| Title: | Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition |
|---|---|
| Description: | Designed to replace the tables which were in the back of the first two editions of Hollander and Wolfe - Nonparametric Statistical Methods. Exact procedures are performed when computationally possible. Monte Carlo and Asymptotic procedures are performed otherwise. For those procedures included in the base packages, our code simply provides a wrapper to standardize the output with the other procedures in the package. |
| Authors: | Grant Schneider [aut, cre], Eric Chicken [aut], Rachel Becvarik [aut] |
| Maintainer: | Grant Schneider <[email protected]> |
| License: | GPL-2 |
| Version: | 1.19 |
| Built: | 2024-11-05 06:45:35 UTC |
| Source: | CRAN |
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.
cAnsBrad(alpha, m, n, method = NA, n.mc = 10000)cAnsBrad(alpha, m, n, method = NA, n.mc = 10000)
alpha |
A numeric value between 0 and 1. |
m |
A numeric value indicating the size of the first data group (X). |
n |
A numeric value indicating the size of the second data group (Y). |
method |
Either "Exact" or "Asymptotic", indicating the desired distribution. When method=NA, if m+n<=200, the "Exact" method will be used to compute the C distribution. Otherwise, the "Asymptotic" method will be used. |
n.mc |
Not used. Only included for standardization with other critical value procedures in the NSM3 package. |
Returns a list with "NSM3Ch5c" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact") |
cutoff.L |
lower tail cutoff at or below user-specified alpha |
true.alpha.L |
true alpha level corresponding to cutoff.L (if method="Exact") |
Grant Schneider
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/.
Also see ansari.test()
##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")##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")
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.
cBohnWolfe(alpha,k,q,c,d,method="Monte Carlo",n.mc=10000)cBohnWolfe(alpha,k,q,c,d,method="Monte Carlo",n.mc=10000)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the set size of the first data group in the RSS (X). |
q |
A numeric value indicating the set size of the second data group in the RSS (Y). |
c |
A numeric value indicating the number of cycles for the first data group in the RSS (X). |
d |
A numeric value indicating the number of cycles for the second data group in the RSS (Y). |
method |
For this procedure, method is currently set automatically to "Monte Carlo" as the only option that is available. For standardization with other critical value procedures in the NSM3 package, "Asymptotic" and "Exact" will be supported in future versions. |
n.mc |
Number of Monte Carlo samples used to estimate the distribution of U. |
Returns a list with "NSM3Ch5c" class containing the following components:
m |
number of observations in RSS for the first data group (X) |
n |
number of observations in RSS for the second data group (Y) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U |
Grant Schneider
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.
cBohnWolfe(.0515,4,4,5,5) cBohnWolfe(.0303,2,3,3,3)cBohnWolfe(.0515,4,4,5,5) cBohnWolfe(.0303,2,3,3,3)
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.
cDurSkiMa(alpha,obs.mat, method=NA, n.mc=10000)cDurSkiMa(alpha,obs.mat, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
obs.mat |
The incidence matrix, explained below. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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.
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
ss |
number of treatments per block |
pp |
number of observations per treatment |
lambda |
number of times each pair of treatments occurs together within a block |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
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.
Grant Schneider
##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)##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)
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.
cFligPoli(alpha,m,n,method=NA,n.mc=10000)cFligPoli(alpha,m,n,method=NA,n.mc=10000)
alpha |
A numeric value between 0 and 1. |
m |
A numeric value indicating the size of the first data group (X). |
n |
A numeric value indicating the size of the second data group (Y). |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch5c" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##Chapter 4 example Hollander-Wolfe-Chicken## cFligPoli(.0504,8,7) cFligPoli(.101,8,7)##Chapter 4 example Hollander-Wolfe-Chicken## cFligPoli(.0504,8,7) cFligPoli(.101,8,7)
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.
cFrd(alpha, k, n, method=NA, n.mc=10000, return.full.distribution=FALSE)cFrd(alpha, k, n, method=NA, n.mc=10000, return.full.distribution=FALSE)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the number of treatments. |
n |
A numeric value indicating the number of blocks. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
return.full.distribution |
If TRUE, and the method used is not asymptotic, the entire probability mass function of S will be returned. |
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
full.distribution |
probability mass function of S |
Grant Schneider
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.
The coin package.
##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")##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")
Function to compute the Campbell-Hollander estimator G-hat
ch.ro (x,n,alpha,mu,...)ch.ro (x,n,alpha,mu,...)
x |
a vector of data of length r |
n |
the sample size |
alpha |
the degrees of confidence in mu |
mu |
the prior guess of the unknown P (a pdf) |
... |
all of the arguments needed for mu |
G.hat |
estimate of the rank order G |
Rachel Becvarik
See Section 16.3 of Hollander, Wolfe, Chicken - Nonparametric Statistical Methods 3.
##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)##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)
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.
cHaySton(alpha,n, method=NA, n.mc=10000)cHaySton(alpha,n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector (of length 2 or greater) indicating the sizes of the data groups. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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.
Returns a list with "NSM3Ch6MCc" class containing the following components:
n |
data group sizes |
num.comp |
number of multiple comparisons to be made (based on the length of n) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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")##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")
This function computes the critical value for the Hayter-Stone W* asymptotic distriburion at the given alpha level.
cHayStonLSA(alpha,k,delta=.001)cHayStonLSA(alpha,k,delta=.001)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the number of the data groups (with assumed equal sizes). |
delta |
Increment used to create the grid on which the distribution will be approximated. |
The Asymptotic distribution requires that all (unspecified) group sizes are equal.
Returns the cutoff (based on the specified grid) with upper tail probability nearest to alpha.
Grant Schneider
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.
##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-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)
Quantile function for the Hollander A distribution.
cHollBivSym(alpha,d.mat,method=NA, n.mc=10000)cHollBivSym(alpha,d.mat,method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
d.mat |
The d matrix, explained below. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. As Kepner and Randles (1984) and Hilton and Gee (1997) have found the large sample approximation to perform poorly, method="Asymptotic" will be treated as method=NA. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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.
Returns a list with "NSM3Ch5c" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) (equal to m, but included for standardization with other procedures) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U |
Grant Schneider
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.
##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)##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)
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.
cJCK(alpha, n, method=NA, n.mc=10000)cJCK(alpha, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector of numeric values indicating the size of each of the k data groups. |
method |
Either "Exact" or "Asymptotic", indicating the desired distribution. When method=NA, if sum(n)<=200, the "Exact" method will be used to compute the J distribution. Otherwise, the "Asymptotic" method will be used. |
n.mc |
Not used. Only included for standardization with other critical value procedures in the NSM3 package. |
Returns a list with "NSM3Ch6c" class containing the following components:
n |
number of observations in the k data groups |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact") |
Grant Schneider
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.
##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")##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")
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.
cKolSmirn(alpha, m, n, method=NA, n.mc=10000)cKolSmirn(alpha, m, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
m |
A numeric value indicating the size of the first data group (X). |
n |
A numeric value indicating the size of the second data group (Y). |
method |
Either "Exact" or "Asymptotic", indicating the desired distribution. When method=NA, if m+n<=200, the "Exact" method will be used to compute the J distribution. Otherwise, the "Asymptotic" method will be used. |
n.mc |
Not used. Only included for standardization with other critical value procedures in the NSM3 package. |
Returns a list with "NSM3Ch5c" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact") |
Grant Schneider
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/.
Also see ks.test().
##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")##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")
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.
cKW(alpha,n, method=NA, n.mc=10000)cKW(alpha,n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector of numeric values indicating the size of each of the k data groups. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch6c" class containing the following components:
n |
number of observations in the k data groups |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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)##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)
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.
cLepage(alpha, m, n, method=NA, n.mc=10000)cLepage(alpha, m, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
m |
A numeric value indicating the size of the first data group (X). |
n |
A numeric value indicating the size of the second data group (Y). |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch5c" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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")##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")
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.
cMackSkil(alpha,k,n,c, method=NA, n.mc=10000)cMackSkil(alpha,k,n,c, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the number of treatments. |
n |
A numeric value indicating the number of blocks. |
c |
A numeric value indicating the number of replications for each treatment-block combination. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
c |
number of replications |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact") |
Grant Schneider
##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)##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)
Uses the integrate function based on the method proposed in Gupta, Panchapakesan and Sohn (1983).
cMaxCorrNor(alpha,k,rho)cMaxCorrNor(alpha,k,rho)
alpha |
A numeric value between 0 and 1. |
k |
Number of random variables. |
rho |
Common correlation between the random variables. |
Returns the upper tail cutoff at or immediately below the user-specified alpha.
Grant Schneider
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.
##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)##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)
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.
cNDWol(alpha,n, method=NA, n.mc=10000)cNDWol(alpha,n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector of numeric values indicating the size of each of the k data groups, with the first element indicating the treatment group size. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch6MCc" class containing the following components:
n |
number of observations in the k data groups |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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")##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")
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.
cNWWM(alpha, k, n, method=NA, n.mc=10000)cNWWM(alpha, k, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the number of treatments. |
n |
A numeric value indicating the number of blocks. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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")##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")
This function is based on the computations in Hollander (1967).
CorrUpperBound(n)CorrUpperBound(n)
n |
number of observations |
Returns a numeric value indicating the upper bound.
Grant Schneider
Hollander, Myles. "Rank tests for randomized blocks when the alternatives have an a priori ordering." The Annals of Mathematical Statistics (1967): 867-877.
##Hollander-Wolfe-Chicken Example 7.12 Effect of Weight on Forearm Tremor Frequency CorrUpperBound(6)##Hollander-Wolfe-Chicken Example 7.12 Effect of Weight on Forearm Tremor Frequency CorrUpperBound(6)
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.
cPage(alpha, k, n, method=NA, n.mc=10000)cPage(alpha, k, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the number of treatments. |
n |
A numeric value indicating the number of blocks. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##Hollander-Wolfe-Chicken Example 7.2 Breaking Strength of Cotton Fibers #cPage(.0097, 5, 3,"Exact") cPage(.0097, 5, 3,"Monte Carlo")##Hollander-Wolfe-Chicken Example 7.2 Breaking Strength of Cotton Fibers #cPage(.0097, 5, 3,"Exact") cPage(.0097, 5, 3,"Monte Carlo")
Uses the integrate function based on the method proposed in Harter (1960).
cRangeNor(alpha,k)cRangeNor(alpha,k)
alpha |
A numeric value between 0 and 1. |
k |
Number of independent Normal random variables. |
Returns the upper tail cutoff at or immediately below the user-specified alpha.
Grant Schneider
Harter, H. Leon. "Tables of range and studentized range." The Annals of Mathematical Statistics (1960): 1122-1147.
##Hollander-Wolfe-Chicken Example 7.3 Rounding First Base cRangeNor(.01, 3) ##Hollander-Wolfe-Chicken Example 7.7 Chemical Toxicity cRangeNor(.05, 7)##Hollander-Wolfe-Chicken Example 7.3 Rounding First Base cRangeNor(.01, 3) ##Hollander-Wolfe-Chicken Example 7.7 Chemical Toxicity cRangeNor(.05, 7)
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.
cSDCFlig(alpha, n, method=NA, n.mc=10000)cSDCFlig(alpha, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector of numeric values indicating the size of each of the k data groups. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch6c" class containing the following components:
n |
number of observations in the k data groups |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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")##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")
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.
cSkilMack(alpha, obs.mat, method = NA, n.mc = 10000)cSkilMack(alpha, obs.mat, method = NA, n.mc = 10000)
alpha |
A numeric value between 0 and 1. |
obs.mat |
The incidence matrix, explained below. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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.
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
ss |
number of treatments per block |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
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.
Grant Schneider
##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)##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)
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.
cUmbrPK(alpha, n, peak=NA, method=NA, n.mc=10000)cUmbrPK(alpha, n, peak=NA, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector of numeric values indicating the size of each of the k data groups. |
peak |
An integer representing the known peak among the data groups. |
method |
Either "Exact" or "Asymptotic", indicating the desired distribution. When method=NA, if sum(n)<=200, the "Exact" method will be used to compute the A_p distribution. Otherwise, the "Asymptotic" method will be used. |
n.mc |
Not used. Only included for standardization with other critical value procedures in the NSM3 package. |
Returns a list with "NSM3Ch6c" class containing the following components:
n |
number of observations in the k data groups |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact") |
Grant Schneider
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.
##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer cUmbrPK(.0101, c(7, 3, 5, 4, 4,3), peak=4)##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer cUmbrPK(.0101, c(7, 3, 5, 4, 4,3), peak=4)
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.
cUmbrPU(alpha, n, method=NA, n.mc=10000)cUmbrPU(alpha, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
n |
A vector of numeric values indicating the size of each of the k data groups. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch6c" class containing the following components:
n |
number of observations in the k data groups |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##Hollander-Wolfe-Chicken Example 6.4 Learning Comprehension and Age #cUmbrPU(.0495, c(3, 3, 3, 3, 3)) cUmbrPU(.10, c(2, 4, 2))##Hollander-Wolfe-Chicken Example 6.4 Learning Comprehension and Age #cUmbrPU(.0495, c(3, 3, 3, 3, 3)) cUmbrPU(.10, c(2, 4, 2))
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.
cWNMT(alpha, k, n, method=NA, n.mc=10000)cWNMT(alpha, k, n, method=NA, n.mc=10000)
alpha |
A numeric value between 0 and 1. |
k |
A numeric value indicating the number of treatments. |
n |
A numeric value indicating the number of blocks. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch7c" class containing the following components:
k |
number of treatments |
n |
number of blocks |
cutoff.U |
upper tail cutoff at or below user-specified alpha |
true.alpha.U |
true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo") |
Grant Schneider
##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)##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)
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.
data(rhythmicity)data(rhythmicity)
The format varies depending on the dataset.
Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition
data(rhythmicity) data(forearm)data(rhythmicity) data(forearm)
Function to compute the Monte Carlo or asymptotic P-value for the observed Hollander-Proschan V' statistic.
dmrl.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)dmrl.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, dmrl, and imrl with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. This is the same large sample approximation as epstein() |
min.reps |
the minimum number of repetitions for the Monte Carlo Approximation |
max.reps |
the maximum number of reps for the Monte Carlo Approximation. If the maximum number of reps has been reached, and the probability has not converged, a warning is given. |
delta |
the measure of accuracy for the convergence. If the probability converges to within delta, the Monte Carlo procedure stops before reaching the maximum number of reps. |
The function returns a list with two elements:
V |
the value of the dmrl statistic |
p |
the corresponding probability |
Rachel Becvarik
ex11.1<-c(42, 43, 51, 61, 66, 69, 71, 81, 82, 82) dmrl.mc(ex11.1, alt="dmrl", exact=TRUE)ex11.1<-c(42, 43, 51, 61, 66, 69, 71, 81, 82, 82) dmrl.mc(ex11.1, alt="dmrl", exact=TRUE)
This is the Monte Carlo approximation to the function "epstein".
e.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 1000, max.reps = 10000, delta = 10^-4)e.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 1000, max.reps = 10000, delta = 10^-4)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, ifr and dfr with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. This is the same large sample approximation as epstein() |
min.reps |
the minimum number of repetitions for the Monte Carlo Approximation |
max.reps |
the maximum number of reps for the Monte Carlo Approximation. If the maximum number of reps has been reached, and the probability has not converged, a warning is given. |
delta |
the measure of accuracy for the convergence. If the probability converges to within delta, the Monte Carlo procedure stops before reaching the maximum number of reps. |
The function returns a list with two elements:
E |
the value of the Epstein statistic |
p |
the corresponding probability |
Rachel Becvarik
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)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)
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
ecdf.ks.CI(x, main = NULL, sub = NULL, xlab = deparse(substitute(x)), ...)ecdf.ks.CI(x, main = NULL, sub = NULL, xlab = deparse(substitute(x)), ...)
x |
a vector of data of length n |
main |
the title of the plot. The default is ecdf(x) + 95% K.S.Bands |
sub |
subtitle, as used in the function plot() |
xlab |
the label for the x-axis of the plot. The default is x. |
... |
any additional plotting options |
The function returns a list with three elements:
lower |
the values of the lower part of the confidence band |
upper |
the values of the upper part of the confidence band |
D |
the value of Kolmogorov's D statistic |
This function also plots the confidence bands.
Rachel Becvarik
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")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")
Function to compute the P-value for the observed Epstein E statistic
epstein(x, alternative = "two.sided", exact=FALSE)epstein(x, alternative = "two.sided", exact=FALSE)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, ifr (for increasing failure rate) and dfr (for decreasing failure rate) with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. |
The function returns a list with two elements:
E |
the value of the Epstein statistic |
p |
the corresponding probability |
Rachel Becvarik
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")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")
Function to compute an approximation of Ferguson's estimator mu_n.
ferg.df(x, alpha, mu, npoints,...)ferg.df(x, alpha, mu, npoints,...)
x |
a vector of data of length n |
alpha |
the degree of confidence in mu |
mu |
the prior guess of the unknown P (a pdf) |
npoints |
the number of estimated points returned |
... |
all of the arguments needed for mu |
The function returns a vector of length num.points for Ferguson's estimator.
Rachel Becvarik
See Section 16.2 of Hollander, Wolfe, Chicken - Nonparametric Statistical Methods 3.
##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))##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))
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).
HoeffD(x, y, example=FALSE)HoeffD(x, y, example=FALSE)
x |
first data vector |
y |
second data vector |
example |
if true, analyzes the data from Example 8.6 |
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".
Eric Chicken
##Example 8.6 Hollander-Wolfe-Chicken## HoeffD(example=TRUE)##Example 8.6 Hollander-Wolfe-Chicken## HoeffD(example=TRUE)
Function to compute the Hollander A statistic for testing bivariate symmetry.
HollBivSym(x,y=NULL)HollBivSym(x,y=NULL)
x |
Either a matrix containing both groups of data or a vector containing the first group of data. |
y |
If x is a vector, y is a required vector containing the second group of data. Otherwise, not used. |
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))
Returns the observed Hollander A statistic.
Grant Schneider
##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)##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)
Based on sections 8.3 and 8.4 of Hollander, Wolfe & Chicken, Nonparametric Statistical Methods, 3e.
kendall.ci(x=NULL, y=NULL, alpha=0.05, type="t", bootstrap=F, B=1000, example=F)kendall.ci(x=NULL, y=NULL, alpha=0.05, type="t", bootstrap=F, B=1000, example=F)
x |
first data vector |
y |
second data vector |
alpha |
the significance level |
type |
type of confidence interval. Can be "t" (two-sided), "u" (upper) or "l" (lower). |
bootstrap |
if False, will find the asymptotic CI (as in section 8.3). If True, will find a bootstrap CI (as in section 8.4). |
B |
the number of bootstrap replicates |
example |
if True, will analyze data from Example 8.1 |
Eric Chicken
kendall.ci(example=TRUE)kendall.ci(example=TRUE)
Function to compute the P-value for the observed Klefsjo's A* statistic.
klefsjo.ifr (x, alternative = "two.sided", exact=FALSE)klefsjo.ifr (x, alternative = "two.sided", exact=FALSE)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, ifr and dfr with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. |
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.
The function returns a list with two elements:
A.star |
the value of the Klefsjo statistic |
p |
the corresponding probability |
Rachel Becvarik
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)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)
This is the Monte Carlo approximation to the function "klefsjo.ifr".
klefsjo.ifr.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)klefsjo.ifr.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, ifr and dfr with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. This is the same large sample approximation as epstein() |
min.reps |
the minimum number of repetitions for the Monte Carlo Approximation |
max.reps |
the maximum number of reps for the Monte Carlo Approximation. If the maximum number of reps has been reached, and the probability has not converged, a warning is given. |
delta |
the measure of accuracy for the convergence. If the probability converges to within delta, the Monte Carlo procedure stops before reaching the maximum number of reps. |
The function returns a list with two elements:
A.star |
the value of the Klefsjo statistic |
p |
the corresponding probability |
Rachel Becvarik
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)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)
Function to compute the P-value for the observed Klefsjo's B* statistic.
klefsjo.ifra (x, alternative = "two.sided", exact=FALSE)klefsjo.ifra (x, alternative = "two.sided", exact=FALSE)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, ifra and dfra with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. |
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.
The function returns a list with two elements:
B.star |
the value of the Klefsjo statistic |
p |
the corresponding probability |
Rachel Becvarik
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)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)
This is the Monte Carlo approximation to the function "klefsjo.ifra".
klefsjo.ifra.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)klefsjo.ifra.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, ifra and dfra with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. This is the same large sample approximation as epstein() |
min.reps |
the minimum number of repetitions for the Monte Carlo Approximation |
max.reps |
the maximum number of reps for the Monte Carlo Approximation. If the maximum number of reps has been reached, and the probability has not converged, a warning is given. |
delta |
the measure of accuracy for the convergence. If the probability converges to within delta, the Monte Carlo procedure stops before reaching the maximum number of reps. |
The function returns a list with two elements:
B.star |
the value of the Klefsjo statistic |
p |
the corresponding probability |
Rachel Becvarik
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)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)
Function to compute the asymptotic P-value for the observed Kolmogorov D statistic.
kolmogorov(x,fnc,...)kolmogorov(x,fnc,...)
x |
a vector of data of length n |
fnc |
the functional form of the pdf of F0. The first argument must be the data. |
... |
all the parameters besides the data that fnc needs to operate. (See below for an example using pnorm and pexp) |
The function returns a list with two elements:
D |
the value of the Kolmogorov statistic |
p |
the corresponding probability |
Rachel Becvarik
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)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)
This function is used to fit linear models based on Theil-Sen single median, or Siegel repeated medians.
mblm(formula, dataframe, repeated = TRUE)mblm(formula, dataframe, repeated = TRUE)
formula |
A formula of type y ~ x (only linear models are accepted) |
dataframe |
Optional dataframe |
repeated |
If set to true, model is computed using repeated medians. If false, a single median estimators are calculated |
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.
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:
slopes |
The slopes (in single median), or medians of slopes (in repeated medians) between tested point pairs |
intercepts |
The intercepts calculated |
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.
Lukasz Komsta, some fixes by Sven Garbade
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.
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)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)
Function to compute the Miller Jackknife Q statistic.
MillerJack(x,y=NULL)MillerJack(x,y=NULL)
x |
Either a vector containing the first group of data (X) or a matrix containing both groups of data. |
y |
If x is a vector, y is a vector containing the second group of data (Y). Otherwise, not used. |
Returns the observed Q statistic.
Grant Schneider
##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)##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)
Function to return the mean residual life along with Hall and Wellner's upper and lower bounds.
mrl(data, alpha, main=NULL, ylim=NULL, xlab=NULL,...)mrl(data, alpha, main=NULL, ylim=NULL, xlab=NULL,...)
data |
a vector of survival times |
alpha |
(1-alpha) is the approximate coverage probability for the confidence band. |
main |
title of the plot. The default is "Plot of Mean Residual Life and bounds". |
ylim |
the limits of the y-axis. The default is to include all points in the plotting range. |
xlab |
the label for the x-axis. The default is Time. |
... |
additional plotting options |
The function returns a list with three vectors:
PM |
the mean residual life |
PMU |
upper bound for the mean residual life |
PML |
lower bound for the mean residual life |
Rachel Becvarik
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)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)
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
multCh7(our.matrix)multCh7(our.matrix)
our.matrix |
The matrix containing the data which will be rearranged by row. |
The computations involved get very time consuming very quickly, so be careful not to use it for too large of a matrix.
Returns an array, containing (k!)^n distinct matrices of the same size as our.matrix
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.
Grant Schneider
some.matrix<-matrix(c(1,2,7,4,5,9),ncol=3,byrow=TRUE) multCh7(some.matrix)some.matrix<-matrix(c(1,2,7,4,5,9),ncol=3,byrow=TRUE) multCh7(some.matrix)
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
multCh7SM(our.matrix)multCh7SM(our.matrix)
our.matrix |
The matrix containing the data (including NA values) which will be rearranged by row. |
The computations involved get very time consuming very quickly, so be careful not to use it for too large of a matrix.
Returns an array, containing k1!*k2!*...*kn! distinct matrices of the same size as our.matrix
Grant Schneider
##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)##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)
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.
multComb(n.vec)multComb(n.vec)
n.vec |
Contains the group sizes n1,n2,...,nk |
The computations involved get very time consuming very quickly, so be careful not to use it for too many large groups.
Returns a matrix of n!/(n1!*n2!*...*nk!) rows, where each row represents one possible combination.
Grant Schneider
##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))##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))
This is the Monte Carlo approximation to the newbet function.
nb.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)nb.mc(x, alternative = "two.sided", exact=FALSE, min.reps = 100, max.reps = 1000, delta = 10^-3)
x |
a vector of data of length n |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, nbu, and nwu with the default value being two.sided. |
exact |
TRUE/FALSE value that determines whether the exact test or the large sample approximation is used if n >= 9. If n < 9 the exact test is used. The default value is FALSE, so the large sample approximation will be used unless specified not to. This is the same large sample approximation as epstein() |
min.reps |
the minimum number of repetitions for the Monte Carlo Approximation |
max.reps |
the maximum number of reps for the Monte Carlo Approximation. If the maximum number of reps has been reached, and the probability has not converged, a warning is given. |
delta |
the measure of accuracy for the convergence. If the probability converges to within delta, the Monte Carlo procedure stops before reaching the maximum number of reps. |
The function returns a list with two elements:
T |
the value of the Hollander-Proschan statistic |
p |
the corresponding probability |
Rachel Becvarik
table11.4<-c(194,15,41,29,33,181) nb.mc(table11.4, alt="nbu")table11.4<-c(194,15,41,29,33,181) nb.mc(table11.4, alt="nbu")
Function to compute the asymptotic P-value for the observed Hollander-Proschan T* statistic.
newbet(x)newbet(x)
x |
a vector of data of length n |
The function returns a list with two elements:
T |
the value of the Hollander-Proschan statistic |
T.star |
the standardized value of the Hollander-Proschan statistic |
p |
the corresponding probability |
Rachel Becvarik
table11.4<-c(194,15,41,29,33,181) newbet(table11.4)table11.4<-c(194,15,41,29,33,181) newbet(table11.4)
Function to compute the ordered Walsh averages and the value of the Hodges-Lehmann estimator
owa(x,y)owa(x,y)
x |
first vector of data of length n |
y |
second vector of data of length n |
Returns a list containing:
owa |
the ordered Walsh averages |
h.l |
the value of the Hodges-Lehmann estimator |
Rachel Becvarik
##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)##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)
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").
pAnsBrad(x,y=NA,g=NA,method=NA,n.mc=10000)pAnsBrad(x,y=NA,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing either all or the first group of data. |
y |
If x contains the first group of data, y contains the second group of data. Otherwise, not used. |
g |
If x contains a vector of all of the data, g is a vector of 1's and 2's corresponding to group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA and there are no ties in the data, "Exact" will be used. When method=NA and there are ties in the data, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
obs.stat |
the observed C statistic |
p.val |
upper tail P-value |
two.sided |
two-sided P-value |
If method="Monte Carlo" and there are no ties in the data, a warning is displayed and the "Exact" method is used.
Grant Schneider
Also see ansari.test.
##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)##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)
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.
pBohnWolfe(x,y,k,q,c,d,method="Monte Carlo",n.mc=10000)pBohnWolfe(x,y,k,q,c,d,method="Monte Carlo",n.mc=10000)
x |
A vector containing the data in the first group. |
y |
A vector containing the data in the Second group. |
k |
A numeric value indicating the set size of the first data group in the RSS (X). |
q |
A numeric value indicating the set size of the second data group in the RSS (Y). |
c |
A numeric value indicating the number of cycles for the first data group in the RSS (X). |
d |
A numeric value indicating the number of cycles for the second data group in the RSS (Y). |
method |
For this procedure, method is currently set automatically to "Monte Carlo" as the only option that is available. For standardization with other critical value procedures in the NSM3 package, "Asymptotic" and "Exact" will be supported in future versions. |
n.mc |
Number of Monte Carlo samples used to estimate the distribution of U. |
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in RSS for the first data group (X) |
n |
number of observations in RSS for the second data group (Y) |
obs.stat |
the observed U statistic |
p.val |
upper tail P-value |
Grant Schneider
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
##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)##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)
Function to compute the P-value for the observed Durbin, Skillings-Mack D statistic.
pDurSkiMa(x,b=NA,trt=NA,method=NA,n.mc=10000)pDurSkiMa(x,b=NA,trt=NA,method=NA,n.mc=10000)
x |
Either a matrix or a vector containing the data. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch7p" class containing the following components:
k |
number of treatments in the data |
n |
number of blocks in the data |
ss |
number of treatments per block |
pp |
number of observations per treatment |
lambda |
number of times each pair of treatments occurs together within a block |
obs.stat |
the observed D statistic |
p.val |
upper tail P-value |
Grant Schneider
##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)##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)
Function to compute the P-value for the observed Fligner-Policello U statistic.
pFligPoli(x,y=NA,g=NA,method=NA,n.mc=10000)pFligPoli(x,y=NA,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing either all or the first group of data. |
y |
If x contains the first group of data, y contains the second group of data. Otherwise, not used. |
g |
If x contains a vector of all of the data, g is a vector of 1's and 2's corresponding to group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
obs.stat |
the observed U statistic |
p.val |
upper tail P-value |
two.sided |
two-sided P-value |
Grant Schneider
##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)##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)
The method used to compute the P-value is from the reference by Van de Wiel, Bucchianico, and Van der Laan.
pFrd(x,b=NA,trt=NA,method=NA, n.mc=10000)pFrd(x,b=NA,trt=NA,method=NA, n.mc=10000)
x |
Either a matrix or a vector containing the data. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch7p" class containing the following components:
k |
number of treatments in the data |
n |
number of blocks in the data |
obs.stat |
the observed D statistic |
p.val |
upper tail P-value |
Grant Schneider
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.
Also see the coin package.
##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)##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)
Function to compute the P-value for the observed Hayter-Stone W statistic.
pHaySton(x,g=NA,method=NA,n.mc=10000)pHaySton(x,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing the data. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch6MCp" class containing the following components:
n |
a vector containing the number of observations in each of the data groups |
obs.stat |
the observed W statistic for each of the k*(k-1)/2 comparisons |
p.val |
upper tail P-value corresponding to each W statistic |
Grant Schneider
##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")##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")
Function to compute the upper tail probability of the Hayter-Stone W asymptotic distribution for a given cutoff.
pHayStonLSA(h,k,delta=.001)pHayStonLSA(h,k,delta=.001)
h |
Cutoff used to calculate the P-value. |
k |
Number of groups. |
delta |
Defines the fineness of the grid used to calculate the asymptotic distribution of W. |
Returns the asymptotic upper tail P-value.
Grant Schneider
pHayStonLSA(2.491,3) pHayStonLSA(4.112,4)pHayStonLSA(2.491,3) pHayStonLSA(4.112,4)
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".
pHoeff(n=5, reps=10000, r=4)pHoeff(n=5, reps=10000, r=4)
n |
the sample size |
reps |
the number of Monte Carlo runs to produce |
r |
the number of digits for rounding the results |
Returns a matrix containing the Monte Carlo distribution of the D statistic.
Eric Chicken
Also see the Hmisc package.
pHoeff(n=5, reps=10000, r=4) pHoeff(n=10, reps=1000, r=5)pHoeff(n=5, reps=10000, r=4) pHoeff(n=10, reps=1000, r=5)
Function to compute the P-value for the observed Hollander A statistic.
pHollBivSym(x,y=NA,g=NA,method=NA,n.mc=10000)pHollBivSym(x,y=NA,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing either all or the first group of data. |
y |
If x contains the first group of data, y contains the second group of data. Otherwise, not used. |
g |
If x contains a vector of all of the data, g is a vector of 1's and 2's corresponding to group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. As Kepner and Randles (1984) and Hilton and Gee (1997) have found the large sample approximation to perform poorly, method="Asymptotic" will be treated as method=NA. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
obs.stat |
the observed A statistic |
p.val |
upper tail P-value |
Grant Schneider
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.
##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)##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)
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.
pJCK(x,g=NA,method=NA, n.mc=10000)pJCK(x,g=NA,method=NA, n.mc=10000)
x |
Either a list or a vector containing the data. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA and ties are not present, "Exact" will be used. When method=NA and ties are present, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch6p" class containing the following components:
n |
a vector containing the number of observations in each of the data groups |
obs.stat |
the observed J statistic |
p.val |
upper tail P-value |
Grant Schneider
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.
##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")##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")
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.
pKolSmirn(x,y=NA,g=NA,method=NA,n.mc=10000)pKolSmirn(x,y=NA,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing either all or the first group of data. |
y |
If x contains the first group of data, y contains the second group of data. Otherwise, not used. |
g |
If x contains a vector of all of the data, g is a vector of 1's and 2's corresponding to group labels. Otherwise, not used. |
method |
Either "Exact" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
obs.stat |
the observed C statistic |
p.val |
upper tail P-value |
Grant Schneider
Also see ks.test().
##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)##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)
Function to compute the P-value for the observed Kruskal-Wallis H statistic.
pKW(x,g=NA, method=NA, n.mc=10000)pKW(x,g=NA, method=NA, n.mc=10000)
x |
Either a list or a vector containing the data. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA and ties are not present, "Exact" will be used. When method=NA and ties are present, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch6p" class containing the following components:
n |
a vector containing the number of observations in each of the data groups |
obs.stat |
the observed H statistic |
p.val |
upper tail P-value |
Grant Schneider
Also see kruskal.test().
##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)##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 compute the P-value for the observed Lepage D statistic.
pLepage(x,y=NA,g=NA,method=NA,n.mc=10000)pLepage(x,y=NA,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing either all or the first group of data. |
y |
If x contains the first group of data, y contains the second group of data. Otherwise, not used. |
g |
If x contains a vector of all of the data, g is a vector of 1's and 2's corresponding to group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
obs.stat |
the observed C statistic |
p.val |
upper tail P-value |
Grant Schneider
##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)##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)
Function to compute the P-value for the observed Mack-Skillings MS statistic.
pMackSkil(x,b=NA,trt=NA,method=NA,n.mc=10000)pMackSkil(x,b=NA,trt=NA,method=NA,n.mc=10000)
x |
Either a 3 dimensional array or a vector containing the data. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch7p" class containing the following components:
k |
number of treatments in the data |
n |
number of blocks in the data |
c |
number of repetitions for each treatment and block combination |
obs.stat |
the observed MS statistic |
p.val |
upper tail P-value |
Grant Schneider
##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)##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)
Uses the integrate function based on the method proposed in Gupta, Panchapakesan and Sohn (1983).
pMaxCorrNor(x,k,rho)pMaxCorrNor(x,k,rho)
x |
Cutoff at which the upper-tail P-value is to be calculated. |
k |
Number of random variables. |
rho |
Common correlation between the random variables. |
Returns the upper tail probability at the user-specified cutoff.
Grant Schneider
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.
##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)##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)
Function to compute the P-value for the observed Nemenyi, Damico-Wolfe Y statistic.
pNDWol(x,g=NA,method=NA, n.mc=10000)pNDWol(x,g=NA,method=NA, n.mc=10000)
x |
Either a list or a vector containing the data. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
Returns a list with "NSM3Ch6MCp" class containing the following components:
n |
number of observations in the k data groups, with the first group representing the control |
obs.stat |
the observed Y statistic for each treatment vs. control comparison |
p.val |
upper tail P-value corresponding to each of the k-1 observed Y statistics |
The data group containing the treatment values should be entered as the first group.
Grant Schneider
##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")##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")
Function to compute the P-value for the observed Nemenyi, Wilcoxon-Wilcox, Miller R* statistic.
pNWWM(x,b=NA,trt=NA,method=NA, n.mc=10000)pNWWM(x,b=NA,trt=NA,method=NA, n.mc=10000)
x |
Either a matrix or a vector containing the data, with control assumed to be the first group. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch7MCp" class containing the following components:
k |
number of treatments (including the control) |
n |
number of blocks |
obs.stat |
the observed R* statistic for each treatment vs. control comparison |
p.val |
upper tail P-value corresponding to each of the k-1 observed R* statistics |
The data group containing the treatment values should be entered as the first group.
Grant Schneider
##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)##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)
Function to compute the P-value for the observed Page L statistic.
pPage(x,b=NA,trt=NA,method=NA, n.mc=10000)pPage(x,b=NA,trt=NA,method=NA, n.mc=10000)
x |
Either a matrix or a vector containing the data. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch7p" class containing the following components:
k |
number of treatments in the data |
n |
number of blocks in the data |
obs.stat |
the observed L statistic |
p.val |
upper tail P-value |
Grant Schneider
##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")##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")
Function to extend wilcox.test to compute the (exact or Monte Carlo) P-value for paired Wilcoxon data in the presence of ties.
pPairedWilcoxon(x,y=NA,g=NA,method=NA,n.mc=10000)pPairedWilcoxon(x,y=NA,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing either all or the first group of data. |
y |
If x contains the first group of data, y contains the second group of data. Otherwise, not used. |
g |
If x contains a vector of all of the data, g is a vector of 1's and 2's corresponding to group labels. Otherwise, not used. |
method |
Either "Exact" or "Monte Carlo", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch5p" class containing the following components:
m |
number of observations in the first data group (X) |
n |
number of observations in the second data group (Y) |
obs.stat |
the observed T+ statistic |
p.val |
upper tail P-value |
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.
Grant Schneider
Also see stats::wilcox.test()
##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)##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)
Uses the integrate function based on the method proposed in Harter (1960).
pRangeNor(x,k)pRangeNor(x,k)
x |
Cutoff at which the upper-tail P-value is to be calculated. |
k |
Number of independent Normal random variables. |
Returns the upper tail probability at the user-specified cutoff.
Grant Schneider
Harter, H. Leon. "Tables of range and studentized range." The Annals of Mathematical Statistics (1960): 1122-1147.
##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)##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)
These methods are used to display the list output from the functions used to perform the various nonparametric statistical procedures in the NSM3 package.
## S3 method for class 'NSM3Ch5p' print(x, ...)## S3 method for class 'NSM3Ch5p' print(x, ...)
x |
The list object returned by a procedure in the NSM3 package. |
... |
Other options to be specified. |
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.
Grant Schneider
Function to compute the P-value for the observed Dwass, Steel, Critchlow, Fligner W statistic.
pSDCFlig(x,g=NA,method=NA,n.mc=10000)pSDCFlig(x,g=NA,method=NA,n.mc=10000)
x |
Either a list or a vector containing the data. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch6MCp" class containing the following components:
n |
a vector containing the number of observations in each of the k data groups |
obs.stat |
the observed W statistic for each of the k*(k-1)/2 comparisons |
p.val |
upper tail P-value corresponding to each W statistic |
Grant Schneider
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")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")
Function to compute the P-value for the observed Skillings-Mack SM statistic.
pSkilMack(x, b = NA, trt = NA, method = NA, n.mc = 10000)pSkilMack(x, b = NA, trt = NA, method = NA, n.mc = 10000)
x |
Either a matrix or a vector containing the data. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch7p" class containing the following components:
k |
number of treatments in the data |
n |
number of blocks in the data |
ss |
number of treatments per block |
obs.stat |
the observed D statistic |
p.val |
upper tail P-value |
Grant Schneider
##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)##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)
The function generalizes Harding's (1984) algorithm to quickly generate the distribution of A_p.
pUmbrPK(x,peak=NA,g=NA,method=NA, n.mc=10000)pUmbrPK(x,peak=NA,g=NA,method=NA, n.mc=10000)
x |
Either a list or a vector containing the data. |
peak |
An integer representing the known peak among the k data groups. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA, and there are ties in the data, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. When method=NA and there are no ties in the data, if sum(n)<=200, the "Exact" method will be used to compute the A_p distribution. Otherwise, the "Asymptotic" method will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch6p" class containing the following components:
n |
a vector containing the number of observations in each of the data groups |
obs.stat |
the observed A_p statistic |
p.val |
the upper tail P-value |
Grant Schneider
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.
##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")##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")
Function to compute the P-value for the observed Mack-Wolfe Peak Unknown A_p-hat distribution.
pUmbrPU(x,g=NA,method=NA, n.mc=10000)pUmbrPU(x,g=NA,method=NA, n.mc=10000)
x |
Either a list or a vector containing the data. |
g |
If x is a vector, g is a required vector of group labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
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))
Returns a list with "NSM3Ch6p" class containing the following components:
n |
a vector containing the number of observations in each of the data groups |
obs.stat |
the observed A_p-hat statistic |
p.val |
the upper tail P-value |
Grant Schneider
##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)##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)
Function to compute the P-value for the observed Wilcoxon, Nemenyi, McDonald-Thompson R statistic.
pWNMT(x,b=NA,trt=NA,method=NA, n.mc=10000, standardized=FALSE)pWNMT(x,b=NA,trt=NA,method=NA, n.mc=10000, standardized=FALSE)
x |
Either a matrix or a vector containing the data. |
b |
If x is a vector, b is a required vector of block labels. Otherwise, not used. |
trt |
If x is a vector, trt is a required vector of treatment labels. Otherwise, not used. |
method |
Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. |
n.mc |
If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used. |
standardized |
If TRUE, divide the observed statistic by (nk(k+1)/12)^0.5 before returning. |
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))
Returns a list with "NSM3Ch7MCp" class containing the following components:
k |
number of treatments |
n |
number of blocks |
obs.stat |
the observed R* statistic for each of the k*(k-1)/2 comparisons |
p.val |
upper tail P-value corresponding to each observed R statistic |
Grant Schneider
##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)##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)
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.
qKolSmirnLSA(alpha)qKolSmirnLSA(alpha)
alpha |
A numeric value between 0 and 1. |
Returns the upper tail cutoff at or below user-specified alpha
Grant Schneider
##Hollander-Wolfe-Chicken Section 5.4 LSA qKolSmirnLSA(.05)##Hollander-Wolfe-Chicken Section 5.4 LSA qKolSmirnLSA(.05)
Function to compute the P-value for the observed Randles-Fligner-Policello-Wolfe V statistic.
RFPW(z)RFPW(z)
z |
A vector containing the data. |
Returns a list containing:
obs.stat |
the observed V statistic |
p.val |
the asymptotic two-sided P-value |
Grant Schneider
##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)##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)
Function to obtain a ranked-set sample of given set size and number of cycles based on a specified auxiliary variable.
RSS(k,m,ranker)RSS(k,m,ranker)
k |
set size |
m |
number of cycles |
ranker |
auxiliary variable used for judgment ranking |
Returns a vector of the indices corresponding to the observations selected to be in the RSS.
Grant Schneider
##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)]##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)]
This code tests for parallel lines based on chapter 9 of Hollander, Wolfe, & Chicken, Nonparametric Statistical Methods, 3e.
sen.adichie(z, example=F, r=3)sen.adichie(z, example=F, r=3)
z |
a list of paired vectors. Each item in the list is a set of two paired vectors in the form of a matrix. The first column of each matrix is the x vector, the second in the y vector. |
example |
if true, analyzes the data from Example 9.5 |
r |
determines the amount of rounding. Increase it if your P-values are coming out as 0 or 1. |
Eric Chicken
##Example 9.5 Hollander-Wolfe-Chicken## sen.adichie(example=TRUE)##Example 9.5 Hollander-Wolfe-Chicken## sen.adichie(example=TRUE)
Function to compute the Susarla-van Ryzin estimator
svr.df (z, delta, lambda.hat=0.001, alpha = 3, npoints=2053)svr.df (z, delta, lambda.hat=0.001, alpha = 3, npoints=2053)
z |
the vector of zi = min(Xi, Yi) |
delta |
the vector of indicators which is 1 when Xi<=Yi and 0 otherwise |
lambda.hat |
the estimate of lambda from the data |
alpha |
the degree of faith in F0 |
npoints |
the number of estimated points returned |
Returns a list containing:
x |
the x values |
F.hat |
the Susarla-van Ryzin estimator |
Requires the survival library.
Rachel Becvarik
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,])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,])
Function to compute the asymptotic P-value for the observed Guess-Hollander-Proschan T_1 statistic.
tc(x, tau, alternative = "two.sided")tc(x, tau, alternative = "two.sided")
x |
a vector of data of length n |
tau |
the known value of the turning point,T |
alternative |
the direction of the alternative hypothesis. The choices are two.sided, idmrl, and dimrl with the default value being two.sided. |
The function returns a list with four elements:
T1 |
the value of the idmrl statistic |
T1* |
the standardized value of the idmrl statistic |
p |
the corresponding probability for T1* |
sigma.hat |
the standard deviation for T1 |
Rachel Becvarik
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")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")
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.
theil(x=NULL, y=NULL, alpha=0.05, beta.0=0, type="t", example=FALSE, r=3, slopes=F, doplot=TRUE)theil(x=NULL, y=NULL, alpha=0.05, beta.0=0, type="t", example=FALSE, r=3, slopes=F, doplot=TRUE)
x |
first data vector |
y |
second data vector |
alpha |
the significance level |
beta.0 |
the null hypothesized value |
type |
can be "t" (two-sided), "u" (upper) or "l" (lower). The type refers both to the test and the confidence interval. |
example |
if true, will analyze the data from Example 9.1 |
r |
the number of places for rounding. Increase it if your P-values are coming out as 0 or 1. |
slopes |
if true, will print all n(n-1)/2 slopes |
doplot |
if true, will plot the data and estimated line |
Returns a list with "NSM3Ch9ChickFn" class containing the following components:
alpha |
same as input argument |
beta.0 |
same as input argument |
type |
same as input argument |
r |
same as input argument |
slopes |
same as input argument |
C.stat |
the observed C statistic |
C.bar |
the observed C.bar statistic |
alpha.hat |
the observed alpha.hat statistic |
beta.hat |
the observed beta.hat statistic |
slopes.table |
table containing all n(n-1)/2 |
p.val |
the P-value corresponding to the selected type of test/confidence interval |
L |
the lower endpoint of the confidence interval |
U |
the upper endpoint of the confidence interval |
Eric Chicken
##Example 9.1 Hollander-Wolfe-Chicken## theil (x, y, example=TRUE, slopes=TRUE)##Example 9.1 Hollander-Wolfe-Chicken## theil (x, y, example=TRUE, slopes=TRUE)
Zelen's test based on section 10.4 of Hollander, Wolfe, & Chicken, Nonparametric Statistical Methods, 3e.
zelen.test(z, example=F, r=3)zelen.test(z, example=F, r=3)
z |
data as an array of k 2x2 matrices. Small data sets only! |
example |
if true, analyzes the data from comment 24 of Chapter 10 |
r |
determines the amount of rounding. Increase it if your P-values are coming out as 0 or 1. |
Eric Chicken
##Chapter 10 Coment 24 Hollander-Wolfe-Chicken## zelen.test(example=TRUE)##Chapter 10 Coment 24 Hollander-Wolfe-Chicken## zelen.test(example=TRUE)