="Qn1",5])

Calculate the probability atom of the count of concordant pairs among indpendent pairs of random variables.

Description

Calculate the probability atom of the count of concordant pairs among indpendent pairs of random variables.

Usage

dconcordant(ss, nn)

Arguments

Value

real probability

Mann Whitney Probability Mass function

Description

Calculates the Mann Whitney Probability Mass function recursively.

Usage

dmannwhitney(u, m, n)

Arguments

Value

Probability that the Mann-Whitney statistic takes the value u under H0

Confidence Intervals for Empirical Cumulative Distribution Functions

Description

Confidence Intervals for Empirical Cumulative Distribution Functions

Usage

ecdfcis(data, alpha = 0.05, dataname = NA, exact = TRUE, newplot = TRUE)

Arguments

Exact Quantile Confidence Interval

Description

Calculates exact quanitle confidence intervals by inverting the generalization of the sign test.

Usage

exactquantileci(xvec, tau = 0.5, alpha = 0.05, md = 0)

Arguments

Value

A list with components cis, an array with two columns, representing lower and upper bounds, and a vector pvals, of p-values.

Normal-theory two sample scorestatistic.

Description

Calculates the p-value from the normal approximation to the permutation distribution of a two-sample score statistic.

Usage

genscorestat(scores, group, correct = 0)

Arguments

Value

Object of class htest containing the p-value.

Fisher's LSD method applied to the Kruskal-Wallis test

Description

This function applies a rank-based method for controlling experiment-wise error. Two hypothesis have to be respected: normality of the distribution and no ties in the data. The aim is to be able to detect, among k treatments, those who lead to significant differencies in the values for a variable of interest.

Usage

higgins.fisher.kruskal.test(resp, grp, alpha = 0.05)

Arguments

Details

First, the Kruskal-Wallis test is used to test the equality of the distributions of each treatment. If the test is significant at the level alpha, the method can be applied.

Value

A matrix with two columns. Each row indicates a combinaison of two groups that have significant different distributions.

References

J.J. Higgins, (2004), Introduction to Modern Nonparametric Statistics, Brooks/Cole, Cengage Learning.

Sample Size for the Kruskal-Wallis test.

Description

kweffectsize approximates effect size for the Kruskal-Wallis test, using a chi-square approximation under the null, and a non-central chi-square approximation under the alternative. The noncentrality parameter is calculated using alternative means and the null variance structure.

Usage

kweffectsize(
  totsamp,
  shifts,
  distname = c("normal", "logistic", "cauchy"),
  targetpower = 0.8,
  proportions = rep(1, length(shifts))/length(shifts),
  level = 0.05
)

Arguments

Details

The standard noncentral chi-square power formula, or Monte Carlo, is used.

Value

A list with components power, giving the power approximation, ncp, giving the noncentrality parameter, cv, giving the critical value, probs, giving the intermediate output from pairwiseprobability, and expect, the quantities summed before squaring in the noncentrality parameter.

Examples

#Calculate the effecct size necessary to have the desired power .8 for a test
#with the level .5 with sample size 60, group centers 0, 1, and 2, 
#normally distributed observations, evenly split among the three groups.
kweffectsize(60,c(0,1,2),"normal")

Power for the Kruskal-Wallis test.

Description

kwpower approximates power for the Kruskal-Wallis test, using a chi-square approximation under the null, and a non-central chi-square approximation under the alternative. The noncentrality parameter is calculated using alternative means and the null variance structure.

Usage

kwpower(
  nreps,
  shifts,
  distname = c("normal", "cauchy", "logistic"),
  level = 0.05,
  mc = 0,
  taylor = FALSE
)

Arguments

Details

The standard noncentral chi-square power formula, or Monte Carlo, is used.

Value

A list with components power, giving the power approximation, ncp, giving the noncentrality parameter, cv, giving the critical value, probs, giving the intermediate output from pairwiseprobability, and expect, the quantities summed before squaring in the noncentrality parameter.

Examples

#Calculate the power for the Kruskal Wallis test for normal observations,
#10 observations in each of three groups, with groups centered at 0, 1, 2.
#Level is 0.05 by default.
kwpower(rep(10,3),c(0,1,2),"normal")

Sample Size for the Kruskal-Wallis test.

Description

kwsamplesize approximates sample size for the Kruskal-Wallis test, using a chi-square approximation under the null, and a non-central chi-square approximation under the alternative. The noncentrality parameter is calculated using alternative means and the null variance structure.

Usage

kwsamplesize(
  shifts,
  distname = c("normal", "logistic", "cauchy"),
  targetpower = 0.8,
  proportions = rep(1, length(shifts))/length(shifts),
  level = 0.05,
  taylor = FALSE
)

Arguments

Details

The standard noncentral chi-square power formula, is used.

Value

A list with the total number of observations needed to obtain approximate power, as long as this number is split amomg groups according to argument proportion.

Examples

#Calculate the sample size necessary to detect differences among three
#groups with centers at 0,1,2, from normal observations, using a test of
#level 0.05 and power 0.80.
kwsamplesize(c(0,1,2),"normal")

Perform the Mann Whitney two-sample test

Description

Perform the Mann Whitney two-sample test

Usage

mannwhitney.test(x, y, alternative = c("two.sided", "less", "greater"))

Arguments

Value

Test results of class htest

Examples

mannwhitney.test(rnorm(10),rnorm(10)+.5)

Mood's Median test, extended to odd sample sizes.

Description

Test whether two samples come from the same distribution. This version of Mood's median test is presented for pedagogical purposes only. Many authors successfully argue that it is not very powerful. The name "median test" is a misnomer, in that the null hypothesis is equality of distributions, and not just equality of median. Exact calculations are not optimal for the odd sample size case.

Usage

mood.median.test(x, y, exact = FALSE)

Arguments

Details

The exact case reduces to Fisher's exact test.

Value

The two-sided p-value.

Next permutation

Description

Cycles through permutations of first argument

Usage

nextp(perm, b = 1)

Arguments

Value

The next permutation

Perform Page test for unbalanced two-way design

Description

Perform Page test for unbalanced two-way design

Usage

page.test.unbalanced(x, trt, blk, sides = 2)

Arguments

Value

P-value for Page test.

Examples

page.test.unbalanced(rnorm(15),rep(1:3,5),rep(1:5,rep(3,5)))

Pairwise probabilities of Exceedence

Description

pairwiseprobabilities calculates probabilities of one variable exceeding another, where the variables are independent, and with identical distributions except for a location shift. This calculation is useful for power of Mann-Whitney-Wilcoxon, Jonckheere-Terpstra, and Kruskal-Wallis testing.

Usage

pairwiseprobabilities(
  shifts,
  distname = c("normal", "cauchy", "logistic"),
  taylor = FALSE
)

Arguments

Details

Probabilities of particular families must be calculated analytically.

Value

A matrix with as many rows and colums as there are shift parameters. Row i and column j give the probability of an observation from group j exceeding one from group i.

Examples

pairwiseprobabilities(c(0,1,2),"normal")

Calculate the cumulative distribution of the count of concordant pairs among indpendent pairs of random variables.

Description

Calculate the cumulative distribution of the count of concordant pairs among indpendent pairs of random variables.

Usage

pconcordant(ss, nn)

Arguments

Value

real probability

Power Plot

Description

Plots powers for the Kruskall-Wallis test, via Monte Carlo and two approximations.

Usage

powerplot(
  numgrps = 3,
  thetadagger = NULL,
  nnvec = 5:30,
  nmc = 50000,
  targetpower = 0.8,
  level = 0.05
)

Arguments

Derivative of pairwise probabilities of Exceedence

Description

probabilityderiv calculates derivatives probabilities of one variable exceeding another, where the variables are independent, and with identical distributions except for a location shift, at the null hypothesis. This calculation is useful for power of Mann-Whitney-Wilcoxon, Jonckheere-Terpstra, and Kruskal-Wallis testing.

Usage

probabilityderiv(distname = c("normal", "cauchy", "logistic"))

Arguments

Details

Probabilities of particular families must be calculated analytically, and then differentiated.

Value

The scalar derivative.

Stratified Multivariate Kawaguchi Koch Wang Estimators

Description

Function that return the estimators and their variance-covariance matrix calculated with the Kawaguchi - Koch - Wang method.

Usage

probest(ds, resp, grp, str = NULL, covs = NULL, delta = NA, correct = FALSE)

Arguments

Details

The function calls a Fortran code to calculate the estimators b and their variance-covariance matrix Vb

Value

A list with components b, the vector of adjusted estimates from the method, and Vb, the corresponding estimated covariance matrix.

References

A. Kawaguchi, G. G. Koch and X. Wang (2012), "Stratified Multivariate Mann-Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment", Statistics in Biopharmaceutical Research 3 (2) 217-231.

J. E. Kolassa and Y. Seifu (2013), Nonparametric Multivariate Inference on Shift Parameters, Academic Radiology 20 (7), 883-888.

Examples

# Breast cancer data from the MultNonParam package.
data(sotiriou)
attach(sotiriou)
#First simple plot of the data
plot(AGE,TUMOR_SIZE,pch=(recur+1),main="Age and Tumor Size",
  sub="Breast Cancer Recurrence Data",xlab="Age (years)",
  ylab="Tumor Size",col=c("blue","darkolivegreen"))
legend(31,8,legend=c("Not Recurrent","Recurrent"),
  pch=1:2,col=c("blue","darkolivegreen"))
#AGE and TUMOR_SIZE are the response variables, recur is used for the groups,
#TAMOXIFEN_TREATMENT for the stratum and ELSTON.ELLIS_GRADE is a covariate.
po<-probest(sotiriou,c("AGE","TUMOR_SIZE"),"recur",
  "TAMOXIFEN_TREATMENT","ELSTON.ELLIS_GRADE")

prostate

Description

221 prostate cancer patients are collected in this data set.

Format

• hosp : Hospital in which the patient is hospitalized.

• stage : stage of the cancer.

• gleason score : used to help evaluate the prognosis of the cancer.

• psa : prostate-specific antigen.

• age : age of the patient.

• advanced : boolean. TRUE if the cancer is advanced.

References

A. V. D'Amico, R. Whittington, S. B. Malkowicz, D. Schultz, K. Blank, G. A. Broderick, J. E. Tomaszewski, A. A. Renshaw, I. Kaplan, C. J. Beard, A. Wein (1998) , Biochemical outcome after radical prostatectomy, external beam radiation therapy, or interstitial radiation therapy for clinically localized prostate cancer, JAMA : the journal of the American Medical Association 280 969-74.

Examples

data(prostate)
attach(prostate)
plot(age,psa,main="Age and PSA",sub="Prostate Cancer Data",
   xlab="Age (years)",ylab="PSA")

Calculate the quantiles of the count of concordant pairs among indpendent pairs of random variables.

Description

Calculate the quantiles of the count of concordant pairs among indpendent pairs of random variables.

Usage

qconcordant(qq, nn, exact = TRUE)

Arguments

Value

Integer quantile

Compare the sensitivity of different statistics.

Description

Compare the sensitivity of different statistics.

Usage

sensitivity.plot(y, sub, stats)

Arguments

Details

To compare the sensitivity, outliers are added to the original data. The shift of each statistics due to the new value is measured and plotted.

Nonparametric Confidence Region for a Vector Shift Parameter

Description

Inversion of a one-sample bivariate rank test is used to produce a confidence region. The region is constructed by building a grid of potential parameter values, evaluating the test statistic on each grid point, collecting the p-values, and then drawing the appropriate countour of the p-values. The grid is centered at the bivariate median of the data set.

Usage

shiftcr(xm,  hpts = 50)

Arguments

Value

nothing

Noncentrality Parameter for a Given Level and Power

Description

This function calculates the noncentrality parameter required to give a test whose null distribution is central chi-square and whose alternative distribution is noncentral chi-square the required level and power.

Usage

solvencp(df, level = 0.05, targetpower = 0.8)

Arguments

Value

required noncentrality parameter.

Examples

solvencp(4)

Breast cancer data set

Description

187 breast cancer patients are collected in this data set.

Usage

data(sotiriou)

Format

A data set with the following variables

• AGE : Age of the patient

• TUMOR_SIZE : The size of the tumor, numeric variable

• recur : 1 if the patient has a recurent breast cancer, 0 if it is not reccurent.

• ELSTON.ELLIS_GRADE : Elston Ellis grading system in order toclassify the breast cancers. It can be a low, intermediate or high grade (high being the worst prognosis)

• TAMOXIFEN_TREATMENT : boolean. TRUE if the patient is treated with the Tamoxifen treatment.

Source

https://gdoc.georgetown.edu/gdoc/

References

S. Madhavan, Y. Gusev, M. Harris, D. Tanenbaum, R. Gauba, K. Bhuvaneshwar, A. Shinohara, K. Rosso, L. Carabet, L. Song, R. Riggins, S. Dakshanamurthy, Y. Wang, S. Byers, R. Clarke, L. Weiner (2011), A systems medicine platform for personalized oncology, Neoplasia 13.

C. Sotiriou, P. Wirapati, S. Loi, A. Harris, S. Fox, J. Smeds, H. Nordgren, P. Farmer, V. Praz, B. Haibe-Kains, C. Desmedt, D. Larsimont, F. Cardoso, H. Peterse, D. Nuyten, M. Buyse, M. Van de Vijver, J. Bergh, M. Piccart, M. Delorenzi (2006), Gene expression profiling in breast cancer: understanding the molecular basis of histologic grade to improve prognosis, Journal of the National Cancer Institute 98 262-72.

Examples

data(sotiriou)
plot(sotiriou$AGE,sotiriou$TUMOR_SIZE,pch=(sotiriou$recur+1),
   main="Age and Tumor Size",
   sub="Breast Cancer Recurrence Data",
   xlab="Age (years)",ylab="Tumor Size",
   col=c("blue","darkolivegreen"))
legend(31,8,legend=c("Not Recurrent","Recurrent"),pch=1:2,
   col=c("blue","darkolivegreen"))

Generalization of Wilcoxon signed rank test

Description

This function returns either exact or asymptotic p-values for score tests of the null hypothesis of univariate symmetry about 0.

Usage

symscorestat(y, scores = NULL, exact = F, sides = 1)

Arguments

Details

The statistic considered here is the sum of scores corresponding to those entries in y that are positive. If exact=T, the function calls a Fortran code to cycle through all permutations. If exact=F, the expectation of the statistic is calculated as half the sum of the scores, the variance is calculated as one quarter the sum of squares of scores about their mean, and the statistic is compared to its approximating normal distribution.

Value

A list with components pv, the p-value obtained with the permutation tests, and tot, the total number of rearrangements of the data considred in calculating the p-value.

References

J.J. Higgins, (2004), Introduction to Modern Nonparametric Statistics, Brooks/Cole, Cengage Learning.

Examples

symscorestat(y=c(1,-2,3,-4,5),exact=TRUE)

Perform the Terpstra version of the multi-ordered-sample test

Description

Perform the Terpstra version of the multi-ordered-sample test

Usage

terpstra.test(x, g, alternative = c("two.sided", "less", "greater"))

Arguments

Value

Test results of class htest

Examples

terpstra.test(rnorm(15),rep(1:3,5))

Power for the nonparametric Terpstra test for an ordered effect.

Description

terpstrapower approximates power for the one-sided Terpstra test, using a normal approximation with expectations under the null and alternative, and using the null standard deviation.

Usage

terpstrapower(
  nreps,
  shifts,
  distname = c("normal", "logistic"),
  level = 0.025,
  mc = 0
)

Arguments

Details

The standard normal-theory power formula is used.

Value

A list with components power, giving the power approximation, expect, giving null and alternative expectations, var, giving the null variance, probs, giving the intermediate output from pairwiseprobability, and level.

Examples

terpstrapower(rep(10,3),c(0,1,2),"normal")
terpstrapower(c(10,10,10),0:2,"normal",mc=1000)

Diagnosis for multivariate stratified Kawaguchi - Koch - Wang method

Description

Diagnostic tool that verifies the normality of the estimates of the probabilities b with the Kawaguchi - Koch - Wang method. The diagnostic method is based on a Monte Carlo method.

Usage

testve(n, m, k, nsamp = 100, delta = 0, beta = 0, disc = 0)

Arguments

Details

This functions serves as a diagnosis to prove that the Kawaguchi - Koch - Wang method gives Gaussian estimates for b. It generates random data sets, to which the Mann Whitney test gets applied. y is the generated response variable and x the generated covariable related to y through a regression model.

Value

Nothing is returned. A QQ plot is drawn.

References

A. Kawaguchi, G. G. Koch and X. Wang (2012), "Stratified Multivariate Mann-Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment", Statistics in Biopharmaceutical Research 3 (2) 217-231.

J. E. Kolassa and Y. Seifu (2013), Nonparametric Multivariate Inference on Shift Parameters, Academic Radiology 20 (7), 883-888.

Examples

testve(10,15,3,100,0.4)

Perform the Theil nonparametric estimation and confidence interval for a slope parameter.

Description

Perform the Theil nonparametric estimation and confidence interval for a slope parameter.

Usage

theil(x, y, conf = 0.9)

Arguments

Value

A list with letters and numbers.

• est - An estimate, the median of pairwise slopes.

• ci - A vector of confidence interval endpoints.

Examples

a<-0:19;b<-a^2.5
theil(a,b)

Tukey HSD procedure

Description

Rank-based method for controlling experiment-wise error. Assume normality of the distribution for the variable of interest.

Usage

tukey.kruskal.test(resp, grp, alpha = 0.05)

Arguments

Details

The original Tuckey HSD procedure is supposed to be applied for equal sample sizes. However, the tukey.kruskal.test function performs the Tukey-Kramer procedure that works for unequal sample sizes.

Value

A logical vector for every combinaison of two groups. TRUE if the distribution in one group is significantly different from the distribution in the other group.

References

J.J. Higgins, (2004), Introduction to Modern Nonparametric Statistics, Brooks/Cole, Cengage Learning.

Two Sample Omnibus Tests of Survival Curves

Description

Returns the Kolmogorov-Smirnov and Anderson-Darling test statistics for two right-censored data sets.

Usage

twosamplesurvpvs(times, delta, grp, nmc = 10000, plotme = TRUE, exact = FALSE)

Arguments

Details

The function calls a Fortran code to calculate the estimators b and their variance-covariance matrix Vb

Value

A vector of length two, with the Kolmogorov-Smirnov and Anderson-Darling statistics.

Examples

twosamplesurvpvs(rexp(20),rbinom(20,1,.5),rbinom(20,1,.5))

Two Sample Omnibus Tests of Survival Curves

Description

Returns the Kolmogorov-Smirnov and Anderson-Darling test statistics for two right-censored data sets.

Usage

twosamplesurvtests(times, delta, grp)

Arguments

Value

A vector of length two, with the Kolmogorov-Smirnov and Anderson-Darling statistics.

Examples

twosamplesurvpvs(rexp(20),rbinom(20,1,.5),rbinom(20,1,.5))

Plot a curve, skipping bits where there is a large jump.

Description

Plot a curve, skipping bits where there is a large jump.

Usage

util.jplot(x, y, ...)

Arguments