Computes the upper bound for the null correlation between two overlapping signed rank statistics.

Description

This function is based on the computations in Hollander (1967).

Usage

CorrUpperBound(n)

Arguments

Value

Returns a numeric value indicating the upper bound.

Author(s)

Grant Schneider

References

Hollander, Myles. "Rank tests for randomized blocks when the alternatives have an a priori ordering." The Annals of Mathematical Statistics (1967): 867-877.

Examples

##Hollander-Wolfe-Chicken Example 7.12 Effect of Weight on Forearm Tremor Frequency
CorrUpperBound(6)

Function to compute Hoeffding's D statistic for small sample sizes.

Description

This will calculate Hoeffding's D statistic following section 8.6 of Hollander, Wolfe & Chicken, Nonparametric Statistical Methods, 3e. Uses the correction for ties given at (8.92).

Usage

HoeffD(x, y, example=FALSE) 

Arguments

Note

This function is intended for small sample sizes n only. For large n, use the asymptotic equivalence of D to the Blum-Kliefer-Rosenblatt statistic in the R package "Hmisc", command "hoeffd".

Author(s)

Eric Chicken

Examples

##Example 8.6 Hollander-Wolfe-Chicken##
HoeffD(example=TRUE)

Hollander Bivariate Symmetry

Description

Function to compute the Hollander A statistic for testing bivariate symmetry.

Usage

HollBivSym(x,y=NULL)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent:

HollBivSym(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) HollBivSym(x=c(1,3,5),y=c(2,4,6))

Value

Returns the observed Hollander A statistic.

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Table 3.16 example
recipient<-c(61.4,63.3,63.7,80,77.3,84,105)
donor<-c(70.8,89.2,65.8,67.1,87.3,85.1,88.1)

HollBivSym(recipient,donor)

##Or, equivalently
table3.16<-matrix(c(61.4,63.3,63.7,80,77.3,84,105,70.8,89.2,65.8,67.1,87.3,85.1,88.1),ncol=2)
HollBivSym(table3.16)

Miller Jackknife

Description

Function to compute the Miller Jackknife Q statistic.

Usage

MillerJack(x,y=NULL)

Arguments

Value

Returns the observed Q statistic.

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 5.2 Southern Armyworm and Pokeweed
kentucky.pokeweed<-c(6.2,5.9,8.9,6.5,8.6)
florida.pokeweed<-c(9.5,9.8,9.5,9.6,10.3)
MillerJack(kentucky.pokeweed,florida.pokeweed)

Randles-Fligner-Policello-Wolfe

Description

Function to compute the P-value for the observed Randles-Fligner-Policello-Wolfe V statistic.

Usage

RFPW(z)

Arguments

Value

Returns a list containing:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 3.10 Percentage Chromium in Stainless Steel
table3.9.subset<-c(17.4,17.9,17.6,18.1,17.6)
RFPW(table3.9.subset)

Ranked-Set Sample

Description

Function to obtain a ranked-set sample of given set size and number of cycles based on a specified auxiliary variable.

Usage

RSS(k,m,ranker)

Arguments

Value

Returns a vector of the indices corresponding to the observations selected to be in the RSS.

Author(s)

Grant Schneider

Examples

##Simulate 100 observations of a response variable we are interested in 
##and an auxiliary variable we use for ranking

set.seed(1)
response<-rnorm(100)
auxiliary<-rnorm(100)

##Get the indices for a ranked-set sample with set size 3 and 2 cycles
RSS(2,3,auxiliary) #Tells us to measure observations 2, 19, 32,..., 91

##Alternatively, get the responses for those observations. 
##In practice, response will not be available ahead of time.
response[RSS(2,3,auxiliary)]

Function to compute a critical value for the Ansari-Bradley C distribution.

Description

This function uses pAnsari and qAnsari from the base stats package to compute the critical value for the Ansari-Bradley C distribution at (or typically in the "Exact" case, close to) the given alpha level. The program is reasonably quick for large data, well after the asymptotic approximation suffices, so Monte Carlo methods are not included.

Usage

cAnsBrad(alpha, m, n, method = NA, n.mc = 10000)

Arguments

Value

Returns a list with "NSM3Ch5c" class containing the following components:

Author(s)

Grant Schneider

References

This function uses the source code ansari.c from the stats package by: R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.

See Also

Also see ansari.test()

Examples

##Hollander, Wolfe, Chicken - NSM3 - Example 5.1 (Serum Iron Determination):
cAnsBrad(0.05,20,20,"Asymptotic")
cAnsBrad(0.05,20,20,"Exact")

##Bigger data
cAnsBrad(0.05,100,100,"Exact")

Function to compute a critical value for the Bohn-Wolfe U distribution.

Description

This function uses Monte Carlo sampling to compute the critical value for the Bohn-Wolfe U distribution at (or close to) the given alpha level. The Monte Carlo samples are simulated based on the order statistics of a uniform(0,1) distribution.

Usage

cBohnWolfe(alpha,k,q,c,d,method="Monte Carlo",n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch5c" class containing the following components:

Author(s)

Grant Schneider

References

Bohn, Lora L., and Douglas A. Wolfe. "Nonparametric two-sample procedures for ranked-set samples data." Journal of the American Statistical Association 87.418 (1992): 552-561.

Examples

cBohnWolfe(.0515,4,4,5,5)
cBohnWolfe(.0303,2,3,3,3)

Computes a critical value for the Durbin, Skillings-Mack D distribution.

Description

This function computes the critical value for the Durbin, Skillings-Mack D distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cDurSkiMa(alpha,obs.mat, method=NA, n.mc=10000)

Arguments

Details

The incidence matrix, obs.mat, will be an n x k matrix of ones and zeroes, which indicate where the data are observed and unobserved, respectively. Methods for finding the incidence matrix for various BIBD designs are given in the literature. While the incidence matrix will not be unique for a given (k, n, s, lambda, p) combination, the distribution of D under H0 will be the same.

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Note

The syntax of this procedure differs from the others in the NSM3 package due to the fact that creating a BIBD for a given k,n,s,p,lambda is not trivial. We therefore require obs.mat, the incidence matrix.

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Chapter 7, comment 49 
obs.mat<-matrix(c(1,1,0,1,0,1,0,1,1),ncol=3,byrow=TRUE)
cDurSkiMa(.75,obs.mat)

Computes a critical value for the Fligner-Policello U distribution.

Description

This function computes the critical value for the Fligner-Policello U distriburion at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cFligPoli(alpha,m,n,method=NA,n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch5c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Chapter 4 example Hollander-Wolfe-Chicken##
cFligPoli(.0504,8,7)
cFligPoli(.101,8,7)

Computes a critical value for the Friedman, Kendall-Babington Smith S distribution.

Description

This function computes the critical value for the Friedman, Kendall-Babington Smith S distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level. The method used to compute the distribution is from the reference by Van de Wiel, Bucchianico, and Van der Laan.

Usage

cFrd(alpha, k, n, method=NA, n.mc=10000, return.full.distribution=FALSE)

Arguments

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Author(s)

Grant Schneider

References

Van de Wiel, M. A., A. Di Bucchianico, and P. Van der Laan. "Symbolic computation and exact distributions of nonparametric test statistics." Journal of the Royal Statistical Society: Series D (The Statistician) 48.4 (1999): 507-516.

See Also

The coin package.

Examples

##Hollander-Wolfe-Chicken Example 7.1 Rounding First Base
#cFrd(0.01,3,22,"Exact")
cFrd(0.01,3,22,n.mc=5000)
cFrd(0.01,3,22,"Asymptotic")

Computes a critical value for the Hayter-Stone W* distribution.

Description

This function computes the critical value for the Hayter-Stone W* distriburion at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cHaySton(alpha,n, method=NA, n.mc=10000)

Arguments

Details

The Asymptotic distribution requires that all group sizes are equal. If method="Asymptotic" and there are different group sizes in n, method="Monte Carlo" will be used.

Value

Returns a list with "NSM3Ch6MCc" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 6.7 Motivational Effect of Knowledge of Performance:
#cHaySton(.0553,rep(6,3),"Monte Carlo")
cHaySton(.05,c(6,6,6),"Asymptotic")

Computes a critical value for the Hayter-Stone W* asymptotic distribution.

Description

This function computes the critical value for the Hayter-Stone W* asymptotic distriburion at the given alpha level.

Usage

cHayStonLSA(alpha,k,delta=.001)

Arguments

Details

The Asymptotic distribution requires that all (unspecified) group sizes are equal.

Value

Returns the cutoff (based on the specified grid) with upper tail probability nearest to alpha.

Author(s)

Grant Schneider

References

Hayter, Anthony J., and Wei Liu. "Exact calculations for the one-sided studentized range test for testing against a simple ordered alternative." Computational statistics & data analysis 22.1 (1996): 17-25.

Examples

##Hollander-Wolfe-Chicken Example 6.7 Motivational Effect of Knowledge of Performance:
cHayStonLSA(.0553,3,delta=0.01)

##Section preceding Example 6.7 (explaining LSA)
cHayStonLSA(.05,6,delta=0.01)

Hollander Bivariate Symmetry

Description

Quantile function for the Hollander A distribution.

Usage

cHollBivSym(alpha,d.mat,method=NA, n.mc=10000)

Arguments

Details

The d matrix, d.mat, will be an n*n matrix of ones and zeroes, where the (i,j)th element is 1 if min(Xj,Yj)<max(Xi,Yi)<=max(Xj,Yj) and min(Xi,Yi)<=min(Xj,Yj), 0 otherwise. An illustration may be found in the example section of this document and Section 3.10 of Hollander, Wolfe, and Chicken - NSM3.

Value

Returns a list with "NSM3Ch5c" class containing the following components:

Author(s)

Grant Schneider

References

Kepner, James L., and Ronald H. Randies. "Comparison of tests for bivariate symmetry versus location and/or scale alternatives." Communications in Statistics-Theory and Methods 13.8 (1984): 915-930.

Hilton, Joan F., and Lauren Gee. "The size and power of the exact bivariate symmetry test." Computational statistics & data analysis 26.1 (1997): 53-69.

Examples

##Hollander-Wolfe-Chicken Example 3.11 Insulin Clearance in Kidney Transplants
x<-c(61.4,63.3,63.7,80,77.3,84,105)
y<-c(70.8,89.2,65.8,67.1,87.3,85.1,88.1)
obs.data<-cbind(x,y)
a.vec<-apply(obs.data,1,min)
b.vec<-apply(obs.data,1,max)
test<-function(r,c) {as.numeric((a.vec[c]<b.vec[r])&&(b.vec[r]<=b.vec[c])&&(a.vec[r]<=a.vec[c]))}
myVecFun <- Vectorize(test,vectorize.args = c('r','c')) 

d.mat<-outer(1:length(x), 1:length(x), FUN=myVecFun) 

##Cutoff based on the exact distribution
cHollBivSym(.10,d.mat)

Computes a critical value for the Jonckheere-Terpstra J distribution.

Description

This function computes the critical value for the Jonckheere-Terpstra J distribution at (or typically in the "Exact" case, close to) the given alpha level. The function takes advantage of Harding's (1984) algorithm to quickly generate the distribution.

Usage

cJCK(alpha, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6c" class containing the following components:

Author(s)

Grant Schneider

References

Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.

Examples

##Hollander-Wolfe-Chicken Example 6.2 Motivational Effect of Knowledge of Performance
cJCK(.0490, c(6,6,6),"Exact")
cJCK(.0490, c(6,6,6),"Monte Carlo")
cJCK(.0231, c(6,6,6),"Exact")

Computes a critical value for the Kruskal-Wallis H distribution.

Description

This function computes the critical value for the Kruskal-Wallis H distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cKW(alpha,n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 6.1 Half-Time of Mucociliary Clearance
#cKW(0.0503,c(5,4,5),"Exact")
cKW(0.7147,c(5,4,5),"Asymptotic")
cKW(0.7147,c(5,4,5),"Monte Carlo",n.mc=20000)

Computes a critical value for the Kolmogorov-Smirnov J distribution.

Description

This function uses pSmirnov2x from the base stats package to compute the critical value for the Kolmogorov-Smirnov J distribution at (or typically in the "Exact" case, close to) the given alpha level. The program is reasonably quick for large data, well after the asymptotic approximation suffices, so Monte Carlo methods are not included.

Usage

cKolSmirn(alpha, m, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch5c" class containing the following components:

Author(s)

Grant Schneider

References

This function uses the source code ks.c from the stats package by: R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.

See Also

Also see ks.test().

Examples

##Hollander-Wolfe-Chicken Example 5.4 Effect of Feedback on Salivation Rate:
cKolSmirn(0.0524,10,10,"Exact")

##or
cKolSmirn(0.06,10,10,"Exact")

##LSA
cKolSmirn(0.0551,10,10,"Asymptotic")

Computes a critical value for the Lepage D distribution.

Description

This function computes the critical value for the Lepage D distriburion at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cLepage(alpha, m, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch5c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 5.3 Platelet Counts of Newborn Infants
cLepage(0.02,10,6,"Exact")
cLepage(0.02,10,6,"Monte Carlo")
cLepage(0.02,10,6,"Asymptotic")

Computes a critical value for the Mack-Skillings MS distribution.

Description

This function computes the critical value for the Mack-Skillings MS distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cMackSkil(alpha,k,n,c, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.9 Determination of Niacin in Bran Flakes
cMackSkil(.0501,4,3,3)
##Hollander-Wolfe-Chicken Chapter 7 Comment 72
cMackSkil(.0502,4,4,3)

Quantile function for the maximum of k N(0,1) random variables with common correlation rho.

Description

Uses the integrate function based on the method proposed in Gupta, Panchapakesan and Sohn (1983).

Usage

cMaxCorrNor(alpha,k,rho)

Arguments

Value

Returns the upper tail cutoff at or immediately below the user-specified alpha.

Author(s)

Grant Schneider

References

Gupta, Shanti S., S. Panchapakesan, and Joong K. Sohn. "On the distribution of the studentized maximum of equally correlated normal random variables." Communications in Statistics-Simulation and Computation 14.1 (1985): 103-135.

Examples

##Hollander-Wolfe-Chicken Section 7.4 LSA
cMaxCorrNor(.04584,4,.5)
##Hollander-Wolfe-Chicken Section 7.14
cMaxCorrNor(.02337,5,.3)
##Hollander-Wolfe-Chicken Example 7.14
cMaxCorrNor(.10,5,.452)

Function to compute a critical value for the Nemenyi, Damico-Wolfe Y distribution.

Description

This function computes the critical value for the Nemenyi, Damico-Wolfe Y distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cNDWol(alpha,n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6MCc" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 6.8 Motivational Effect of Knowledge of Performance
cNDWol(.0554, c(6, 6, 6),"Monte Carlo")
cNDWol(.0554, c(6, 6, 6),"Monte Carlo",n.mc=25000)
cNDWol(.0371, c(6, 6, 6),"Monte Carlo")

Computes a critical value for the Nemenyi, Wilcoxon-Wilcox, Miller R* distribution.

Description

This function computes the critical value for the Nemenyi, Wilcoxon-Wilcox, Miller R* distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cNWWM(alpha, k, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.4 Stuttering Adaptation
#cNWWM(.0492, 3, 18, "Monte Carlo") 
cNWWM(.0492, 3, 18, method="Monte Carlo",n.mc=2500) 
##Comment 7.35
cNWWM(.0093, 3, 3, "Exact")
#cNWWM(.0093, 3, 3, "Monte Carlo")

Function to compute a critical value for the Page L distribution.

Description

This function computes the critical value for the Page L distriburion at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cPage(alpha, k, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.2 Breaking Strength of Cotton Fibers
#cPage(.0097, 5, 3,"Exact")
cPage(.0097, 5, 3,"Monte Carlo")

Quantile function for the range of k independent N(0,1) random variables.

Description

Uses the integrate function based on the method proposed in Harter (1960).

Usage

cRangeNor(alpha,k)

Arguments

Value

Returns the upper tail cutoff at or immediately below the user-specified alpha.

Author(s)

Grant Schneider

References

Harter, H. Leon. "Tables of range and studentized range." The Annals of Mathematical Statistics (1960): 1122-1147.

Examples

##Hollander-Wolfe-Chicken Example 7.3 Rounding First Base
cRangeNor(.01, 3)

##Hollander-Wolfe-Chicken Example 7.7 Chemical Toxicity
cRangeNor(.05, 7)

Computes a critical value for the Dwass, Steel, Critchlow-Fligner W distribution.

Description

This function computes the critical value for the Dwass, Steel, Critchlow-Fligner W distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cSDCFlig(alpha, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Chapter 6 Comment 55
#cSDCFlig(.0331, c(3, 5, 7),n.mc=10000)
cSDCFlig(.0331, c(3, 5, 7),n.mc=2500)

##Another example
#cSDCFlig(alpha=0.05,n=rep(4,3),method="Exact")
cSDCFlig(alpha=0.05,n=rep(4,3),method="Monte Carlo",n.mc=2500)
#cSDCFlig(alpha=0.05,n=rep(4,3),method="Asymptotic")

Computes a critical value for the Skillings-Mack SM distribution.

Description

This function computes the critical value for the Skillings-Mack SM distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cSkilMack(alpha, obs.mat, method = NA, n.mc = 10000)

Arguments

Details

The incidence matrix, obs.mat, will be an n x k matrix of ones and zeroes, which indicate where the data are observed and unobserved, respectively.

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Note

The syntax of this procedure differs from the others in the NSM3 package due to the fact that the distribution is calculated conditionally on the pattern of missingness. We therefore require obs.mat, the incidence matrix.

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Example 7.8 Effect of Rhythmicity of a Metronome on Speech Fluency
obs.mat<-matrix(c(rep(1,10),0,rep(1,13)),ncol=3,byrow=TRUE)
#cSkilMack(.01,obs.mat)
cSkilMack(.01,obs.mat,n.mc=5000)

Computes a critical value for the Mack-Wolfe Peak Known A_p distribution.

Description

This function computes the critical value for the Mack-Wolfe Peak Known A_p distribution at (or typically in the "Exact" case, close to) the given alpha level. The function generalizes Harding's (1984) algorithm to quickly generate the distribution.

Usage

cUmbrPK(alpha, n, peak=NA, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6c" class containing the following components:

Author(s)

Grant Schneider

References

Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.

Examples

##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer
cUmbrPK(.0101, c(7, 3, 5, 4, 4,3), peak=4)

Computes a critical value for the Mack-Wolfe Peak Unknown A_p-hat distribution.

Description

This function computes the critical value for the Mack-Wolfe Peak Unknown A_p-hat distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cUmbrPU(alpha, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 6.4 Learning Comprehension and Age
#cUmbrPU(.0495, c(3, 3, 3, 3, 3))

cUmbrPU(.10, c(2, 4, 2))

Computes a critical value for the Wilcoxon, Nemenyi, McDonald-Thompson R distribution.

Description

This function computes the critical value for the Wilcoxon, Nemenyi, McDonald-Thompson R distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

Usage

cWNMT(alpha, k, n, method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch7c" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.3 Rounding First Base
#cWNMT(.047, 3, 15)
cWNMT(.047, 3, 15,n.mc=5000)

##Chapter 7 Comment 26
#cWNMT(.083, 4, 2)
cWNMT(.083, 4, 2,n.mc=5000)

Campbell-Hollander

Description

Function to compute the Campbell-Hollander estimator G-hat

Usage

ch.ro (x,n,alpha,mu,...)

Arguments

Value

Author(s)

Rachel Becvarik

References

See Section 16.3 of Hollander, Wolfe, Chicken - Nonparametric Statistical Methods 3.

Examples

##Hollander-Wolfe-Chicken Example 16.2 Swimming in the Women's 50 yard Freestyle
freestyle<-c(22.43, 21.88, 22.39, 22.78, 22.65, 22.60)
ch.ro(freestyle,12,10,pnorm,22.52,.24)

Dataset

Description

These are the datasets used in the Examples of Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods Third Edition. More extensive details about the data may be found there.

Usage

data(rhythmicity)

Format

The format varies depending on the dataset.

Source

Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

Examples

data(rhythmicity)
data(forearm)

Hollander-Proschan

Description

Function to compute the Monte Carlo or asymptotic P-value for the observed Hollander-Proschan V' statistic.

Usage

dmrl.mc(x, alternative = "two.sided", exact=FALSE,
        min.reps = 100, max.reps = 1000, delta = 10^-3)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

ex11.1<-c(42, 43, 51, 61, 66, 69, 71, 81, 82, 82)
dmrl.mc(ex11.1, alt="dmrl", exact=TRUE)

Function to compute the Monte Carlo P-value for the observed Epstein E statistic

Description

This is the Monte Carlo approximation to the function "epstein".

Usage

e.mc(x, alternative = "two.sided", exact=FALSE,
     min.reps = 1000, max.reps = 10000, delta = 10^-4)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

ex11.1<-c(42, 43, 51, 61, 66, 69, 71, 81, 82, 82)
Ep <- e.mc(ex11.1, alt="ifr", exact=TRUE)
Ep$E
Ep$p

#Large Sample Approximation
Ep.lsa <- e.mc(ex11.1, alt="ifr")

table11.2<-c(487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130)
Ep=e.mc(table11.2,alt="i", exact=TRUE)
#Failing to converge
Ep=e.mc(table11.2,alt="i", exact=TRUE, min.reps=5, max.reps=5)

Kolmogorov's Confidence Band

Description

Function to compute and plot Kolmogorov's 95% confidence band for the distribution function F(x). This code is adapted from the code by Kjetil Halvorsen found at: https://stat.ethz.ch/pipermail/r-help/2003-July/036643.html

Usage

ecdf.ks.CI(x, main = NULL, sub = NULL, xlab = deparse(substitute(x)), ...)

Arguments

Value

The function returns a list with three elements:

Note

This function also plots the confidence bands.

Author(s)

Rachel Becvarik

Examples

methyl<-c(42, 43, 51, 61, 66, 69, 71, 81, 82, 82)
ecdf.ks.CI(methyl)

ecdf.ks.CI(methyl, lwd=2, main="KS Confidence Bands") 

Epstein

Description

Function to compute the P-value for the observed Epstein E statistic

Usage

epstein(x, alternative = "two.sided", exact=FALSE)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

ex11.1<-c(42, 43, 51, 61, 66, 69, 71, 81, 82, 82)
Ep <- epstein(ex11.1, alt="ifr", exact=TRUE)
Ep$E
Ep$p

#Large Sample Approximation
Ep.lsa <- epstein(ex11.1, alt="ifr")

Ferguson's Estimator

Description

Function to compute an approximation of Ferguson's estimator mu_n.

Usage

ferg.df(x, alpha, mu, npoints,...)

Arguments

Value

The function returns a vector of length num.points for Ferguson's estimator.

Author(s)

Rachel Becvarik

References

See Section 16.2 of Hollander, Wolfe, Chicken - Nonparametric Statistical Methods 3.

Examples

##Hollander-Wolfe-Chicken Figure 16.2
framingham<-c(2273, 2710, 141, 4725, 5010, 6224, 4991, 458, 1587, 1435, 2565, 1863)
plot.ecdf(framingham)
lines(sort(framingham),pexp(sort(framingham), 1/2922), lty=3)
temp.x = seq(min(framingham), max(framingham), length.out=100)
lines(temp.x,ferg.df(sort(framingham), 4, npoints=100,pexp,1/2922), col=2, type="s", lty=2)
legend("bottomright",  lty=c(1,3,2), legend=c("ecdf", "prior", "ferguson"), col=c(1,1,2))

Function to produce a confidence interval for Kendall's tau.

Description

Based on sections 8.3 and 8.4 of Hollander, Wolfe & Chicken, Nonparametric Statistical Methods, 3e.

Usage

kendall.ci(x=NULL, y=NULL, alpha=0.05, type="t", bootstrap=F, B=1000, example=F) 

Arguments

Author(s)

Eric Chicken

Examples

kendall.ci(example=TRUE)

Klefsjo's IFR

Description

Function to compute the P-value for the observed Klefsjo's A* statistic.

Usage

klefsjo.ifr (x, alternative = "two.sided", exact=FALSE)

Arguments

Details

If the sample size is too large to allow for an exact value, due to duplicate coefficients, a note will be displayed and the large sample approximation will be used.

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

velocity<-c(12.8, 12.9, 13.3, 13.4, 13.7, 13.8, 14.5)
klefsjo.ifr(velocity)

#Example of forced Large Sample Approximation
tb<-c(43, 45, 53, 56, 56, 57, 58, 66, 67, 73, 74, 79, 80, 80, 81, 81, 81, 82, 83, 83, 84, 88,
89,  91,  91,  92,  92,  97,  99,  99, 100, 100, 101, 102, 102, 102, 103, 104, 107, 108, 109,
113, 114, 118, 121, 123, 126, 128, 137, 138, 139, 144, 145, 147, 156, 162, 174, 178, 179, 184,
191, 198, 211, 214, 243, 249, 329, 380, 403, 511, 522, 598)
klefsjo.ifr(tb, exact=TRUE)

Function to compute the Monte Carlo P-value for the observed Klefsjo's A* statistic.

Description

This is the Monte Carlo approximation to the function "klefsjo.ifr".

Usage

klefsjo.ifr.mc(x, alternative = "two.sided", exact=FALSE,
               min.reps = 100, max.reps = 1000, delta = 10^-3)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

temp.data<-c(0.33925023, 0.84005767, 0.29066189, 1.95163010, 0.74536608, 0.16714902, 0.06950791,
1.14919291, 1.93210982, 1.06006126, 0.14651009, 0.28776282, 0.72242750, 1.02227211, 1.71243334)
klefsjo.ifr.mc(temp.data, exact=TRUE)

Klefsjo's IFRA

Description

Function to compute the P-value for the observed Klefsjo's B* statistic.

Usage

klefsjo.ifra (x, alternative = "two.sided", exact=FALSE)

Arguments

Details

If the sample size is too large to allow for an exact value, due to duplicate coefficients, a note will be displayed and the large sample approximation will be used.

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

velocity<-c(12.8, 12.9, 13.3, 13.4, 13.7, 13.8, 14.5)
klefsjo.ifra(velocity)

#Example of forced Large Sample Approximation
tb<-c(43, 45, 53, 56, 56, 57, 58, 66, 67, 73, 74, 79, 80, 80, 81, 81, 81, 82, 83, 83, 84, 88,
89,  91,  91,  92,  92,  97,  99,  99, 100, 100, 101, 102, 102, 102, 103, 104, 107, 108, 109,
113, 114, 118, 121, 123, 126, 128, 137, 138, 139, 144, 145, 147, 156, 162, 174, 178, 179, 184,
191, 198, 211, 214, 243, 249, 329, 380, 403, 511, 522, 598)
klefsjo.ifra(tb, exact=TRUE)

Function to compute the Monte Carlo P-value for the observed Klefsjo's B* statistic.

Description

This is the Monte Carlo approximation to the function "klefsjo.ifra".

Usage

klefsjo.ifra.mc(x, alternative = "two.sided", exact=FALSE,
                min.reps = 100, max.reps = 1000, delta = 10^-3)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

temp.data<-c(0.33925023, 0.84005767, 0.29066189, 1.95163010, 0.74536608, 0.16714902, 0.06950791, 
1.14919291,1.93210982, 1.06006126, 0.14651009, 0.28776282, 0.72242750, 1.02227211, 1.71243334)
klefsjo.ifra.mc(temp.data, exact=TRUE)

Kolmogorov

Description

Function to compute the asymptotic P-value for the observed Kolmogorov D statistic.

Usage

kolmogorov(x,fnc,...)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

velocity<-c(12.8, 12.9, 13.3, 13.4, 13.7, 13.8, 14.5)
kolmogorov(velocity,pnorm, mean=14,sd=2)
kolmogorov(velocity,pexp,1/2)

Fitting Median-Based Linear Models (from 'mblm' oackage)

Description

This function is used to fit linear models based on Theil-Sen single median, or Siegel repeated medians.

Usage

mblm(formula, dataframe, repeated = TRUE)

Arguments

Details

This function is from the 'mblm' package, which is no longer available on CRAN.

Theil-Sen single median method computes slopes of lines crossing all possible pairs of points, when x coordinates differ. After calculating these n(n-1)/2 slopes (these value are true only if x is distinct), the median of them is taken as slope estimator. Next, the intercepts of n lines, crossing each point and having calculated slope are calculated. The median from them is intercept estimator.

Siegel repeated medians is more complicated. For each point, the slopes between it and the others are calcuated (resulting n-1 slopes) and the median is taken. This results in n medians and median from this medians is slope estimator. Intercept is calculated in similar way, for more information please take a look in function source.

The breakdown point of Theil-Sen method is about 29%, Siegel extended it to 50%, so these regression methods are very robust. Additionally, if the errors are normally distributed and no outliers are present, the estimators are very similar to classic least squares.

Value

An object of class c("mblm","lm"), containing minimal set of data to perform basic operations, such as in case of lm model. Additionally, the return value contains 2 fields:

Note

This function should have compatibility with all 'lm' methods, but it is not guaranteed that they will work or have any cognitive value (this method is nonparametric). The compatibility was only introduced to use some basic methods from 'lm' without programming new functions.

Author(s)

Lukasz Komsta, some fixes by Sven Garbade

References

Theil, H. (1950) A rank invariant method for linear and polynomial regression analysis. Nederl. Akad. Wetensch. Proc. Ser. A 53, 386-392 (Part I), 521-525 (Part II), 1397-1412 (Part III).

Sen, P.K. (1968). Estimates of Regression Coefficient Based on Kendall's tau. J. Am. Stat. Ass. 63, 324, 1379-1389.

Siegel, A.F. (1982). Robust Regression Using Repeated Medians. Biometrika, 69, 1, 242-244.

Examples

set.seed(1234)
x <- 1:100+rnorm(100)
y <- x+rnorm(100)
y[100] <- 200
fit <- mblm(y~x)
fit
summary(fit)
fit2 <- lm(y~x)
plot(x,y)
abline(fit)
abline(fit2,lty=2)
plot(fit)
residuals(fit)
fitted(fit)
plot(density(fit$slopes))
plot(density(fit$intercepts))
anova(fit)
anova(fit2)
anova(fit,fit2)
confint(fit)
AIC(fit,fit2)

Mean Residual Life

Description

Function to return the mean residual life along with Hall and Wellner's upper and lower bounds.

Usage

mrl(data, alpha, main=NULL, ylim=NULL, xlab=NULL,...)

Arguments

Value

The function returns a list with three vectors:

Author(s)

Rachel Becvarik

Examples

leukemia<-c(7, 429, 579, 968, 1877, 47, 440, 581, 1077, 1886, 58,
445,  650, 1109, 2045, 74, 455, 702, 1314, 2056, 177, 468,
715, 1334, 2260, 232, 495, 779, 1367, 2429, 273, 497, 881,
1534, 2509, 285, 532, 900, 1712, 317,  571, 930, 1784)
mrl(leukemia, .05)

Possible arrangements by row for a matrix

Description

Similar to multComb, this function will generate all of the possible arrangements of the data by row within a matrix. For a given matrix of n rows and k columns, this will give (k!)^n possible arrangements

Usage

multCh7(our.matrix)

Arguments

Details

The computations involved get very time consuming very quickly, so be careful not to use it for too large of a matrix.

Value

Returns an array, containing (k!)^n distinct matrices of the same size as our.matrix

Note

This function is used to generate the possible permutations for the Exact methods used in Chapter 7 of Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods Third Edition.

Author(s)

Grant Schneider

Examples

some.matrix<-matrix(c(1,2,7,4,5,9),ncol=3,byrow=TRUE)
multCh7(some.matrix)

Possible arrangements by row a matrix, where NA values are ignored

Description

Similar to multCh7, this function will generate all of the possible arrangements of the data by row within a matrix, except for NA values, which will remain fixed. This function is used in pSkilMack and cSkilMack to generate the Exact distribution. For a given matrix of with k1,...kn non-missing values, this will give k1!*k2!*...*kn! possible arrangements

Usage

multCh7SM(our.matrix)

Arguments

Details

The computations involved get very time consuming very quickly, so be careful not to use it for too large of a matrix.

Value

Returns an array, containing k1!*k2!*...*kn! distinct matrices of the same size as our.matrix

Author(s)

Grant Schneider

Examples

##Get a matrix with some NA's
our.matrix<-matrix(c(NA,1,2,3,5,7,NA,NA,11),ncol=3,byrow=TRUE)
##Get every possible arrangement by row, treating the NA's as fixed
multCh7SM(our.matrix)

Combinations of the first n integers in k groups

Description

This is a function, used for generating the permutations used for the Exact distribution of many of the statistical procedures in Hollander, Wolfe, Chicken - Nonparametric Statistical Methods Third Edition, to generate possible combinations of the first n=n1+n2+...+nk integers within k groups.

Usage

multComb(n.vec)

Arguments

Details

The computations involved get very time consuming very quickly, so be careful not to use it for too many large groups.

Value

Returns a matrix of n!/(n1!*n2!*...*nk!) rows, where each row represents one possible combination.

Author(s)

Grant Schneider

Examples

##What are the ways that we can group 1,2,3,4,5 into groups of 2, 2, and 1?
multComb(c(2,2,1))

##Another example, with four groups
multComb(c(2,2,3,2))

Function to compute the Monte Carlo P-value for the observed Hollander-Proschan T statistic.

Description

This is the Monte Carlo approximation to the newbet function.

Usage

nb.mc(x, alternative = "two.sided", exact=FALSE, 
      min.reps = 100, max.reps = 1000, delta = 10^-3)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

table11.4<-c(194,15,41,29,33,181)
nb.mc(table11.4, alt="nbu")

Hollander-Proschan T*

Description

Function to compute the asymptotic P-value for the observed Hollander-Proschan T* statistic.

Usage

newbet(x)

Arguments

Value

The function returns a list with two elements:

Author(s)

Rachel Becvarik

Examples

table11.4<-c(194,15,41,29,33,181)
newbet(table11.4)

Ordered Walsh Averages

Description

Function to compute the ordered Walsh averages and the value of the Hodges-Lehmann estimator

Usage

owa(x,y)

Arguments

Value

Returns a list containing:

Author(s)

Rachel Becvarik

Examples

##Hollander-Wolfe-Chicken Example 3.3 
x<-c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
y<-c(0.878, 0.647, 0.598, 2.050, 1.060, 1.290, 1.060, 3.140, 1.290)
owa(x,y)

Function to compute the P-value for the observed Ansari-Bradley C statistic.

Description

When there are no ties in the data, this function uses pansari and cansari from the base stats package to compute the C statistic and P-value ("Exact" or "Asymptotic"). The program is reasonably quick for large data in the absence of ties, well after the asymptotic approximation suffices, so Monte Carlo methods are not included.

When there are ties in the data, this function computes the C statistic and P-value ("Exact", "Monte Carlo", or "Asymptotic").

Usage

pAnsBrad(x,y=NA,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the two groups of data can be entered in any of three ways. For data a=1,2 and b=3,4 all of the following are equivalent:

pAnsBrad(x=c(1,2),y=c(3,4)) pAnsBrad(x=list(c(1,2),c(3,4))) pAnsBrad(x=c(1,2,3,4),g=c(1,1,2,2))

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Note

If method="Monte Carlo" and there are no ties in the data, a warning is displayed and the "Exact" method is used.

Author(s)

Grant Schneider

See Also

Also see ansari.test.

Examples

##Hollander, Wolfe, Chicken Example 5.1 Serum Iron Determination:
serum<-list(ramsay = c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99, 101, 96, 97, 102, 107,
113, 116, 113, 110, 98),
jung.parekh = c(107, 108, 106, 98, 105, 103, 110, 105, 104, 100, 96, 108, 103, 104, 114, 114,
113, 108, 106, 99))


pAnsBrad(serum)

##or, equivalently:
pAnsBrad(serum$ramsay, serum$jung.parekh)

Function to compute the P-value for the observed Bohn-Wolfe U statistic.

Description

This function computes the U statistic and then uses Monte Carlo sampling to compute the corresponding P-value. The Monte Carlo samples are simulated based on the order statistics of a uniform(0,1) distribution.

Usage

pBohnWolfe(x,y,k,q,c,d,method="Monte Carlo",n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Author(s)

Grant Schneider

References

Bohn, Lora L., and Douglas A. Wolfe. "Nonparametric two-sample procedures for ranked-set samples data." Journal of the American Statistical Association 87.418 (1992): 552-561

Examples

##Hollander, Wolfe, Chicken Example 15.4 Body Mass Index:
male<-c(18.0, 20.5, 21.3, 21.3, 22.3, 23.8, 23.8, 24.6, 25.0, 25.2, 25.3, 25.9, 26.1, 27.0,
27.4, 27.4, 28.4, 29.4, 29.6, 32.8)
female<-c(17.2, 17.8, 19.9, 20.0, 21.7, 22.0, 22.3, 23.1, 23.9, 25.8, 27.1, 29.6, 30.1, 30.3,
30.7, 31.1, 35.2, 35.6, 38.1, 42.5)

pBohnWolfe(male,female,4,4,5,5)
##To use more Monte Carlo samples:
#pBohnWolfe(male,female,4,4,5,5,n.mc=100000)

Durbin, Skillings-Mack

Description

Function to compute the P-value for the observed Durbin, Skillings-Mack D statistic.

Usage

pDurSkiMa(x,b=NA,trt=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent: pDurSkiMa(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) pDurSkiMa(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Example 7.6 Chemical Toxicity
table7.12<-matrix(nrow=7,ncol=7)
table7.12[1,c(1,2,4)]<-c(0.465,0.343,0.396)
table7.12[2,c(1,3,5)]<-c(0.602,0.873,0.634)
table7.12[3,c(3,4,7)]<-c(0.875,0.325,0.330)
table7.12[4,c(1,6,7)]<-c(0.423,0.987,0.426)
table7.12[5,c(2,3,6)]<-c(0.652,1.142,0.989)
table7.12[6,c(2,5,7)]<-c(0.536,0.409,0.309)
table7.12[7,c(4,5,6)]<-c(0.609,0.417,0.931)

pDurSkiMa(table7.12)

##or, equivalently:
x<-c(.465,.602,.423,.343,.652,.536,.873,.875,1.142,.396,.325,.609,.634,.409,.417,.987,.989,
.931,.330,.426,.309)
b<-c(1,2,4,1,5,6,2,3,5,1,3,7,2,6,7,4,5,7,3,4,6)
trt<-c(rep("A",3),rep("B",3),rep("C",3),rep("D",3),rep("E",3),rep("F",3),rep("g",3))

pDurSkiMa(x,b,trt)

Fligner-Policello

Description

Function to compute the P-value for the observed Fligner-Policello U statistic.

Usage

pFligPoli(x,y=NA,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the two groups of data can be entered in any of three ways. For data a=1,2 and b=3,4 all of the following are equivalent:

pFligPoli(x=c(1,2),y=c(3,4)) pFligPoli(x=list(c(1,2),c(3,4))) pFligPoli(x=c(1,2,3,4),g=c(1,1,2,2))

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Example 4.5 Plasma Glucose in Geese
plasma.glucose<-list(healthy.geese = c(297, 340, 325, 227, 277, 337, 
250, 290), poisoned.geese = c(293, 291, 289, 430, 510, 353, 318
))

pFligPoli(plasma.glucose)

Function to compute the P-value for the observed Friedman, Kendall-Babington Smith S statistic.

Description

The method used to compute the P-value is from the reference by Van de Wiel, Bucchianico, and Van der Laan.

Usage

pFrd(x,b=NA,trt=NA,method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent:

pFrd(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) pFrd(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7p" class containing the following components:

Author(s)

Grant Schneider

References

Van de Wiel, M. A., A. Di Bucchianico, and P. Van der Laan. "Symbolic computation and exact distributions of nonparametric test statistics." Journal of the Royal Statistical Society: Series D (The Statistician) 48.4 (1999): 507-516.

See Also

Also see the coin package.

Examples

##Hollander-Wolfe-Chicken Example 7.1 Rounding First Base
rounding.times<-matrix(c(5.40, 5.50, 5.55,
                         5.85, 5.70, 5.75,
                         5.20, 5.60, 5.50,
                         5.55, 5.50, 5.40,
                         5.90, 5.85, 5.70,
                         5.45, 5.55, 5.60,
                         5.40, 5.40, 5.35,
                         5.45, 5.50, 5.35,
                         5.25, 5.15, 5.00,
                         5.85, 5.80, 5.70,
                         5.25, 5.20, 5.10,
                         5.65, 5.55, 5.45,
                         5.60, 5.35, 5.45,
                         5.05, 5.00, 4.95,
                         5.50, 5.50, 5.40,
                         5.45, 5.55, 5.50,
                         5.55, 5.55, 5.35,
                         5.45, 5.50, 5.55,
                         5.50, 5.45, 5.25,
                         5.65, 5.60, 5.40,
                         5.70, 5.65, 5.55,
                         6.30, 6.30, 6.25),ncol=3,byrow=TRUE)
#pFrd(rounding.times,n.mc=20000)
pFrd(rounding.times,n.mc=2000)

Hayter-Stone

Description

Function to compute the P-value for the observed Hayter-Stone W statistic.

Usage

pHaySton(x,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pHaySton(x=list(c(1,2),c(3,4,5))) pHaySton(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6MCp" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Example 6.7 Motivational Effect of Knowledge of Performance:
motivational.effect<-list(no.Info = c(40, 35, 38, 43, 44, 41), rough.Info = c(38, 
40, 47, 44, 40, 42), accurate.Info = c(48, 40, 45, 43, 46, 44
))

#pHaySton(motivational.effect,method="Monte Carlo")
pHaySton(motivational.effect,method="Asymptotic")
#pHaySton(rnorm(10),rep(1:3,c(3,3,4)),method="Asymptotic")

Hayter-Sone LSA

Description

Function to compute the upper tail probability of the Hayter-Stone W asymptotic distribution for a given cutoff.

Usage

pHayStonLSA(h,k,delta=.001)

Arguments

Value

Returns the asymptotic upper tail P-value.

Author(s)

Grant Schneider

Examples

pHayStonLSA(2.491,3)
pHayStonLSA(4.112,4)

Hoeffding's D

Description

Function to approximate the distribution of Hoeffding's D statistic using a Monte Carlo Sample under the null hypothesis. This code follows section 8.6 of Hollander, Wolfe & Chicken, Nonparametric Statistical Methods, 3e. This calls HoeffD, a small bit of code that produces the value of D without any inference. It is intended for small sample sizes n only. For large n, use the asymptotic equivalence of D to the Blum-Kliefer-Rosenblatt statistic in the R package "Hmisc", command "hoeffd".

Usage

pHoeff(n=5, reps=10000, r=4)

Arguments

Value

Returns a matrix containing the Monte Carlo distribution of the D statistic.

Author(s)

Eric Chicken

See Also

Also see the Hmisc package.

Examples

pHoeff(n=5, reps=10000, r=4)
pHoeff(n=10, reps=1000, r=5)

Hollander Bivariate Symmetry

Description

Function to compute the P-value for the observed Hollander A statistic.

Usage

pHollBivSym(x,y=NA,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the two groups of data can be entered in any of three ways. For data a=1,2 and b=3,4 all of the following are equivalent:

pHollBivSym(x=c(1,2),y=c(3,4)) pHollBivSym(x=list(c(1,2),c(3,4))) pHollBivSym(x=c(1,2,3,4),g=c(1,1,2,2))

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Author(s)

Grant Schneider

References

Kepner, James L., and Ronald H. Randies. "Comparison of tests for bivariate symmetry versus location and/or scale alternatives." Communications in Statistics-Theory and Methods 13.8 (1984): 915-930.

Hilton, Joan F., and Lauren Gee. "The size and power of the exact bivariate symmetry test." Computational statistics & data analysis 26.1 (1997): 53-69.

Examples

##Hollander-Wolfe-Chicken Example 3.11 Insulin Clearance in Kidney Transplants
x<-c(61.4,63.3,63.7,80,77.3,84,105)
y<-c(70.8,89.2,65.8,67.1,87.3,85.1,88.1)

##Exact p-value
pHollBivSym(x,y)

Function to compute the P-value for the observed Jonckheere-Terpstra J statistic.

Description

This function computes the observed J statistic for the given data and corresponding P-value. When there are no ties in the data, the function takes advantage of Harding's (1984) algorithm to quickly generate the exact distribution of J.

Usage

pJCK(x,g=NA,method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pJCK(x=list(c(1,2),c(3,4,5))) pJCK(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6p" class containing the following components:

Author(s)

Grant Schneider

References

Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.

Examples

##Hollander-Wolfe-Chicken Example 6.2 Motivational Effect of Knowledge of Performance
motivational.effect<-list(no.Info=c(40,35,38,43,44,41),rough.Info=c(38,40,47,44,40,42),
                          accurate.Info=c(48,40,45,43,46,44))
#pJCK(motivational.effect,method="Monte Carlo")
pJCK(motivational.effect,method="Asymptotic")

Kruskal-Wallis

Description

Function to compute the P-value for the observed Kruskal-Wallis H statistic.

Usage

pKW(x,g=NA, method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pKW(x=list(c(1,2),c(3,4,5))) pKW(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6p" class containing the following components:

Author(s)

Grant Schneider

See Also

Also see kruskal.test().

Examples

##Hollander-Wolfe-Chicken Example 6.1 Half-Time of Mucociliary Clearance
mucociliary<-list(Normal = c(2.9, 3, 2.5, 2.6, 3.2), Obstructive = c(3.8, 
2.7, 4, 2.4), Asbestosis = c(2.8, 3.4, 3.7, 2.2, 2))

pKW(mucociliary)

Function to copute the P-value for the observed Kolmogorov-Smirnov J statistic.

Description

This function uses psmirnov2x from the base stats package to compute the J statistic and corresponding P-value. The program is reasonably quick for large data, well after the asymptotic approximation suffices, so Monte Carlo methods are not included. This function primarily serves as a wrapper to the ks.test function with the output standardized to the format of the other functions included in the NSM3 package.

Usage

pKolSmirn(x,y=NA,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the two groups of data can be entered in any of three ways. For data a=1,2 and b=3,4 all of the following are equivalent:

pKolSmirn(x=c(1,2),y=c(3,4)) pKolSmirn(x=list(c(1,2),c(3,4))) pKolSmirn(x=c(1,2,3,4),g=c(1,1,2,2))

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Author(s)

Grant Schneider

See Also

Also see ks.test().

Examples

##Hollander-Wolfe-Chicken Example 5.4 Effect of Feedback on Salivation Rate:
feedback<-c(-0.15, 8.6, 5, 3.71, 4.29, 7.74, 2.48, 3.25, -1.15, 8.38)
no.feedback<-c(2.55, 12.07, 0.46, 0.35, 2.69, -0.94, 1.73, 0.73, -0.35, -0.37)
pKolSmirn(x=feedback,y=no.feedback)

Lepage

Description

Function to compute the P-value for the observed Lepage D statistic.

Usage

pLepage(x,y=NA,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the two groups of data can be entered in any of three ways. For data a=1,2 and b=3,4 all of the following are equivalent:

pLepage(x=c(1,2),y=c(3,4)) pLepage(x=list(c(1,2),c(3,4))) pLepage(x=c(1,2,3,4),g=c(1,1,2,2))

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 5.3 Platelet Counts of Newborn Infants
platelet.counts<-list(x = c(120000, 124000, 215000, 90000, 67000, 95000, 
190000, 180000, 135000, 399000), y = c(12000, 20000, 112000, 
32000, 60000, 40000))

pLepage(platelet.counts)

##or equivalently,

pLepage(platelet.counts$x,platelet.counts$y)

Mack-Skillings

Description

Function to compute the P-value for the observed Mack-Skillings MS statistic.

Usage

pMackSkil(x,b=NA,trt=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent:

pMackSkil(x=array(c(1,2,3,4,5,6),dim=c(1,2,3)) pMackSkil(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Example 7.9 Determination of Niacin in Bran Flakes
niacin<-array(dim=c(3,4,3))
niacin[,,1]<-c(7.58,7.87,7.71,8,8.27,8,7.6,7.3,7.82,8.03,7.35,7.66)
niacin[,,2]<-c(11.63,11.87,11.4,12.2,11.7,11.8,11.04,11.5,11.49,11.5,10.10,11.7)
niacin[,,3]<-c(15,15.92,15.58,16.6,16.4,15.9,15.87,15.91,16.28,15.1,14.8,15.7)

Function to compute the upper tail probability of the maximum of k N(0,1) random variables with common correlation for a given cutoff.

Description

Uses the integrate function based on the method proposed in Gupta, Panchapakesan and Sohn (1983).

Usage

pMaxCorrNor(x,k,rho)

Arguments

Value

Returns the upper tail probability at the user-specified cutoff.

Author(s)

Grant Schneider

References

Gupta, Shanti S., S. Panchapakesan, and Joong K. Sohn. "On the distribution of the studentized maximum of equally correlated normal random variables." Communications in Statistics-Simulation and Computation 14.1 (1985): 103-135.

Examples

##Hollander-Wolfe-Chicken Section 7.14
pMaxCorrNor(2.575,5,.3)

##Hollander-Wolfe-Chicken Example 7.14 Effect of Weight on Forearm Tremor Frequency
pMaxCorrNor(1.93,5,.452)

Nemenyi, Damico-Wolfe

Description

Function to compute the P-value for the observed Nemenyi, Damico-Wolfe Y statistic.

Usage

pNDWol(x,g=NA,method=NA, n.mc=10000)

Arguments

Value

Returns a list with "NSM3Ch6MCp" class containing the following components:

Note

The data group containing the treatment values should be entered as the first group.

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 6.8 Motivational Effect of Knowledge of Performance
motivational.effect<-list(no.Info = c(40, 35, 38, 43, 44, 41), 
rough.Info = c(38, 40, 47, 44, 40, 42), 
accurate.Info = c(48, 40, 45, 43, 46, 44))

pNDWol(motivational.effect,method="Asymptotic")
pNDWol(motivational.effect,method="Monte Carlo")

Nemenyi, Wilcoxon-Wilcox, Miller

Description

Function to compute the P-value for the observed Nemenyi, Wilcoxon-Wilcox, Miller R* statistic.

Usage

pNWWM(x,b=NA,trt=NA,method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent:

pNWWM(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) pNWWM(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7MCp" class containing the following components:

Note

The data group containing the treatment values should be entered as the first group.

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.4 Stuttering Adaptation
adaptation.scores<-matrix(c(57,59,44,51,43,49,48,56,44,50,44,50,70,42,58,54,38,48,38,48,50,53,53,
56,37,58,44,50,58,48,60,58,60,38,48,56,51,56,44,44,50,54,50,40,50,50,56,46,74,57,74,48,48,44),
ncol=3,dimnames = list(1 : 18,c("No Shock", "Shock Following", "Shock During")))

#pNWWM(adaptation.scores)
pNWWM(adaptation.scores,n.mc=2500)

Page

Description

Function to compute the P-value for the observed Page L statistic.

Usage

pPage(x,b=NA,trt=NA,method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent:

pPage(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) pPage(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.2 Breaking Strength of Cotton Fibers
strength.index<-matrix(c(7.46, 7.68, 7.21, 7.17, 7.57, 7.80, 7.76, 7.73, 7.74, 8.14, 8.15,
7.87, 7.63, 8.00, 7.93),byrow=FALSE,ncol=5)

#pPage(strength.index,method="Exact")
pPage(strength.index,method="Monte Carlo")

Paired Wilcoxon

Description

Function to extend wilcox.test to compute the (exact or Monte Carlo) P-value for paired Wilcoxon data in the presence of ties.

Usage

pPairedWilcoxon(x,y=NA,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the two groups of data can be entered in any of three ways. For data a=1,2 and b=3,4 all of the following are equivalent:

pPairedWilcoxon(x=c(1,2),y=c(3,4)) pPairedWilcoxon(x=list(c(1,2),c(3,4))) pPairedWilcoxon(x=c(1,2,3,4),g=c(1,1,2,2))

Value

Returns a list with "NSM3Ch5p" class containing the following components:

Note

If there are 0s in the Z values (the difference between X and Y), these will be removed and the calculations will be done based on the smaller sample size, as detailed section 3.1 of Hollander, Wolfe, and Chicken - NSM3.

Author(s)

Grant Schneider

See Also

Also see stats::wilcox.test()

Examples

##Hollander-Wolfe-Chicken Example 3.1 Hamilton Depression Scale Factor IV
x <-c(1.83, .50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
y <-c(0.878, .647, .598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)

wilcox.test(y,x,paired=TRUE,alternative="less")
pPairedWilcoxon(x,y)

Function to compute the upper-tail probability of the range of k independent N(0,1) random variables for a given cutoff.

Description

Uses the integrate function based on the method proposed in Harter (1960).

Usage

pRangeNor(x,k)

Arguments

Value

Returns the upper tail probability at the user-specified cutoff.

Author(s)

Grant Schneider

References

Harter, H. Leon. "Tables of range and studentized range." The Annals of Mathematical Statistics (1960): 1122-1147.

Examples

##Hollander-Wolfe-Chicken Example 7.3 Rounding First Base
pRangeNor(4.121,3)

##Hollander-Wolfe-Chicken Example 7.7 Chemical Toxicity
pRangeNor(4.171,7)

Dwass, Steel, Critchlow, Fligner

Description

Function to compute the P-value for the observed Dwass, Steel, Critchlow, Fligner W statistic.

Usage

pSDCFlig(x,g=NA,method=NA,n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pSDCFlig(x=list(c(1,2),c(3,4,5))) pSDCFlig(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6MCp" class containing the following components:

Author(s)

Grant Schneider

Examples

gizzards<-list(site.I=c(46,28,46,37,32,41,42,45,38,44),
              site.II=c(42,60,32,42,45,58,27,51,42,52),
              site.III=c(38,33,26,25,28,28,26,27,27,27),
              site.IV=c(31,30,27,29,30,25,25,24,27,30))
##Takes a little while 
#pSDCFlig(gizzards,method="Monte Carlo")

##Shorter version for demonstration
pSDCFlig(gizzards[1:2],method="Asymptotic")

Skillings-Mack

Description

Function to compute the P-value for the observed Skillings-Mack SM statistic.

Usage

pSkilMack(x, b = NA, trt = NA, method = NA, n.mc = 10000)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent: pSkilMack(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) pSkilMack(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander, Wolfe, Chicken Example 7.8 Effect of Rhythmicity of a Metronome on Speech Fluency
rhythmicity<-matrix(c(3, 5, 15, 1, 3, 18, 5, 4, 21, 2, NA, 6, 0, 2, 17, 0, 2, 10, 0, 3, 8,
0, 2, 13),ncol=3,byrow=TRUE)
#pSkilMack(rhythmicity)
pSkilMack(rhythmicity,n.mc=5000)

Function to compute the P-value for the observed Mack-Wolfe Peak Known A_p distribution.

Description

The function generalizes Harding's (1984) algorithm to quickly generate the distribution of A_p.

Usage

pUmbrPK(x,peak=NA,g=NA,method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pUmbrPK(x=list(c(1,2),c(3,4,5))) pUmbrPK(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6p" class containing the following components:

Author(s)

Grant Schneider

References

Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.

Examples

##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer
x<-c(36,33.6,26.9,35.8,30.1,31.2,35.3,39.9,29.1,43.4,44.6,54.4,48.2,55.7,50,53.8,53.9,62.5,46.6,
44.3,34.1,35.7,35.6,31.7,22.1,30.7)
g<-c(rep(1,7),rep(2,3),rep(3,5),rep(4,4),rep(5,4),rep(6,3))

pUmbrPK(x,4,g,"Exact")
pUmbrPK(x,4,g,"Asymptotic")

Mack-Wolfe Peak Unknown

Description

Function to compute the P-value for the observed Mack-Wolfe Peak Unknown A_p-hat distribution.

Usage

pUmbrPU(x,g=NA,method=NA, n.mc=10000)

Arguments

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pUmbrPU(x=list(c(1,2),c(3,4,5))) pUmbrPU(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6p" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 6.4 Learning Comprehension and Age
wechsler<-list("16-19"=c(8.62,9.94,10.06),"20-34"=c(9.85,10.43,11.31),"35-54"=c(9.98,10.69,11.40),
"55-69"=c(9.12,9.89,10.57),"70+"=c(4.80,9.18,9.27))

#pUmbrPU(wechsler,method="Monte Carlo",n.mc=20000)
pUmbrPU(wechsler,method="Monte Carlo",n.mc=1000)

Wilcoxon, Nemenyi, McDonald-Thompson

Description

Function to compute the P-value for the observed Wilcoxon, Nemenyi, McDonald-Thompson R statistic.

Usage

pWNMT(x,b=NA,trt=NA,method=NA, n.mc=10000, standardized=FALSE)

Arguments

Details

The data entry is intended to be flexible, so that the data can be entered in either of two ways. The following are equivalent: pWNMT(x=matrix(c(1,2,3,4,5,6),ncol=2,byrow=T)) pWNMT(x=c(1,2,3,4,5,6),b=c(1,1,2,2,3,3),trt=c(1,2,1,2,1,2))

Value

Returns a list with "NSM3Ch7MCp" class containing the following components:

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Example 7.3 Rounding First Base
RoundingTimes<-matrix(c(5.40, 5.50, 5.55, 5.85, 5.70, 5.75, 5.20, 5.60, 5.50, 5.55, 5.50, 5.40,
5.90, 5.85, 5.70, 5.45, 5.55, 5.60, 5.40, 5.40, 5.35, 5.45, 5.50, 5.35, 5.25, 5.15, 5.00, 5.85,
5.80, 5.70, 5.25, 5.20, 5.10, 5.65, 5.55, 5.45, 5.60, 5.35, 5.45, 5.05, 5.00, 4.95, 5.50, 5.50,
5.40, 5.45, 5.55, 5.50, 5.55, 5.55, 5.35, 5.45, 5.50, 5.55, 5.50, 5.45, 5.25, 5.65, 5.60, 5.40,
5.70, 5.65, 5.55, 6.30, 6.30, 6.25),nrow = 22,byrow = TRUE,dimnames = list(1 : 22,
c("Round Out", "Narrow Angle", "Wide Angle")))

pWNMT(RoundingTimes,n.mc=2500)

Methods to control displayed output of NSM3 tests.

Description

These methods are used to display the list output from the functions used to perform the various nonparametric statistical procedures in the NSM3 package.

Usage

## S3 method for class 'NSM3Ch5p'
print(x, ...)

Arguments

Value

The exact wording of the displayed output will vary depending on the setting. For example two sample procedures and k-sample procedures will be worded in a slightly different manner.

Author(s)

Grant Schneider

Quantile function for the asymptotic distribution of the Kolmogorov-Smirnov J* statistic.

Description

This function computes the Q() function defined in Section 5.4 of Hollander, Wolfe, and Chicken on a grid and then searches for the cutoff based on alpha.

Usage

qKolSmirnLSA(alpha)

Arguments

Value

Returns the upper tail cutoff at or below user-specified alpha

Author(s)

Grant Schneider

Examples

##Hollander-Wolfe-Chicken Section 5.4 LSA
qKolSmirnLSA(.05)

Function to test for parallel lines.

Description

This code tests for parallel lines based on chapter 9 of Hollander, Wolfe, & Chicken, Nonparametric Statistical Methods, 3e.

Usage

sen.adichie(z, example=F, r=3) 

Arguments

Author(s)

Eric Chicken

Examples

##Example 9.5 Hollander-Wolfe-Chicken##
sen.adichie(example=TRUE)

Susarla-van Ryzin

Description

Function to compute the Susarla-van Ryzin estimator

Usage

svr.df (z, delta, lambda.hat=0.001, alpha = 3, npoints=2053)

Arguments

Value

Returns a list containing:

Note

Requires the survival library.

Author(s)

Rachel Becvarik

Examples

hodgkins.affected<-matrix(c(1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1,0, 1, 1, 0, 1, 0, 1, 0, 1, 0,
0, 1, 346, 141, 296, 1953, 1375, 822, 2052, 836, 1910, 419,  107, 570, 312,1818, 364, 401, 1645,
330, 1540, 688, 1309, 505, 1378, 1446, 86),nrow=2,byrow=TRUE)
svr.df(hodgkins.affected[2,], hodgkins.affected[1,])

Guess-Hollander-Proschan

Description

Function to compute the asymptotic P-value for the observed Guess-Hollander-Proschan T_1 statistic.

Usage

tc(x, tau, alternative = "two.sided")

Arguments

Value

The function returns a list with four elements:

Author(s)

Rachel Becvarik

Examples

tb<-c(43, 45, 53, 56, 56, 57, 58, 66, 67, 73, 74, 79, 80, 80, 81, 81, 81, 82, 83, 83, 84, 88,  
89,  91,  91,  92,  92,  97,  99,  99, 100, 100, 101, 102, 102, 102, 103, 104, 107, 108, 109,
113, 114, 118, 121, 123, 126, 128, 137, 138, 139, 144, 145, 147, 156, 162, 174, 178, 179, 184,
191, 198, 211, 214, 243, 249, 329, 380, 403, 511, 522, 598)
tc(tb, tau=91.9, alt="dimrl")
tc(tb, tau=91.9, alt="idmrl")

Function to estimate and perform tests on the slope and intercept of a simple linear model.

Description

This code estimates and performs tests on the slope and intercept of a simple linear model. Based on chapter 9 of Hollander, Wolfe & Chicken, Nonparametric Statistical Methods, 3e.

Usage

theil(x=NULL, y=NULL, alpha=0.05, beta.0=0, type="t", 
      example=FALSE, r=3, slopes=F, doplot=TRUE) 

Arguments

Value

Returns a list with "NSM3Ch9ChickFn" class containing the following components:

Author(s)

Eric Chicken

Examples

##Example 9.1 Hollander-Wolfe-Chicken##
theil (x, y, example=TRUE, slopes=TRUE)

Function to perform Zelen's test.

Description

Zelen's test based on section 10.4 of Hollander, Wolfe, & Chicken, Nonparametric Statistical Methods, 3e.

Usage

zelen.test(z, example=F, r=3)

Arguments

Author(s)

Eric Chicken

Examples

##Chapter 10 Coment 24 Hollander-Wolfe-Chicken##
zelen.test(example=TRUE)