Hogg's Q1 and Q2.

Description

Q1 is a measure of skewness and Q2 is a measure of tail heaviness.

Usage

Q1(z)

Arguments

Details

Used as selector statistics in adaptive schemes. Both Q1 and Q2 are ratios. For Q1, the numerator is upper 5% mean minus the middle 50% mean, while the denominator is difference between the middle 5% mean and the lower 5% mean. For Q2, the numerator is upper 5% mean minus the lower 5% mean, while the denominator is difference between the upper 50% mean and the lower 50% mean. These statistics are not robust.

Value

Returns the calculated ratio as a numeric scalar.

Author(s)

John Kloke

References

Hogg, R. McKean, J, Craig, A (2013) Introduction to Mathematical Statistics, 7th Ed. Boston: Pearson.

See Also

hogg.test

Cyclone Data

Description

A data set discussed in Hollander and Wolfe (1999) and Exercise 5.8.9 of Kloke and McKean (2014)/Exercise 5.9.15 of Kloke and McKean (2024). It contains part of a study on the effects of cloud seeding of cyclones.

Usage

data(SCUD)

Format

Twenty-one observations on three variables.

trt

treatment indicator (1) is Seeded and (2) is control

M

predictor M, the geostrophic meridional circulation index

RI

measure of precipitation

References

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

plot(RI ~ M,data=SCUD)

Analysis of Covariance Example for a two by three two-way design

Description

This a simulated data set which is used as an example of analysis of covariance. The data frame acov231 contains the data. The responses are in column 1, column 2 contains the levels of factor A, column 3 contains the levels of factor B, and the 4th column contains the covariate. All true parameters (effects) are 0 in this generated data set.

Usage

data(acov231)

Format

A data frame with 33 observations and 4 variables.

response

numeric. the response.

fA

numeric. factor A with 2 levels.

fB

numeric. factor B with 3 levels.

covariate

numeric. a covariate.

References

Kloke, J. and McKean J.W. (2014), Nonparametric Statistical Methods using R, Boca Raton, FL: Chapman-Hall.

Examples

levs = c(2,3)
data = acov231[,1:3]
xcov = matrix(acov231[,4],ncol=1)
temp = kancova(levs,data,xcov)

Aligned Rank Test

Description

Aligned rank test for a group/treatment effect after adjusting for covariates.

Usage

aligned.test(x, y, g, scores = Rfit::wscores,...)

Arguments

Details

Data are aligned based on the design matrix x using a rank-based fit via rfit.

Value

Author(s)

John Kloke

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

See Also

rfit

Examples

y<-rt(30,2)
x<-runif(30)
g<-rep(1:3,each=10)
aligned.test(x,y,g)

Career Information for a Random Sample of 1000 Baseball Players

Description

Demographics and position information on 1000 randomly selected baseball players who debuted after 1945.

Usage

data("baseball_players1000")

Format

A data frame with 1000 observations on the following 28 variables.

playerID

a character vector

birthYear

a numeric vector

birthMonth

a numeric vector

birthDay

a numeric vector

birthCountry

a character vector

birthState

a character vector

nameFirst

a character vector

nameLast

a character vector

weight

a numeric vector

height

a numeric vector

bats

a character vector

throws

a character vector

debutYear

a numeric vector

G_all

a numeric vector

G_p

a numeric vector

G_c

a numeric vector

G_1b

a numeric vector

G_2b

a numeric vector

G_3b

a numeric vector

G_ss

a numeric vector

G_lf

a numeric vector

G_cf

a numeric vector

G_rf

a numeric vector

G_of

a numeric vector

G_dh

a numeric vector

G_ph

a numeric vector

G_pr

a numeric vector

pitcher

a logical vector

Details

A random subset of baseball players who debuted after 1945 and played in at least 160 games. Includes information on birth (date and location); height (inches) and weight (pounds); whether they bat left (L), right (R), or switch (B); and games played at each postion. The variable pitcher is a derived variable based on if the majority of games were played as a pitcher (i.e.; G_pr/G_all > 0.5).

Source

https://github.com/chadwickbureau/baseballdatabank

References

https://github.com/chadwickbureau/baseballdatabank/blob/master/readme2014.txt

Examples

data(baseball_players1000)
hist(baseball_players1000$weight,xlab="Weight (lbs)",
     probability=TRUE, ylim=c(0,0.02),
     main="Histogram of Weight for 1000 Baseball Players")
lines(density(baseball_players1000$weight,na.rm=TRUE))

Batting statistics for the 2010 baseball season.

Description

Batting (average, home runs, RBIs) statistics for 2010 full time players. By full time we mean that the batter had at least 450 official at bats during the season.

Usage

data(bb2010)

Format

A data frame with 122 observations on the following 3 variables.

ave

batting average

hr

home runs

rbi

runs batted in

Source

baseballguru.com

Examples

plot(hr~ave,data=bb2010)

Blood plasma measurements related to total triglyceride level

Description

Data table from Table 9.11 of Hollander and Wolfe (1999). The data consists of triglyceride levels on 13 patients. Two factors, each at two levels, were recorded: Sex and Obesity. The concomitant variables are chylomicrons, age, and three lipid variables (very low-density lipoproteins (VLDL), low-density lipoproteins (LDL), and high-density lipoproteins (HDL)).

Usage

data(blood.plasma)

Format

A data frame with 13 observations on 8 variables.

Total

Triglyceride level, response

Sex

Sex, 2 levels

Obese

Obesity, 2 levels

Chylo

Chylomicrons, covariate

VLDL

Very low density, lipids, covariate

LDL

Low density, lipids, covariate

HDL

High density, lipids, covariate

Age

Age

Source

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

References

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

Examples

data(blood.plasma)
plot(Total~Age,data=blood.plasma)
boxplot(Total~Obese,data=blood.plasma)

Basic Summaries of Boxscores for the Milwaukee Brewers 1982 Season

Description

Basic Summaries of Boxscores for the Major League Baseball team Milwaukee (WI) Brewers 1982 Season. The Brewers won the American League championship that year. Brewer, Robin Yount won the Most Valueable Player (MVP) award. #Robin Yount. MVP.

Usage

data("brewers1982")

Format

A data frame with 163 observations on the following 8 variables.

Date

a character vector

Opp

a character vector

R

a numeric vector

RA

a numeric vector

Time

a character vector

Attendance

a numeric vector

home

a logical vector

win

a logical vector

Examples

data(brewers1982)
# proportion of wins for a given number of runs scored
pwin <- with(brewers1982,tapply(win,R,mean))
pwin
# graphical display of the above
plot(names(pwin),pwin,xlab='Runs', ylab='Proportion of Wins',main='Brewers 1982')

Survival time based on two treatments

Description

Survival times (in days) for undergoing standard treatment (S) and a new treatment (N).

Usage

data("cancertrt")

Format

A data frame with 17 observations on the following 3 variables.

time

Survival time in days

event

Indicator for event

trt

a factor with levels N S

References

Higgins (2004), Introduction to Modern Nonparametric Statistics, Pacific Grove, CA:Brooks/Cole–Thomson Learning

Examples

data(cancertrt)
with(cancertrt,gehan.test(time,event,trt))

Center Matrix

Description

Centers a matrix.

Usage

centerx(x)

Arguments

Details

Returns a centered matrix, i.e., each column of the matrix is replaced by deviations from its column mean.

Value

The centered matrix.

Author(s)

John Kloke, Joseph McKean

See Also

scale

Examples

x <- cbind(seq(1,5,length=5),seq(10,20,length=5))
xc <- centerx(x)
apply(xc,1,mean)

Cloud Dewpoint

Description

A regression example with response cloud point of a liquid and predictor the percent of Iodine 8 added to the liquid; see Chapter 3 of Hettmansperger and McKean (2011) or Exercise 4.9.10 of Kloke and McKean (2014)/Exercise 4.7.7 of Kloke and McKean (2024).

Usage

data(cloud)

Format

Nineteen observations on two variables.

cloud.point

Cloud point of the liquid

I8

Percent Iodine 8 added

Source

Draper, N.R. and Smith, H. (1966), Applied Regression Analysis, New York: John Wiley and Sons.

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods Using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods Using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

rfit(cloud.point ~ I8,data=cloud)

Confidence interval for a correlation based on a bootstrap.

Description

Returns a bootstrap confidence interval for any of the correlations available in the base R cor function.

Usage

cor.boot.ci(x, y, method = "spearman", conf = 0.95, nbs = 3000)

Arguments

Details

Obtains a percentile bootstrap confidence interval. The bootstrap samples are obtained via the function boot.

Value

A confidence interval.

Author(s)

John Kloke, Joseph McKean

See Also

See Also as cor

Examples

library(boot)
with(bb2010,cor.boot.ci(ave,hr))

Energy as a Function of temperature difference.

Description

A regression example with response energy output in watts and the predictor temperature difference in degrees Kevin; see Devore (2012) and Exercise 4.9.11 of Kloke and McKean (2014)/Exercise 4.7.8 of Kloke and McKean (2024).

Usage

data(energy)

Format

Twenty-four observations on two variables.

output

Energy output in watts

temp.diff

Temperature difference in K

Source

Devore, J. (2012), Probaility and statistics for engineering and the sciences, 8th ed., Boston: Brooks/Cole.

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

rfit(output ~ temp.diff,data=energy)

Rounding First Base.

Description

The amount of time it took 22 baseball players to round first base for each of three methods of rounding.

Usage

data(firstbase)

Format

A data frame with 22 observations on the following 3 variables.

round.out

Time when using round out method.

narrow.angle

Time when using narrow angle method.

wide.angle

Time when using wide angle method.

Details

Rounding methods are illustrated in Figure 7.1 of Hollander and Wolfe (1999).

Source

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

References

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

Two-sample Fligner-Kileen test for homogeneous scales.

Description

Returns the Fligner-Kileen test for homogeneous scales for two-samples. Also estimates of ratio of scales based on the logs of folded median-aligned samples and a corresponding confidence interval is computed. fk.test computes the value of the statistic based on squared-normal scores following the optimal (for normal errors) such test described in Section 2.10 of Hettmansperger and McKean (2011). Hence, it will differ from the core R routine fligner.test; see the discussion in Section 3.3 of Kloke and McKean (2014)/Section 3.5 of Kloke and McKean (2024).

Usage

fk.test(x,y,alternative = c("two.sided", "less", "greater"),conf.level = 0.95)

Arguments

Details

Returns the Fligner-Kileen test for the two-sample scale problem.

Value

Author(s)

John Kloke, Joseph McKean

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

See Also

fkk.test

Examples

x<-rnorm(18)
y<-rnorm(22)*3
fk.test(x,y)

k-Sample version of the Fligner-Kileen test for homogeneous scales.

Description

Returns the Fligner-Kileen test for homogeneous scales for k-samples. Also estimates of ratio of scales based on the logs of folded median-aligned samples and a corresponding confidence interval is computed. The first level (sample) is referenced. See the discussion in Section 5.7 of Kloke and McKean (2014)/Section 5.8 of Kloke and McKean (2024).

Usage

fkk.test(y,ind,conf.level = 0.95)

Arguments

Details

Returns the Fligner-Kileen test for the k-sample scale problem.

Value

Author(s)

John Kloke, Joseph McKean

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

See Also

fk.test

Examples

y1 <- rnorm(10)
y2 <- rnorm(12)*3
y3 <- rnorm(15)*5
y<-c(y1,y2,y3)
ind<-rep(1:3,times=c(10,12,15))
fkk.test(y,ind)

Placement Test for the Behrens-Fisher problem.

Description

Returns the test based on placements for the Behrens-Fisher problem. This test was developed by Fligner and Policello (1981); see, also, Section 2.11 of Hettmansperger and McKean (2011) and Section 4.4 of Hollander and Wolfe (1999). The version computed by fp.test is discussed in Section 3.4 of Kloke and McKean (2014)/Section 3.6 of Kloke and McKean (2024).

Usage

fp.test(x,y,delta0=0,alternative = "two.sided")

Arguments

Details

Returns the Placement Test for the Behrens-Fisher problem.

Value

Author(s)

John Kloke, Joseph McKean

References

Fligner, M.~A. and Policello, G.~E. (1981), Robust rank procedures for the Behrens-Fisher problem, Journal of the American Statistical Association, 76, 162–168.

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Hollander, M. and Wolfe, D.~A. (1999), Nonparametric statistical methods, 2nd Edition, New York: John Wiley and Sons.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Gehan generalization the Wilcoxon two-sample test

Description

Generalization of the Wilcoxon rank sum which allows for censored data.

Usage

 gehan.test(time, event, trt) 

Arguments

Value

Author(s)

John Kloke

References

Higgins (2004), Introduction to Modern Nonparametric Statistics, Pacific Grove, CA:Brooks/Cole–Thomson Learning

Examples

n<-76
y<-rexp(n)
event<-rbinom(n,1,0.7) # about 30%  censored
trt<-sample(c(0,1),n,replace=TRUE)
gehan.test(y,event,trt)

Design Function for Robust Analysis of Covariance

Description

Returns the hetrogeneous slopes design matrix used in ANCOVA. It refereences the first level.

Usage

getxact(amat,bmat)

Arguments

Details

Returns the heterogeneous slopes analysis of covariance matrix.

Value

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Design Function for Robust Analysis of Covariance

Description

Returns the hetrogeneous slopes design matrix used in ANCOVA. It refereences the first level. Also, column names are supplied.

Usage

getxact2(amat,bmat)

Arguments

Details

Returns the heterogeneous slopes analysis of covariance matrix.

Value

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Hemorrhage data from Dupont.

Description

Hemorrhage data from Dupont.

Usage

data(hemorrhage)

Format

A data frame with 71 observations on the following 3 variables.

genotype

a numeric vector

time

a numeric vector

recur

a numeric vector

References

Dupont

Examples

data(hemorrhage)
## maybe str(hemorrhage) ; plot(hemorrhage) ...

Hodges-Lehmann type estimation and confidence intervals.

Description

Hodges-Lehmann type estimation and confidence intervals.

Usage

hodges_lehmann.ci(x, y, var.equal = FALSE, conf.level = 0.95, ...)

Arguments

Details

Currently implements 2-sample estimation and confidence intervals based on methods purposed by Hodges and Lehnmann.

Value

Author(s)

John Kloke, Joseph McKean

References

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall.

See Also

wilcox.test

Examples

zoo<-c(390,258,298,255,324,240,416,319,225,284)
rh <- c(187,186,179,269,382,264,353 ,38,350,267,229,383,254,302,195, 43,337,390)
hodges_lehmann.ci(zoo,rh)

Relapse-Free Survival Times for Hodgkin's Disease Patients

Description

These data are described in Example~11.7 of Hollander and Wolfe (1999). Results from a clinical trial in early Hodgkin's disease. Subjects received one of two treatments: radiation of affected node (AN) or total nodal radiation (TN).

Usage

data("hodgkins")

Format

A data frame with 49 observations on the following 3 variables.

time

Survival time

relapse

Indicator variable for relapse

trt

treatment: a factor with levels AN TN

References

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

Hogg's Adaptive Test

Description

Based on selector statistics (Q1 & Q2) one of four score functions is choosen. A rank test and p-value is then calculated based on it.

Usage

hogg.test(x, y, ...)

Arguments

Value

Author(s)

John Kloke, Patrick Kimes

References

Hogg, R. McKean, J, Craig, A (2013) Introduction to Mathematical Statistics, 7th Ed. Boston: Pearson.

Examples

hogg.test(rt(20,1),rt(22,1)+0.2)

Analysis of Covarince Data Set

Description

A data set presented on Page 496 of huitema (2011). The design is a 2 by 2 with one covariate.

Usage

data(huitema496)

Format

A 16 by 4 array with the following 4 columns:

y

number of novel responses.

i

type of reinforcement (2 levels).

j

type of program (2 levels).

x

covariate, a measure of verbal fluency.

Details

Discussion can be found in both references listed below.

Source

Huitema, B.E. (2011), The analysis of covariance and alternatives, 2nd ed., New York: Wiley.

References

Huitema, B.E. (2011), The analysis of covariance and alternatives, 2nd ed., New York: Wiley.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Examples

huitema496 <- data.frame(huitema496)
fit <- rfit(y~factor(i)+factor(j)+x,data=huitema496)
summary(fit)

Insulating Fluid Data

Description

Study the breakdown time of an electrical insulating fluid subject to seven different levels of voltage stress.

Usage

data("insulation")

Format

A data frame with 76 observations on the following 2 variables.

log.stress

log of voltage stress

log.time

log of failure time

Source

Nelson, W. (1982), Applied lifetime data analysis, New York: John Wiley and Sons.

Lawless, J.F. (1982), Statistical models and methods for lifetime data, New York: John Wiley and Sons.

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Examples

myscores <- logGFscores
myscores@param <- c(1,5)
fit <- rfit(log.time ~ log.stress,scores=myscores,data=insulation)
summary(fit)
fit$tauhat

Internal Functions

Description

Internal functions not intended for general use. Used in calculation of Hogg's Qs.

Usage

lmean(z, p)

Arguments

Value

Returns the calculated value as a numeric scalar.

Author(s)

John Kloke, Joseph McKean

See Also

hogg.test,HoggsQs

Jonckheere's Test for Ordered Alternatives

Description

Computes Jonckheere's Test for Ordered Alternatives; see Section 5.6 of Kloke and McKean (2014)/Section 5.7 of Kloke and McKean (2024).

Usage

jonckheere(y, groups)

Arguments

Details

Computes Jonckheere's Test for Ordered Alternatives. The main source was downloaded from the site:

smtp.biostat.wustl.edu/sympa/biostat/arc/s-news/2000-10/msg00126.html

Value

Author(s)

John Kloke, Joseph McKean

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

smtp.biostat.wustl.edu/sympa/biostat/arc/s-news/2000-10/msg00126.html

Examples

 r<-rnorm(30)
 gp<-c(rep(1,10),rep(2,10),rep(3,10))
jonckheere(r,gp)

Robust Analysis of Covariance under Heterogeneous Slopes for a k-way layout

Description

Returns a robust rank-based analysis of covariance for a k-way layout assuming heterogenous slopes; see Section 5.4 of Kloke and McKean (2014)/Sections 5.6 and 7.3 of Kloke and McKean (2024). Currently only wilcoxon scores are used.

Usage

kancova(levs,data,xcov,print.table=TRUE)

Arguments

Details

Returns the analysis of covariance table assuming heterogenous slopes for a k-way layout.

Value

Author(s)

John Kloke, Joseph McKean

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

 levels <- c(2,2)
 y.group <- huitema496[,c('y','i','j')]
 xcov <- huitema496[,'x']
 kancova(levels,y.group,xcov)

routine used in the ANCOVA table obtained by kancova

Description

routine used in making the display of the ANCOVA table obtained by kancova.

Usage

kancovarown(vec)

Arguments

Details

Returns the labels.

Value

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Train a k nearest neighbors (knn) classifer via cross validation (cv).

Description

Train a k nearest neighbors (knn) classifer via cross validation (cv). The number of folds and the set of the number of neihbors to consider may be specified.

Usage

knn_cv(xy, k.cv = 5, kvec = seq(1, 47, by = 2))

Arguments

Value

Author(s)

John Kloke

References

Hastie, T., Tibshiani, R., and Friedman, J. (2017), The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, New York: Springer.

James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013), An Introduction to Statistical Learning with Applications in R, New York: Springer.

Venables, W. N. and Ripley, B. D. (2002) _Modern Applied Statistics with S._ Fourth edition. Springer.

See Also

knn

Examples

train_set <- sim_class2[sim_class2$train==1,-1]
set.seed(19180511)
fit_cv <- knn_cv(train_set,k.cv=10)
fit_cv

Chateau Latour Wine Data

Description

The response variable is the quality of a vintage based on a scale of 1 to 5 over the years 1961 to 2004. The predictor is end of harvest, days between August 31st and the end of harvest for that year, and the factor of interest is whether or not it rained at harvest time.

Usage

data(latour)

Format

A data frame with 44 rows and 4 columns.

year

Year of harvest

quality

Rating on a scale of 1-5

end.of.harvest

Days August 31 and the end of harvest

rain

indicator variable for rain

References

Sheather, SJ (2009), A Modern Approach to Regression with R, New York: Springer.

Examples

data(latour)
plot(quality~end.of.harvest,pch='',data=latour)
points(quality~end.of.harvest,data=latour[latour$rain==0,],pch=3)
points(quality~end.of.harvest,data=latour[latour$rain==1,],pch=4)

Mood Median Confidence Interval

Description

Mood's classical nonparametric method for calculating a difference in population medians.

Usage

mood.ci(x, y, var.equal = FALSE, conf.level = 0.95, ...)

Arguments

Value

A vector of length 2 containing the lower and upper endpoints of the confidence interval.

Author(s)

John Kloke, Joseph McKean

References

Hollander, M. and Wolfe, D.A. (1999), Nonparametric Statistical Methods, New York: Wiley.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall.

See Also

hl.ci,wilcox.test

Examples

x <- rt(101,9)
y <- rt(108,9)+0.3
mood.ci(x,y)

Robust Analysis of Covariance under Heterogeneous Slopes

Description

Returns tests for homogeneous slopes and also assuming homogeneous slopes a test for differences in level. Currently only wilcoxon scores are used.

Usage

onecova(levs,data,xcov,print.table=TRUE)

Arguments

Details

Returns the analysis of covariance table.

Value

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Examples

data=latour[,c('quality','rain')]
xcov<-cbind(latour['end.of.harvest'])
onecova(2,data,xcov,print.table=TRUE)

Robust Analysis of Covariance under Heterogeneous Slopes

Description

Returns a robust rank-based analysis of covariance for a one-way layout assuming heterogenous slopes; see Section 5.4 of Kloke and McKean (2014)/Sections 5.6 and 7.3 of Kloke and McKean (2024). Currently only wilcoxon scores are used.

Usage

onecovaheter(levs,data,xcov,print.table=TRUE)

Arguments

Details

Returns the analysis of covariance table assuming heterogenous slopes.

Value

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

data=latour[,c('quality','rain')]
xcov<-cbind(latour['end.of.harvest'])
onecovaheter(2,data,xcov,print.table=TRUE)

Robust Analysis of Covariance under Heterogeneous Slopes

Description

Returns a robust rank-based analysis of covariance for a one-way layout assuming homogeneous slopes; see Section 5.4 of Kloke and McKean (2014)/Sections 5.6 and 7.3 of Kloke and McKean (2024). Currently only wilcoxon scores are used.

Usage

onecovahomog(levs,data,xcov,print.table=TRUE)

Arguments

Details

Returns the analysis of covariance table assuming homogeneous slopes.

Value

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

data=latour[,c('quality','rain')]
xcov<-cbind(latour['end.of.harvest'])
onecovahomog(2,data,xcov,print.table=TRUE)

Placements.

Description

Returns the placements of the first vector in terms of the second vector used the R function fp.test; see Section 2.11 of Hettmansperger and McKean (2011) and Section 4.4 of Hollander and Wolfe (1999). The version computed by fp.test is discussed in Section 3.4 of Kloke and McKean (2014)/Section 3.6 of Kloke and McKean (2024).

Usage

place(x,y)

Arguments

Details

Returns the Placements for the routine fp.test.

Value

Author(s)

John Kloke, Joseph McKean

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Hollander, M. and Wolfe, D.~A. (1999), Nonparametric statistical methods, 2nd Edition, New York: John Wiley and Sons.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Plank data

Description

Abebe et al. (2001) discuss a dataset resulting from a three-way layout for a neurological experiment in which the time required for a mouse to exit a narrow elevated wooden plank is measured. The response is the log of time (in seconds) to exit. Interest lies in assessing the effects of three factors: the Mouse Strain (Tg+, Tg-), the mouse's Gender (female, male), and the mouse's Age (Aged, Middle, Young). The design is a 2 by 2 by 3 factorial design.

Usage

data(plank)

Format

A data frame with 64 observations on the following 4 variables.

response

a numeric vector

strain

a factor with levels 1 2

gender

a factor with levels 1 2

age

a factor with levels 1 2 3

References

Abebe, A., Crimin, K., McKean, J. W., Vidmar, T. J., and Haas, J. V. (2001) “Rank-Based Procedures for Linear Models: Applications to Pharmaceutical Science Data" Drug Information Journal,

Examples

data(plank)
boxplot(response~strain,data=plank)
raov(response~strain:gender:age,data=plank)

plot function for knn_cv

Description

plots the misclassification error rate versus number of neighbors based on call to knn_cv

Usage

## S3 method for class 'knn_cv'
plot(x, ...)

Arguments

Details

The list x is assumed to have attributes kvec and error representing the number of neighbors and the corresponding misclassification rate, respectively.

Value

No return value, called for side effects of creating plot.

Author(s)

John Kloke

References

Hastie, T., Tibshiani, R., and Friedman, J. (2017), The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, New York: Springer.

James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013), An Introduction to Statistical Learning with Applications in R, New York: Springer.

Venables, W. N. and Ripley, B. D. (2002) _Modern Applied Statistics with S._ Fourth edition. Springer.

See Also

knn_cv

A Simulated Polynomial Data Set.

Description

A simulated polynomial (3rd degree) model discussed in Section 4.7.1 of Kloke and McKean (2014)/4.6.1 of Kloke and McKean (2024).

Usage

data(poly)

Format

One-hundred observations on two variables.

y

response variable

x

predictor

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

plot(y ~ x,data=poly)

Degree of Polynomial Determination

Description

Tests for the degree of a polnomial. This test was suggested by Graybill (1976) and is discussed from a robust point-of-view in Section 4.7.1. of Kloke and McKean (2014)/4.6.1 of Kloke and McKean (2024).

Usage

polydeg(y, x, P, alpha = 0.05) 

Arguments

Details

Returns the degree of the polynomial based on the algorithm.

Value

References

Graybill, F.A. (1976), Theory and application of the linear model, North Scituate, Ma: Duxbury Press.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

 x <- 1:20
 xc <- x - mean(x)
 y<- .2*xc + xc^3 +rt(20,3)*90
 plot(y~x)
 polydeg(y,xc,6)

Internal print functions

Description

Internal print functions

Usage

## S3 method for class 'hogg.test'
print(x, digits = max(5, .Options$digits - 2), ...)
## S3 method for class 'rank.test'
print(x,...)
## S3 method for class 'fkk.test'
print(x,...)
## S3 method for class 'knn_cv'
print(x,...)
## S3 method for class 'npsm.ci'
print(x, estimate=FALSE,stderr=FALSE,digits = max(5, .Options$digits - 2),...)

Arguments

Value

No return value, called for side effects

Author(s)

John Kloke, Joseph McKean

DES for treatment of prostate cancer.

Description

Under investigation in this clinical trial was the pharmaceutical agent diethylstilbestrol DES; subjects were assigned treatment to 1.0 mg DES (treatment = 2) or to placebo (treatment = 1).

Usage

data(prostate)

Format

A data frame with 38 observations on the following 8 variables.

patient

a numeric vector

treatment

a numeric vector

time

a numeric vector

status

a numeric vector

age

a numeric vector

shb

a numeric vector

size

a numeric vector

index

a numeric vector

Source

http://www.crcpress.com/product/isbn/9781584883258

References

Collett, D. (2003) Modeling survival data in medical research CRC press.

Examples

data(prostate)
boxplot(size~treatment,data=prostate)

qhic

Description

A regression example with response yearly upkeep of a home and the predictor value of home; see Bowerman et al. (2005) and Exercise 4.9.8 of Kloke and McKean (2014)/Exercise 7.6.2 of Kloke and McKean (2024).

Usage

data(qhic)

Format

Forty observations on two variables.

upkeep

annual upkeep expenditure of home (y)

value

value of the home (x)

References

Bowerman, B.L., O'Connell, R.T., and Koehler, A.B. (2005), Forecasting, time series, and regression: An applied approach, Australia: Thomson.

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

plot(upkeep~value,data=qhic,xlab='Value (in $1000s)',ylab='Annual upkeep (in $10s)')

Quail from a two-factor experiment.

Description

Two sample quail data.

Usage

data(quail2)

Format

A data frame with 30 observations on the following 2 variables.

treat

indicator variable for treatment

ldl

ldl measurement

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

McKean J.W., Vidmar, T.J., and Sievers, G.L. (1989), A robust two stage multiple comparison procedure with application to a random drug screen, Biometrics, 45, 1281–1297.

Examples

data(quail2)
boxplot(ldl~treat,data=quail2)

General scores rank test for two sample problem

Description

A generalization of the Wilcoxon rank-sum test where a score function is applied to the ranks. Any scores from Rfit can be used as well as user defined. Default is to perform a Wilcoxon analysis.

Usage

rank.test(x, y, alternative = "two.sided", scores = Rfit::wscores, 
  conf.int = FALSE, conf.level = 0.95)

Arguments

Details

Test is based on T = sum_i a(R(y_i)) where R is the rank based on the combined sample and a(t) = varphi(t/(N+1)). Confidence interval, if requested, is based on call to Rfit.

Value

Author(s)

John Kloke, Joseph McKean

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

See Also

wilcox.test

Examples

rank.test(rt(20,1),rt(22,1)+0.2)

random contaminated normal deviates

Description

Generate a random sample from a contaminated normal distribution.

Usage

rcn(n, eps, sigmac)
rcn_5_5(n)

Arguments

Details

With probability (1-eps) a deviates are drawn from a standard normal distribution. With probability eps deviates are drawn from a normal distribution with mean 0 and standard devation sigmac rcn_5_5 is a special case where eps=0.05 and sigma=5.

Value

n x 1 numeric vector containing the random deviates.

Author(s)

John Kloke, Joseph McKean

References

Hogg, R. McKean, J, Craig, A (2013) Introduction to Mathematical Statistics, 7th Ed. Boston: Pearson.

See Also

rnorm

Examples

qqnorm(rcn(100,.25,10))

set.seed(101); rcn(10,0.05,5)
set.seed(101); rcn_5_5(10)

Fat-Finger Error Contaminated Normal Deviates

Description

Generate random data from a contaminated normal distribution where the contaimation is a multiplicative factor. As, for example, in cases of data recorded in incorrect units or incorrect decimal point.

Usage

rcnx100(n,eps=0.001,x=100,mu=0,sigma=1,...)
rcnx(...)
rcnx_01_100(n)

Arguments

Details

Samples are drawn from a random normal distribution with mean mu and standard deviations. A fraction of the observations (eps) are multiplied by the factor x. rcnx is an alias for rcnx100. rcnx_01_100 is a special case where the observations are drawn from a standard normal distribution (i.e., mu=0 and sigma=1 — the defaults in rcnx100) and eps and x are specified as 0.01 and 100, respectively.

Value

Numeric vector of length n is returned.

Author(s)

John Kloke

References

https://en.wikipedia.org/wiki/Fat-finger_error

See Also

rcn

Examples

set.seed(101); x1 <- rcnx100(10)
set.seed(101); x2 <- rcnx(10)
set.seed(101); x3 <- rcnx_01_100(10)

qqnorm(rcnx(10000,eps=0.005,x=10))
qqnorm(rcnx(1000,eps=0.05,x=1/100))

Random Laplace.

Description

Random generation for the Laplace (double exponential) data with location 0 and scale 1.

Usage

rlaplace(n)

Arguments

Details

A Laplace or double expoential distribution has heavier tails than a normal distribution and so a sample will tend to have additional outliers.

Value

A vector of length n is returned containing the random data.

Author(s)

John Kloke, Joseph McKean

References

Hogg, Robert V.; McKean, Joseph; and Craig, Allen T., "Introduction to Mathematical Statistics (6th Edition)" (2005).

Examples

x <- rlaplace(100)
qqnorm(x)

Simulated Regression Model

Description

A simulated regression model with one response and one predictor. It is discussed in Exercise 6.5.6 of Kloke and McKean (2014)/Exercise 8.11.23 of Kloke and McKean (2024).

Usage

data(rs)

Format

Fifty observations on two variables.

y

simulated response

x

simulated predictor

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

rfit(y ~ x,data=rs)

Seinfeld — the sitcom — viewership counts by episode

Description

Counts of viewers for 9 seasons of Seinfeld

Usage

data("seinfeld")

Format

A data frame with 180 observations on the following 4 variables.

episodeNumberOverall

a numeric vector

season

a numeric vector

episodeNumberSeason

a numeric vector

viewers

a numeric vector

Source

Wikipedia https://en.wikipedia.org/wiki/List_of_Seinfeld_episodes (date unknown).

Examples

data(seinfeld)
#Comparison boxplots of views versus season
boxplot(viewers~season,data=seinfeld,ylab='Number of Viewers (in millions)',xlab='Season')

# Normal q-q plots for selected seasons.
oldpar_mfrow <- par()$mfrow
par(mfrow=c(2,2))
seasons2display <- c(4,5,6,9)
for( s in seasons2display) {
  v <- seinfeld[seinfeld$season==s,'viewers']
  qqnorm(v,main=paste("Season",s))
  abline(a=median(v),b=mad(v))
}
par(mfrow=oldpar_mfrow)

# Normal q-q plots for selected seasons
# using centered and scaled residuals.
oldpar_mfrow <- par()$mfrow
par(mfrow=c(2,2))
seasons2display <- c(4,5,6,9)
for( s in seasons2display) {
  v0 <- seinfeld[seinfeld$season==s,'viewers']
  v1 <- (v0 - median(v0))/mad(v0)
  qqnorm(v1,main=paste("Season",s))
  abline(a=0,b=1)
}
par(mfrow=oldpar_mfrow)

Doksum and Sievers rat data

Description

Doksum and Sievers (1976) describe an experiment involving the effect of ozone on weight gain of rats. The experimental group consisted of 22 rats which were placed in an ozone environment for seven days, while the control group contained 21 rats which were placed in an ozone-free environment for the same amount of time. The response was the weight gain in a rat over the time period.

Usage

data(sievers)

Format

A data frame with 45 observations on the following 2 variables.

group

indicator variable for treatment

weight.gain

response variable of weight gain

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Doksum, K. A. and Sievers, G. L. (1976), Plotting with confidence: Graphical comparisons of two populations, Biometrika, 63, 421-434.

Examples

data(sievers)
boxplot(weight.gain~group,data=sievers)

p-value for a one sample sign test

Description

p-value for a one sample sign test based on the binomial distribution.

Usage

signtest_pvalue(x, alternative = "two.sided", theta0 = 0, ...)

Arguments

Details

Returns p-value using the binomial distribution.

Value

a numeric scalar — the p-value — is returned

Author(s)

John Kloke, Joseph McKean

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall.

Examples

x <- round(rt(19,9) + 2,1)
signtest_pvalue(x,alternative='greater')
S <- sum(x > 0)
M <- sum(x != 0)
1-pbinom(S-1,M,0.5)
x <- round(rt(19,9) + 0,1)
signtest_pvalue(x)
S <- sum(x > 0)
M <- sum(x != 0)
2*min(pbinom(S,M,0.5), 1-pbinom(S-1,M,0.5))

A simulated classification example with two variables and two classes (labels).

Description

A simulated classification example with two variables and two classes (labels).

Usage

data("sim_class2")

Format

A data frame with 1000 observations on the following 4 variables.

train

an indicator for training and test sets

x1

an explantory variable

x2

an explantory variable

y

response variable - a factor with levels 0 1

Details

Random points in the x1,x2 plane were generated. Class labels based on location relative to two circles in the x1,x2 plane with some random variation in the labels simulated.

Examples

data(sim_class2)
dim(sim_class2)

train_set <- sim_class2[sim_class2$train==1,]
dim(train_set)

with(train_set,plot(x1,x2,main='Training Set',cex=0.625))
with(train_set,points(x1,x2,main='Training Set',pch=20,col=y,cex=0.625))

Simon (the memory game) dataset

Description

An experiment in which the members of two groups of students each played the game Simon twice.

Usage

data("simon")

Format

A data frame with 31 observations on the following 3 variables.

game1

score on first trial

game2

score on second trial

class

group variable

Details

Demonstrates the concept of regression toward the mean. Simulated data to represent a realistic realization of the experiment. See Problem 4.9.20 of Kloke and McKean (2014)/Problem 4.7.17 of Kloke and McKean (2024).

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistcal methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

data(simon)
plot(game2~game1,data=simon)
rfit(game2~game1,data=simon)

Sine Cosine Model

Description

Simulated dataset

Usage

data("sincos")

Format

A data frame with 197 observations on the following 2 variables.

x

independent variable

y

dependent variable

Details

The data were generated using x <- seq(1,50,by=.25) ; y <- 5*sin(3*x) + 6*cos(x/4)+rnorm(length(x),0,10)

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall.

Examples

data(sincos)
plot(y~x,sincos)

### code to create Figure 4.9 of Kloke & McKean 2014 ###
my.sincos<-sincos
my.sincos$y3<-my.sincos$y
my.sincos$y3[137] <- 800

plot(y3~x,ylim=c(-50,50),data=my.sincos)
fit4 <- loess(y3 ~ x,data=my.sincos)
# lines(fit4$x,fit4$fitted,lty=2)
with(fit4,lines(x,fitted,lty=2))
fit5 <- loess(y3 ~ x,family="symmetric",data=my.sincos)
with(fit5,lines(x,fitted,lty=1))
legend('bottomleft',legend=c('Local Robust Fit','Local LS Fit'),lty=1:2)
title("loess Fits of Sine-Cosine Data")

Predict top speed based on miles per gallon

Description

A sample of 82 cars with variables speed and miles per gallon collected.

Usage

data("speed")

Format

A data frame with 82 observations on the following 2 variables.

mpg

Miles per gallon

sp

a numeric vector

Source

Higgins (2003) Introduction to modern nonparmetric statistics.

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistcal methods using R, Boca Raton, FL: Chapman-Hall.

Examples

data(speed)
plot(sp~mpg,data=speed)
rfit(sp~mpg+I(mpg^2),data=speed)

Turtle Data

Description

A data frame containg measurements of 48 turtles. The first three columns are the Length, Width, and Height measurements of the carapace of the turtle. The fourth column is a categorical variable sex with values of female and male. Data are drawn from Johnson and Wichern (2007).

Usage

data(turtle)

Format

48 observations on four variables.

Length

numeric vector.

Width

numeric vector.

Height

numeric vector.

sex

character vector.

References

Johnson, R.A. and Wichern, D.W. (2007), Applied Multivariate Statistical Analysis, 6th ed., Upper Saddle River, NJ: Pearson.

Examples

with(turtle,boxplot(Length~sex))
with(turtle,boxplot(Length~sex,ylab='Length (units)'))

vanElteren test for stratified analysis

Description

Performs the vanElteren extension of the Wilcoxon rank sum test for stratified experiments.

Usage

vanElteren.test(g, y, b)

Arguments

Value

January Weather Data for Kalamazoo

Description

January weather data for Kalamazoo, MI for the years 1900 to 1995. It is discussed in Example 4.7.4, page 105-106, of Kloke and McKean (2014)/Example 4.6.4, p.177-178, of Kloke and McKean (2024).

Usage

data(weather)

Format

Ninety-six observations (1900-1995) for twelve weather variables.

avemax

avemax

avemin

avemin

coldestmax

coldestmax

hihest

hihest

lowest

lowest

maxdayprec

maxdayprec

maxdaysnowfall

maxdaysnowfall

meantmp

meantmp

totalprec

totalprec

totalsnow

totalsnow

warmest

warmest

year

year

Source

http://weather-warehouse.com/WeatherHistory/

References

Kloke, J. and McKean, J.W. (2014), Nonparametric statistical methods using R, Boca Raton, FL: Chapman-Hall. Kloke, J. and McKean, J.W. (2024), Nonparametric statistical methods using R, Second Edition, Boca Raton, FL: Chapman-Hall.

Examples

plot(avemax ~ year,data=weather)

Wilson (score) confidence interval for a population proportion.

Description

Wilson (score) confidence interval for a population proportion.

Usage

wilson.ci(x, n, conf.level = 0.95)

Arguments

Details

Uses defintion in Agresti.

Value

Author(s)

John Kloke, Joseph McKean

References

Agresti (2002), Categorical data analysis, New York: John Wiley & Sons, Inc.

See Also

prop.test

Examples

n <- 100
x <- rbinom(1,n,0.33)
wilson.ci(n,x)