Paired Data Analysis

Description

Many datasets and a set of graphics (based on ggplot2), statistics, effect sizes and hypothesis tests are provided for analysing paired data with S4 class.

Details

The DESCRIPTION file:

Index of help topics:

Anorexia                Anorexia data from Pruzek & Helmreich (2009)
Barley                  Barley data from Preece (1982, Table 1)
Blink                   Blink data from Preece (1982, Table 2)
Blink2                  Blink data (2nd example) from Preece (1982,
                        Table 3)
BloodLead               Blood lead levels data from Pruzek & Helmreich
                        (2009)
ChickWeight             Chick weight data from Preece (1982, Table 11)
Corn                    Corn data (Darwin)
Datalcoholic            Datalcoholic: a dataset of paired datasets
GDO                     Agreement study
Grain                   Grain data from Preece (1982, Table 5)
Grain2                  Wheat grain data from Preece (1982, Table 12)
GrapeFruit              Grape Fruit data from Preece (1982, Table 6)
HorseBeginners          Actual and imaginary performances in equitation
IceSkating              Ice skating speed study
Iron                    Iron data from Preece (1982, Table 10)
Meat                    Meat data from Preece (1982, Table 4)
PairedData-package      Paired Data Analysis
PrisonStress            Stress in prison
Rugby                   Agreement study in rugby expert ratings
Sewage                  Chlorinating sewage data from Preece (1982,
                        Table 9)
Shoulder                Shoulder flexibility in swimmers
SkiExperts              Actual and imaginary performances in ski
Sleep                   Sleep hours data from Preece (1982, Table 16)
Tobacco                 Tobacco data from Snedecor and Cochran (1967)
Var.test                Tests of variance(s) for normal distribution(s)
anscombe2               Teaching the paired t test
bonettseier.Var.test    Bonett-Seier test of scale for paired samples
effect.size             Effect size computations for paired data
grambsch.Var.test       Grambsch test of scale for paired samples
imam.Var.test           Imam test of scale for paired samples
lambda.table            Parameters for Generalised Lambda Distributions
levene.Var.test         Levene test of scale for paired samples
mcculloch.Var.test      McCulloch test of scale for paired samples
paired                  Paired
paired-class            Class '"paired"'
paired.plotBA           Bland-Altman plot
paired.plotCor          Paired correlation plot
paired.plotMcNeil       Parallel lines plot
paired.plotProfiles     Profile plot
plot.paired             ~~ Methods for Function 'plot' ~~
rpaired.contaminated    Simulate paired samples
rpaired.gld             Simulate paired samples
sandvikolsson.Var.test
                        Sandvik-Olsson test of scale for paired samples
slidingchart            Sliding square plot
summary                 Summary statistics for paired samples
t.test                  Student's test test for paired data
wilcox.test             Wilcoxon's signed rank test for paired data
winsor.cor.test         Winsorized correlation test (for paired data)
yuen.t.test             Yuen's trimmed mean test

Author(s)

Stephane Champely <champely@univ-lyon1.fr>

Maintainer: Stephane Champely <champely@univ-lyon1.fr>

Anorexia data from Pruzek & Helmreich (2009)

Description

This dataset presents 17 paired data corresponding to the weights of girls before and after treatment for anorexia. A more complete version can be found in the package MASS. There is actually a cluster of four points in this dataset.

Usage

data(Anorexia)

Format

A dataframe with 17 rows and 2 numeric columns:

Source

Hand, D.J., McConway, K., Lunn, D. & Ostrowki, editors (1993) A Handbook of Small Data Sets. Number 232, 285. Chapman & Hall: New-York.

References

Pruzek & Helmreich (2009) Enhancing dependent sample analysis with graphics. Journal of Statistics Education, 17 (1).

See Also

anorexia in MASS

Examples

data(Anorexia)

# Visualization of the cluster
with(Anorexia,plot(paired(Prior,Post),type="profile"))

# The effects of trimming or winsorizing 
# with 4 outliers (n=17)
17*0.2
with(Anorexia,summary(paired(Prior,Post)))
17*0.25
with(Anorexia,summary(paired(Prior,Post),tr=0.25))

Barley data from Preece (1982, Table 1)

Description

This dataset presents 12 paired data corresponding to the yields of Glabron and Velvet Barley, grown on different farms. The values from farm 12 are quite different.

Usage

data(Barley)

Format

A dataframe with 17 rows and 3 columns:

Source

Leonard, W.H. & Clark, A.G. (1939) Field Plot Techniques. Burgess: Minneapolis.

References

Preece D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Barley)

# Visualizing a clear outlier
with(Barley,plot(paired(Glabron,Velvet),type="BA"))

# Results form the paired t test and paired Yuen test are similar
with(Barley,t.test(paired(Glabron,Velvet)))
with(Barley,yuen.t.test(paired(Glabron,Velvet)))

# Nevertheless the outlier inflates the location (numerator) and
# scale (denominator) standard statictics for the difference
with(Barley,summary(paired(Glabron,Velvet)))

Blink data from Preece (1982, Table 2)

Description

This dataset presents paired data corresponding to average blink-rate per minute of 12 subjects in an experiment of a visual motor task. They had to steer a pencil along a moving track. Each subject was tested under two conditions : a straight track and an oscillating one. Note that the values from subjects 1 and 2 are somewhat different.

Usage

data(Blink)

Format

A dataframe with 12 rows and 3 columns:

Source

Wetherhill, G.B. (1972) Elementary Statistical Methods, 2nd ed Chapman and Hall: London.

References

Preece D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Blink)

# Visualizing two "outliers"
with(Blink,plot(paired(Straight,Oscillating),type="profile"))

# Interestingly, the differences for the two outliers are quite "normal"
# so their influence on the t test is negligible
with(Blink,qqnorm(Straight-Oscillating))
with(Blink,qqline(Straight-Oscillating))

Blink data (2nd example) from Preece (1982, Table 3)

Description

This dataset presents paired data corresponding to average blink-rate per minute of 12 subjects in an experiment of a visual motor task. They had to steer a pencil along a moving track. Each subject was tested under two conditions : a straight track and an oscillating one. Data about blink-rate during a pre-experimental resting are also available. Subjects 1 and 2 then appear less extreme than in the dataset Blink.

Usage

data(Blink2)

Format

A dataframe with 12 rows and 4 columns:

Source

Drew, G.C. (1951) Variations in blink-rate during visual-motor tasks. Quarterly Journal of Experimental Psychology, 3, 73-88.

References

Preece D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

See Also

Blink

Blood lead levels data from Pruzek & Helmreich (2009)

Description

This dataset presents matched paired data corresponding to blood lead levels for 33 children of parents who had worked in a lead related factory and 33 control children from their neighborhood. The two samples have different dispersions and their correlation is small.

Usage

data(BloodLead)

Format

A dataframe with 33 rows and 3 columns:

Source

Morton, D., Saah, A., Silberg, S., Owens, W., Roberts, M. & Saah, M. (1982) Lead absorption in children of employees in a lead related industry. American Journal of Epimediology, 115, 549-55.

References

Pruzek, R.M. & Helmreich, J.E. (2009) Enhancing dependent sample analysis with graphics. Journal of Statistics Education, 17 (1).

Examples

data(BloodLead)

# Control values are clealy less dispersed (and inferior)
# than exposed levels
with(BloodLead,plot(paired(Control,Exposed),type="McNeil"))
with(BloodLead,Var.test(paired(Control,Exposed)))

with(BloodLead,grambsch.Var.test(paired(Control,Exposed)))
with(BloodLead,bonettseier.Var.test(paired(Control,Exposed)))

# Correlation is small (bad matching)
with(BloodLead,cor.test(Control,Exposed))
with(BloodLead,winsor.cor.test(Control,Exposed))

Chick weight data from Preece (1982, Table 11)

Description

This dataset presents 10 paired data corresponding to the weights of chicks, two from ten families, reared in confinement or on open range.

Usage

data(ChickWeight)

Format

A dataframe with 10 rows and 3 columns:

Source

Paterson, D.D. (1939) Statistical Techniques in Agricultural Research. McGrw-Hill: New-York.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(ChickWeight)

# Look at the interesting discussion in Preece (1982)
# about degree of precision and t test
with(ChickWeight,plot(paired(Confinement,OpenRange)))
with(ChickWeight,stem(Confinement-OpenRange,scale=2))

Corn data (Darwin)

Description

This dataset presents 15 paired data corresponding to the final height of corn data (Zea Mays), one produced by cross-fertilization and the other by self-fertilization. These data were used by Fisher (1936) and were published in Andrews and Herzberg (1985).

Usage

data(Corn)

Format

A dataframe with 15 rows and 4 columns:

Source

Darwin, C. (1876). The Effect of Cross- and Self-fertilization in the Vegetable Kingdom, 2nd Ed. London: John Murray.

References

• Andrews, D. and Herzberg, A. (1985) Data: a collection of problems from many fields for the student and research worker. New York: Springer.

• Fisher, R.A. (1936) The design of Experiments. Oliver & Boyd: London

Examples

data(Corn)

# Visualizing two outliers
with(Corn,slidingchart(paired(Crossed,Self)))

# Very bad matching in these data
with(Corn,cor.test(Crossed,Self))
with(Corn,winsor.cor.test(Crossed,Self))


# So the two-sample test is slightly 
# more interesting than the paired test
with(Corn,t.test(Crossed,Self,var.equal=TRUE))
with(Corn,t.test(Crossed,Self,paired=TRUE))

# The Pitman-Morgan test is influenced by the two outliers
with(Corn,Var.test(paired(Crossed,Self)))
with(Corn,grambsch.Var.test(paired(Crossed,Self)))
with(Corn,bonettseier.Var.test(paired(Crossed,Self)))

# Lastly, is there a pot effect?
with(Corn,plot(paired(Crossed,Self)))
with(Corn,plot(paired(Crossed,Self),group=pot))

Datalcoholic: a dataset of paired datasets

Description

This dataset presents for teaching purposes 50 paired datasets available in different R packages.

Usage

data(Datalcoholic)

Format

A dataframe with 4 columns.

Examples

data(Datalcoholic)
show(Datalcoholic)

Agreement study

Description

This dataset gives the same measurements of muscle activation (EMG) in 3 days corresponding to a reproductibility study for 18 tennis players.

Usage

data(GDO)

Format

A dataframe with 18 rows and 4 columns.

Source

Private communication. Samuel Rota, CRIS, Lyon 1 University, FRANCE

See Also

packages: agreement, irr and MethComp.

Examples

data(GDO)

# Building new vectors for performing
# a repeated measures ANOVA
# with a fixed Day effect
Activation<-c(GDO[,2],GDO[,3],GDO[,4])
Subject<-factor(rep(GDO[,1],3))
Day<-factor(rep(c("D1","D2","D3"),rep(18,3)))
aovGDO<-aov(Activation~Day+Error(Subject))
summary(aovGDO)

# Reliability measurement: SEM and ICC(3,1)
sqrt(12426)
72704/(72704+12426)

Grain data from Preece (1982, Table 5)

Description

This dataset presents 9 paired data corresponding to the grain yields of Great Northern and Big Four oats grown in "adjacent" plots.

Usage

data(Grain)

Format

A dataframe with 9 rows and 3 columns:

Source

LeClerg, E.L., Leonard, W.H. & Clark, A.G. (1962) Field Plot Technique. Burgess: Minneapolis.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Grain)

# Usual visualization for paired data (2 clusters?)
with(Grain, plot(paired(GreatNorthern,BigFour)))

# Are they actually "adjacent" plots? 
# Why this variable Year?
# Is there any time trend?
with(Grain, plot(Year,GreatNorthern,type="o"))
with(Grain, plot(Year,BigFour,type="o"))

Wheat grain data from Preece (1982, Table 12)

Description

This dataset presents 6 paired data corresponding to the grain yields of two wheat varieties grown on pairs of plots.

Usage

data(Grain2)

Format

A dataframe with 6 rows and 3 columns:

Source

Balaam, N.L. (1972) Fundamentals of Biometry. The Science of Biology Series (ed J.D. Carthy and J.F. Sutcliffe), No3, Allen and Unwin: London.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Grain2)

# A very small data set
print(Grain2)

# The paired t test is the test of the differences
with(Grain2,t.test(Variety_1,Variety_2,paired=TRUE))
with(Grain2,t.test(Variety_1-Variety_2))

# The data are actually rounded to the nearest integer
# So they can be somewhere between +0.5 or -0.5
# and thus the differences between +1 or -1
# The possible t values can be simulated by:
simulating.t<-numeric(1000)
for(i in 1:1000){
simulating.t[i]<-with(Grain2,t.test(Variety_1-Variety_2+runif(6,-1,1)))$stat
}
hist(simulating.t)
abline(v=with(Grain2,t.test(Variety_1-Variety_2))$stat,lty=2)

Grape Fruit data from Preece (1982, Table 6)

Description

This dataset presents paired data corresponding to the percentage of solids recorded in the shaded and exposed halves of 25 grapefruits.

Usage

data(GrapeFruit)

Format

A dataframe with 25 rows and 3 columns:

Source

Croxton, F.E. & Coxden, D.J. (1955) Applied Genral Statistics, 2nd ed. Chapman and Hall, London.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(GrapeFruit)

# Visualizing a very strange paired distribution
with(GrapeFruit,plot(paired(Shaded,Exposed)))
with(GrapeFruit,plot(paired(Shaded,Exposed),type="BA"))
with(GrapeFruit,plot(paired(Shaded,Exposed),type="McNeil"))
with(GrapeFruit,plot(paired(Shaded,Exposed),type="profile"))

# As underlined by Preece (1982), have a look to
# the distribution of the final digits
show(GrapeFruit)
table(round((GrapeFruit$Shaded*10-floor(GrapeFruit$Shaded*10))*10))
table(round((GrapeFruit$Exposed*10-floor(GrapeFruit$Exposed*10))*10))

Actual and imaginary performances in equitation

Description

This dataset gives the actual and motor imaginary performances (time) in horse-riding for 8 beginners.

Usage

data(HorseBeginners)

Format

A dataframe with 8 rows and 3 columns.

Source

Private communication. Aymeric Guillot, CRIS, Lyon 1 University, FRANCE.

References

Louis, M. Collet, C. Champely, S. and Guillot, A. (2010) Differences in motor imagery time when predicting task duration. Research Quarterly for Exercise and Sport.

Examples

data(HorseBeginners)

# There is one outlier
with(HorseBeginners,plot(paired(Actual,Imaginary),type="profile"))

# This outlier has a great influence
# on the non robust Pitman-Morgan test of variances
with(HorseBeginners,Var.test(paired(Actual,Imaginary)))
with(HorseBeginners[-1,],Var.test(paired(Actual,Imaginary)))
with(HorseBeginners,grambsch.Var.test(paired(Actual,Imaginary)))
with(HorseBeginners,bonettseier.Var.test(paired(Actual,Imaginary)))

Ice skating speed study

Description

This dataset gives the speed measurement (m/sec) for seven iceskating dancers using the return leg in flexion or in extension.

Usage

data(IceSkating)

Format

A dataframe with 7 rows and 3 columns.

Source

Private communication. Karine Monteil, CRIS, Lyon 1 University, FRANCE.

References

Haguenauer, M., Legreneur, P., Colloud, F. and Monteil, K.M. (2002) Characterisation of the Push-off in Ice Dancing: Influence of the Support Leg extension on Performance. Journal of Human Movement Studies, 43, 197-210.

Examples

data(IceSkating)

# Nothing particular in the paired plot
with(IceSkating,plot(paired(Extension,Flexion),type="McNeil"))

# The differences are normally distributed
with(IceSkating,qqnorm(Extension-Flexion))
with(IceSkating,qqline(Extension-Flexion))

# Usual t test
with(IceSkating,t.test(paired(Extension,Flexion)))

Iron data from Preece (1982, Table 10)

Description

This dataset presents 10 paired data corresponding to percentages of iron found in compounds with the help of two different methods (take a guess: A & B). It is quite intersting to study rounding effect on hypothesis test (have a look at the examples section).

Usage

data(Iron)

Format

A dataframe with 10 rows and 3 columns:

Source

Chatfield, C. (1978) Statistics for Technology: A Course in Applied Statistics, 2nd ed. Chapman and Hall: London.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Iron)

# Visualizing, very nice correlation
# Is this an agreement problem or a comparison problem?
with(Iron,plot(paired(Method_A,MethodB)))

# Significant... p=0.045
with(Iron,t.test(paired(Method_A,MethodB)))

# Looking at data, rounded at 0.1 so they can be +0.05 or -0.05
show(Iron)

# Thus the differences can be +0.1 or -0.1
# Influence of rounding on the t-statistic
with(Iron,t.test(Method_A-MethodB+0.1))
with(Iron,t.test(Method_A-MethodB-0.1))

Meat data from Preece (1982, Table 4)

Description

This dataset presents 20 paired data corresponding to the percentage of fat in samples of meat using two different methods: AOAC and Babcock.

Usage

data(Meat)

Format

A dataframe with 20 rows and 3 columns:

Source

Tippett, L.H.C. (1952) Technological Applications of Statistics. Williams and Norgate: London.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Meat)

# Presence of clusters or...
with(Meat,plot(paired(AOAC,Babcock)))

# group effect according to Meat type?
with(Meat,plot(paired(AOAC,Babcock),group=MeatType))
with(Meat,plot(paired(AOAC,Babcock),group=MeatType,facet=FALSE))

Internal PairedData objects

Description

Internal PairedData objects.

Details

These are not to be called by the user.

Stress in prison

Description

This dataset gives the PSS (stress measurement) for 26 people in prison at the entry and at the exit. Part of these people were physically trained during their imprisonment.

Usage

data(PrisonStress)

Format

A dataframe with 26 rows and 4 columns.

Source

Private communication. Charlotte Verdot, CRIS, Lyon 1 University, FRANCE

References

Verdot, C., Champely, S., Massarelli, R. and Clement, M. (2008) Physical activities in prison as a tool to ameliorate detainees mood and well-being. International Review on Sport and Violence, 2.

Examples

data(PrisonStress)

# The two groups are not randomized! 
# The control group is less stressed before the experiment
with(PrisonStress,boxplot(PSSbefore~Group,ylab="Stress at the eginning of the study"))

# But more stressed at the end!
with(PrisonStress,boxplot(PSSafter~Group,ylab="22 weeks later"))

# So the effects of physical training seems promising
with(PrisonStress,plot(paired(PSSbefore,PSSafter),groups=Group,type="BA",facet=FALSE))

# Testing using gain scores analysis
difference<-PrisonStress$PSSafter-PrisonStress$PSSbefore
t.test(difference~PrisonStress$Group,var.equal=TRUE)

# Testing using ANCOVA
lmJail<-lm(PSSafter~PSSbefore*Group,data=PrisonStress)
anova(lmJail)

# Testing using repeated measures ANOVA
PSS<-c(PrisonStress$PSSbefore,PrisonStress$PSSafter)
Time<-factor(rep(c("Before","After"),c(26,26)))
Subject<-rep(PrisonStress$Subject,2)
Condition<-rep(PrisonStress$Group,2)
aovJail<-aov(PSS~Condition*Time+Error(Subject))
summary(aovJail)

Agreement study in rugby expert ratings

Description

This dataset gives the ratings on a continuous ten-points scale of two experts about 93 actions during several rugby union matches.

Usage

data(Rugby)

Format

A dataframe with 93 rows and 3 columns.

Source

Private communication. Mickael Campo, CRIS, Lyon 1 University, FRANCE.

Examples

data(Rugby)
with(Rugby,plot(paired(EXPERT.1,EXPERT.2)))
with(Rugby,plot(paired(EXPERT.1,EXPERT.2),type="BA"))

Chlorinating sewage data from Preece (1982, Table 9)

Description

This dataset presents 8 paired data corresponding to log coliform densities per ml for 2 sewage chlorination methods on each of 8 days.

Usage

data(Sewage)

Format

A dataframe with 8 rows and 3 columns:

Source

Wetherill, G.B. (1972) Elementary Statistical Methods, 2nd ed. Chapman and Hall: London.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Sewage)

# Visualising
with(Sewage,plot(paired(Method_A,Method_B),type="profile"))

# Basic paired t-test
with(Sewage,t.test(paired(Method_A,Method_B)))

# Influence of the 0.1 rounding on the t-test
 with(Sewage,t.test(Method_A-Method_B-0.1))
 with(Sewage,t.test(Method_A-Method_B+0.1))

Shoulder flexibility in swimmers

Description

This dataset gives the flexibility for the right and left shoulders in 15 swimmers and 15 sedentary people.

Usage

data(Shoulder)

Format

A dataframe with 30 rows and 4 columns.

Source

Private communication. Karine Monteil, CRIS, Lyon 1 University, FRANCE.

References

Monteil, K., Taiar, R., Champely, S. and Martin, J. (2002) Competitive swimmers versus sedentary people: a predictive model based upon normal shoulders flexibility. Journal of Human Movement Studies, 43 , 17-34.

Examples

data(Shoulder)

# Is there some heteroscedasticity?
with(Shoulder,plot(paired(Left,Right)))

# Swimmers are indeed quite different
with(Shoulder,plot(paired(Right,Left),groups=Group))

# A first derived variable to compare the amplitude in flexibilty
with(Shoulder,boxplot(((Left+Right)/2)~Group,ylab="mean shoulder flexibility"))

# A second derived variable to study shoulder asymmetry
with(Shoulder,boxplot((abs(Left-Right))~Group,ylab="asymmetry in shoulder flexibility"))

Actual and imaginary performances in ski

Description

This dataset gives the actual and motor imaginary performances (time) in ski for 12 experts.

Usage

data(SkiExperts)

Format

A dataframe with 12 rows and 3 columns.

Source

Private communication. Aymeric Guillot, CRIS, Lyon 1 University, FRANCE.

References

Louis, M., Collet, C., Champely, S. and Guillot, A. (2012) Differences in motor imagery time when predicting task duration in Alpine skiers and equestrian riders. Research Quarterly for Exercise and Sport, 83(1), 86-93.

Examples

data(SkiExperts)

# Visualising
with(SkiExperts,plot(paired(Actual,Imaginary),type="profile"))

# No underestimation of imaginary time for experts
with(SkiExperts,t.test(paired(Actual,Imaginary)))

# But a very interesting increase in dispersion in their
# predicted times
with(SkiExperts,Var.test(paired(Actual,Imaginary)))

Sleep hours data from Preece (1982, Table 16)

Description

This dataset presents paired data corresponding to the sleep hours gained by 10 patients (these are differences indeed) using two isomers (Dextro- and Laevo-). These data from Student were studied by Fischer (1925). Read the paper of Preece (1982, section 9) for a complete understanding of this quite complex situation.

Usage

data(Sleep)

Format

A dataframe with 10 rows and 2 columns:

Source

Fisher, R.A. (1925) Statistical Metods for Research Workers. Oliver and Boyd: Edinburgh.

References

Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Tobacco data from Snedecor and Cochran (1967)

Description

This dataset presents 8 paired data corresponding to numbers of lesions caused by two virus preparations inoculated into the two halves of each tobacco leaves.

Usage

data(Tobacco)

Format

A dataframe with 8 rows and 3 columns:

Source

Snedecor, G.W. and Cochran, W.G. (1967) Statistical Methods, 6th ed. Iowa State University Press: Ames.

References

• Pruzek, R.M. & Helmreich, J.E. (2009) Enhancing dependent sample analysis with graphics. Journal of Statistics Education, 17 (1).

• Preece, D.A. (1982) t is for trouble (and textbooks): a critique of some examples of the paired-samples t-test. The Statistician, 31 (2), 169-195.

Examples

data(Tobacco)

# A clear outlier
with(Tobacco,plot(paired(Preparation_1,Preparation_2)))


# Comparison of normal and robust tests
with(Tobacco,t.test(paired(Preparation_1,Preparation_2)))
with(Tobacco,yuen.t.test(paired(Preparation_1,Preparation_2)))

with(Tobacco,Var.test(paired(Preparation_1,Preparation_2)))
with(Tobacco,grambsch.Var.test(paired(Preparation_1,Preparation_2)))

with(Tobacco,cor.test(Preparation_1,Preparation_2))
with(Tobacco,winsor.cor.test(Preparation_1,Preparation_2))

# Maybe a transformation
require(MASS)
with(Tobacco,eqscplot(log(Preparation_1),log(Preparation_2)))
abline(0,1,col="red")

Tests of variance(s) for normal distribution(s)

Description

Classical tests of variance for one-sample, two-independent samples or paired samples.

Usage

## Default S3 method:
Var.test(x, y = NULL, ratio = 1, alternative = c("two.sided", 
    "less", "greater"), paired = FALSE, conf.level = 0.95, ...)

## S3 method for class 'paired'
Var.test(x, ...)

## Default S3 method:
pitman.morgan.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), 
    ratio = 1, conf.level = 0.95,...)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Stephane CHAMPELY

References

• Morgan, W.A. (1939) A test for the significance of the difference between two variances in a sample from a normal bivariate distribution. Biometrika, 31, 13-19.

• Pitman, E.J.G. (1939) A note on normal correlation. Biometrika, 31, 9-12.

See Also

bonettseier.Var.test, grambsch.Var.test

Examples

data(HorseBeginners)

#one sample test
Var.test(HorseBeginners$Actual,ratio=15)

# two independent samples test
Var.test(HorseBeginners$Actual,HorseBeginners$Imaginary)

# two dependent samples test
Var.test(HorseBeginners$Actual,HorseBeginners$Imaginary,paired=TRUE)
p<-with(HorseBeginners,paired(Actual,Imaginary))
Var.test(p)

Teaching the paired t test

Description

This dataset presents four sets of paired samples (n=15), giving the same t statistic (t=2.11) and thus the same p-value whereas their situations are really diversified (differences in variances, clustering, heteroscedasticity). The importance of plotting data is thus stressed. The name is given from the famous Anscombe's dataset created to study simple linear regression.

Usage

data(anscombe2)

Format

A dataframe with 15 rows, 8 numeric columns of paired data: (X1,Y1) ; (X2,Y2) ; (X3,Y3) ; (X4,Y4), and 1 factor column: Subjects, giving a label for the subjects.

Source

S. Champely, CRIS, Lyon 1 University, FRANCE

References

F. Anscombe, Graphs in statistical analysis. The American Statistican, 27, 17-21.

Examples

data(anscombe2)
# p=0.05 for the paired t-test
with(anscombe2,plot(paired(X1,Y1),type="BA"))
with(anscombe2,t.test(paired(X1,Y1)))

# Same p but Var(X2)<Var(Y2) and
# correlation in the Bland-Altman plot
with(anscombe2,t.test(paired(X2,Y2)))
with(anscombe2,summary(paired(X2,Y2)))
with(anscombe2,plot(paired(X2,Y2),type="BA"))

# Same p but two clusters
with(anscombe2,plot(paired(X3,Y3),type="BA"))

# Same p but the difference is "linked" to the mean
with(anscombe2,plot(paired(X4,Y4),type="BA"))

Bonett-Seier test of scale for paired samples

Description

Robust test of scale for paired samples based on the mean absolute deviations.

Usage

bonettseier.Var.test(x, ...)

## Default S3 method:
bonettseier.Var.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), 
omega = 1, conf.level = 0.95,...)

## S3 method for class 'paired'
bonettseier.Var.test(x, ...)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Stephane CHAMPELY

References

Bonett, D.G. and Seier E. (2003) Statistical inference for a ratio of dispersions using paired samples. Journal of Educational and Behavioral Statistics, 28, 21-30.

See Also

Var.test, grambsch.Var.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
bonettseier.Var.test(x,y)

data(anscombe2)
p<-with(anscombe2,paired(X1,Y1))
bonettseier.Var.test(p)

Effect size computations for paired data

Description

Robust and classical effects sizes for paired samples of the form: (Mx-My)/S where Mx and My are location parameters for each sample and S is a scale parameter

Usage

## S4 method for signature 'paired'
effect.size(object,tr=0.2)

Arguments

Value

A table with two rows corresponding to classical (means) and robust (trimmed means, tr=0.2) delta-type effect sizes. The four columns correspond to:

Author(s)

Stephane CHAMPELY

References

Algina, J., Keselman, H.J. and Penfield, R.D. (2005) Effects sizes and their intervals: the two-level repeated measures case. Educational and Psychological Measurement, 65, 241-258.

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-rnorm(20)+z+1
p<-paired(x,y)
effect.size(p)

Grambsch test of scale for paired samples

Description

Robust test of scale for paired samples.

Usage

grambsch.Var.test(x, ...)

## Default S3 method:
grambsch.Var.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),...)

## S3 method for class 'paired'
grambsch.Var.test(x, ...)

Arguments

Details

Denoting s=x+y and d=x-y, the test proposed by Grambsch (1994, and called by the author 'modified Pitman test') is based on the fact that var(x)-var(y)=cov(x+y,x-y)=cov(s,d). The values z=(s-mean(s))(d-mean(d)) can be tested for null expectation using a classical t test in order to compare the two variances. Note that the p value is computed using the normal distribution.

Value

A list with class "htest" containing the following components:

Author(s)

Stephane CHAMPELY

References

Grambsch,P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.

See Also

Var.test, bonettseier.Var.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
grambsch.Var.test(x,y)

p<-paired(x,y)
grambsch.Var.test(p)

Imam test of scale for paired samples

Description

Robust test of scale for paired samples based on absolute deviations from the trimmed means (or medians), called Imam test in Wilcox (1989).

Usage

imam.Var.test(x, ...)

## Default S3 method:
imam.Var.test(x, y = NULL,
       alternative = c("two.sided", "less", "greater"),
       mu = 0,conf.level = 0.95,location=c("trim","median"),
tr=0.1,  ...)


## S3 method for class 'paired'
imam.Var.test(x, ...)

Arguments

Details

The data are transformed as deviations from the trimmed mean: X=abs(x-mean(x,tr=0.1)) and Y=(y-mean(y,tr=0.1)). A paired t test is then carried out on the (global) ranks of X and Y.

Value

A list with class "htest" containing the components of a paired t test.

Author(s)

Stephane CHAMPELY

References

• Wilcox, R.R. (1989) Comparing the variances of dependent groups. Psychometrika, 54, 305-315.

• Conover, W.J. and Iman, R.L. (1981) Rank transformations as a bridge between parametric and nonparametric statistics. The American Statistician, 35, 124-129.

See Also

Var.test, grambsch.Var.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
imam.Var.test(x,y)

# some variations
imam.Var.test(x,y,tr=0.2)
imam.Var.test(x,y,location="median")

data(anscombe2)
p<-with(anscombe2,paired(X1,Y1))
imam.Var.test(p)

Parameters for Generalised Lambda Distributions

Description

This dataset gives the parameters for specific 8 Generalized Tukey-lambda distributions with zero mean and unit variance useful for simulation studies as given in Bonett and Seier (2003).

Usage

data(lambda.table)

Format

A dataframe with 8 rows (distributions) and 4 columns (parameters).

References

Bonett, D.G. and Seier, E. (2003) Statistical inference for a ratio of dispersions using paired samples. Journal of Educational and Behavioral Statistics, 28, 21-30.

Levene test of scale for paired samples

Description

Robust test of scale for paired samples based on absolute deviations from the trimmed means (or medians), called extended Brown-Forsythe test in Wilcox (1989).

Usage

levene.Var.test(x, ...)

## Default S3 method:
levene.Var.test(x, y = NULL,
       alternative = c("two.sided", "less", "greater"),
       mu = 0,conf.level = 0.95,location=c("trim","median"),
tr=0.1, ...)


## S3 method for class 'paired'
levene.Var.test(x, ...)

Arguments

Details

The data are transformed as deviations from the trimmed mean: X=abs(x-mean(x,tr=0.1)) and Y=(y-mean(y,tr=0.1)). A paired t test is then carried out on X and Y.

Value

A list with class "htest" containing the components of a paired t test.

Author(s)

Stephane CHAMPELY

References

Wilcox, R.R. (1989) Comparing the variances of dependent groups. Psychometrika, 54, 305-315.

See Also

Var.test, grambsch.Var.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
levene.Var.test(x,y)

# Some variations
levene.Var.test(x,y,tr=0.2)
levene.Var.test(x,y,location="median")


data(anscombe2)
p<-with(anscombe2,paired(X2,Y2))
levene.Var.test(p)

McCulloch test of scale for paired samples

Description

Robust test of scale for paired samples based on spearman coefficient (the default, or kendall or pearson) of the transformed D=x-y and S=x+y.

Usage

mcculloch.Var.test(x, ...)

## Default S3 method:
mcculloch.Var.test(x, y = NULL,

alternative = c("two.sided", "less", "greater"),

method= c("spearman","pearson", "kendall"),

exact = NULL,conf.level = 0.95,continuity = FALSE, ...)

## S3 method for class 'paired'
mcculloch.Var.test(x, ...)

Arguments

Value

A list with class "htest" containing the components of a (Spearman) correlation test.

Author(s)

Stephane CHAMPELY

References

McCulloch, C.E. (1987) Tests for equality of variances for paired data. Communications in Statistics - Theory and Methods, 16, 1377-1391.

See Also

Var.test, grambsch.Var.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
mcculloch.Var.test(x,y)

p<-paired(x,y)
mcculloch.Var.test(p)

# A variation with kendall tau
mcculloch.Var.test(p,method="kendall")

# equivalence with the PitmanMorgan test
mcculloch.Var.test(p,method="pearson")
Var.test(p)

Paired

Description

This function creates objects of class paired

Usage

paired(x, y)

Arguments

Details

The two vectors must share the same class. Moreover, for vectors of class factor, they must have the same levels.

Value

An object of class paired.

Author(s)

Stephane Champely

Examples

x<-rnorm(15)
y<-rnorm(15)
p1<-paired(x,y)
show(p1)

data(IceSkating)
p2<-with(IceSkating,paired(Extension,Flexion))
show(p2)

Class "paired"

Description

An object of class paired is a dataframe with two columns sharing the same class (usually numeric).

Objects from the Class

Objects can be created by calls of the form new("paired", ...).

Slots

.Data:

Object of class "list" ~~

names:

Object of class "character" ~~

row.names:

Object of class "data.frameRowLabels" ~~

.S3Class:

Object of class "character" ~~

Extends

Class "data.frame", directly. Class "list", by class "data.frame", distance 2. Class "oldClass", by class "data.frame", distance 2. Class "vector", by class "data.frame", distance 3.

Methods

effect.size

signature(object = "paired"): ...

summary

signature(object = "paired"): ...

plot

signature(object = "paired"): ...

Author(s)

Stephane Champely

Examples

data(IceSkating)
p<-with(IceSkating,paired(Extension,Flexion))
show(p)
plot(p)
summary(p)
effect.size(p)

Bland-Altman plot

Description

Produce a Bland-Altman plot for paired data, including a confidence region for the mean of the differences.

Usage

paired.plotBA(df, condition1, condition2, groups = NULL, 
facet = TRUE, ...)

Arguments

Value

a graphical object of class ggplot.

Author(s)

Stephane CHAMPELY

References

• Bland, J.M. and Altman D.G. (1999) Measuring agreement in method comparison studies. Statistical Methods in Medical Research, 8, 135-160.

• Meek, D.M. (2007) Two macros for producing graphs to assess agreement between two variables. In Proceedings of Midwest SAS Users Group Annual Meeting, October 2007.

See Also

tmd

Examples

data(PrisonStress)
paired.plotBA(PrisonStress,"PSSbefore","PSSafter")

# Extending the resulting ggplot object by faceting
paired.plotBA(PrisonStress,"PSSbefore","PSSafter")+facet_grid(~Group)

Paired correlation plot

Description

Produce a squared scatterplot for paired data (same units for both axes), including the first bisector line for reference.

Usage

paired.plotCor(df, condition1, condition2, groups = NULL, 
facet = TRUE, ...)

Arguments

Value

a graphical object of class ggplot.

Author(s)

Stephane CHAMPELY

Examples

data(PrisonStress)
paired.plotCor(PrisonStress,"PSSbefore","PSSafter")

# Changing the theme of the ggplot object
paired.plotCor(PrisonStress,"PSSbefore","PSSafter")+theme_bw()

Parallel lines plot

Description

Produce a parallel lines plot for paired data.

Usage

paired.plotMcNeil(df, condition1, condition2, groups = NULL, subjects,facet = TRUE, ...) 

Arguments

Value

a graphical object of class ggplot.

Author(s)

Stephane CHAMPELY

References

McNeil, D.R. (1992) On graphing paired data. The American Statistician, 46 :307-310.

See Also

plotBA

Examples

data(PrisonStress)
paired.plotMcNeil(PrisonStress,"PSSbefore","PSSafter",subjects="Subject")

Profile plot

Description

Produce a profile plot or before-after plot or 1-1 plot for paired data.

Usage

paired.plotProfiles(df, condition1, condition2, groups = NULL,subjects, 
    facet = TRUE, ...) 

Arguments

Value

a graphical object of class ggplot.

Author(s)

Stephane CHAMPELY

References

Cox, N.J. (2004) Speaking data: graphing agreement and disagreement. The Stata Journal, 4, 329-349.

See Also

plotBA,plotMcNeil

Examples

data(PrisonStress)
paired.plotProfiles(PrisonStress,"PSSbefore","PSSafter",subjects="Subject",groups="Group")

# Changing the line colour
paired.plotProfiles(PrisonStress,"PSSbefore","PSSafter")+geom_line(colour="red")

~~ Methods for Function plot ~~

Description

Plot an object of class paired.

Usage

## S4 method for signature 'paired'
plot(x, groups=NULL,subjects=NULL,

 facet=TRUE,type=c("correlation","BA","McNeil","profile"),...)

Arguments

Value

an graphical object of class ggplot.

Examples

data(HorseBeginners)
pd1<-with(HorseBeginners,paired(Actual,Imaginary))
plot(pd1)
plot(pd1,type="BA")
plot(pd1,type="McNeil")
plot(pd1,type="profile")

data(Shoulder)
with(Shoulder,plot(paired(Left,Right),groups=Group))
with(Shoulder,plot(paired(Left,Right),groups=Group,facet=FALSE))
with(Shoulder,plot(paired(Left,Right),
groups=Group,facet=FALSE,type="profile"))+theme_bw()

Simulate paired samples

Description

Simulate paired data with a given correlation (Kendall's tau=(2/pi)arcsine(r)) and marginals being contaminated normal distributions: (1-eps)*F(x)+eps*F(x/K) where F is the cumulative standard normal distribution, eps the percentage of contamination and K a scale parameter. Moreover, this marginal can be multiplied by another scale parameter sigma but usually sigma=1.

Usage

rpaired.contaminated(n, d1 = c(0.1, 10, 1), d2 = c(0.1, 10, 1), r = 0.5)

Arguments

Value

An object of class paired.

Author(s)

Stephane CHAMPELY

References

Grambsch, P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.

See Also

rpaired.gld

Examples

rpaired.contaminated(n=30,r=0.25)

Simulate paired samples

Description

Simulate paired data with a given correlation (Kendall's tau=(2/pi)arcsine(r)) and marginals being Generalized Tukey-Lambda (G-TL) distributions.

Usage

rpaired.gld(n, d1=c(0.000,0.1974,0.1349,0.1349), d2=c(0.000,0.1974,0.1349,0.1349), r)

Arguments

Value

An object of class paired.

Author(s)

Stephane CHAMPELY

References

Grambsch, P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.

See Also

rpaired.contaminated

Examples

rpaired.gld(n=30,r=0.5)

data(lambda.table)
p<-rpaired.gld(n=30,d1=lambda.table[7,],d2=lambda.table[7,],r=0.5)
plot(p)

Sandvik-Olsson test of scale for paired samples

Description

Robust test of scale for paired samples based on the absolute deviations from the trimmed means (or medians).

Usage

sandvikolsson.Var.test(x, ...)

## Default S3 method:
sandvikolsson.Var.test(x, y = NULL,
            alternative = c("two.sided", "less", "greater"),
            mu = 0, exact = NULL, correct = TRUE,
            conf.int = FALSE, conf.level = 0.95,location=c("trim","median"),tr=0.1, ...)

## S3 method for class 'paired'
sandvikolsson.Var.test(x, ...)

Arguments

Details

The data are transformed as deviations from the trimmed mean: X=abs(x-mean(x,tr=0.1)) and Y=(y-mean(y,tr=0.1)). A wilcoxon signed-rank test is then carried out on X and Y.

Value

A list with class "htest" containing the components of a wilcoxon signed-rank test.

Author(s)

Stephane CHAMPELY

References

Sandvik, L. and Olsson, B. (1982) A nearly distribution-free test for comparing dispersion in paired samples. Biometrika, 69, 484-485.

See Also

Var.test, grambsch.Var.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
sandvikolsson.Var.test(x,y)

p<-paired(x,y)
sandvikolsson.Var.test(p)


# some variations
sandvikolsson.Var.test(p,tr=0.2)
sandvikolsson.Var.test(p,location="median")

Sliding square plot

Description

Draw a sliding square plot for paired data which mixes the usual scatterplot with the tukey mean-difference plot.

Usage

## S4 method for signature 'paired'
slidingchart(object,...)

Arguments

Author(s)

Stephane CHAMPELY

References

• Rosenbaum, P.R. (1989) Exploratory plot for paired data. American Statistician, 43, 108-110.

• Pontius, J.S. and Schantz, R.M. (1994) Graphical analyses of a twoperiod crossover design. The American Statistician, 48, 249-253.

• Pruzek, R.M. and Helmreich, J.E. (2009) Enhancing dependent sample analyses with graphics. Journal of Statistics Education, 17.

See Also

plot

Examples

data(PrisonStress)
with(PrisonStress,slidingchart(paired(PSSbefore,PSSafter)))

Summary statistics for paired samples

Description

Classical and robust statistics (location, scale and correlation) for paired samples.

Usage

## S4 method for signature 'paired'
summary(object,tr=0.2)

Arguments

Value

A list with a first table corresponding to location and scale statistics and a second table to Pearson and winsorized correlation.

The first table contains four rows corresponding to calculations for x, y, x-y and (x+y)/2 variables. The location and scale statistics are given in columns.

Author(s)

Stephane CHAMPELY

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-rnorm(20)+z+1
p<-paired(x,y)
summary(p)

Student's test test for paired data

Description

A method designed for objects of class paired.

Usage

## S3 method for class 'paired'
t.test(x, ...)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Stephane Champely

See Also

yuen.t.test

Examples

data(PrisonStress)
with(PrisonStress,t.test(paired(PSSbefore,PSSafter)))

Wilcoxon's signed rank test for paired data

Description

A method designed for objects of class paired.

Usage

## S3 method for class 'paired'
wilcox.test(x, ...)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Stephane Champely

See Also

yuen.test

Examples

data(PrisonStress)
with(PrisonStress,wilcox.test(PSSbefore,PSSafter))
with(PrisonStress,wilcox.test(PSSbefore,PSSafter,paired=TRUE))
with(PrisonStress,wilcox.test(paired(PSSbefore,PSSafter)))

Winsorized correlation test (for paired data)

Description

Test for association between paired samples, using winsorized correlation coefficient.

Usage

winsor.cor.test(x, ...)

## Default S3 method:
winsor.cor.test(x, y, tr=0.2,alternative = c("two.sided", "less", "greater"), ...)


## S3 method for class 'paired'
winsor.cor.test(x,tr=0.2,alternative = c("two.sided", "less", "greater"), ...)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Stephane Champely

See Also

cor.test

Examples

data(PrisonStress)
with(PrisonStress,winsor.cor.test(PSSbefore,PSSafter))
with(PrisonStress,winsor.cor.test(paired(PSSbefore,PSSafter)))

Yuen's trimmed mean test

Description

Yuen's test for one, two or paired samples.

Usage

yuen.t.test(x, ...)

## Default S3 method:
yuen.t.test(x, y = NULL, tr = 0.2, alternative = c("two.sided", "less", "greater"),
mu = 0, paired = FALSE, conf.level = 0.95, ...)

## S3 method for class 'formula'
yuen.t.test(formula, data, subset, na.action, ...)

## S3 method for class 'paired'
yuen.t.test(x, ...)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Stephane CHAMPELY, but some part are mere copy of the code of Wilcox (WRS)

References

• Wilcox, R.R. (2005). Introduction to robust estimation and hypothesis testing. Academic Press.

• Yuen, K.K. (1974) The two-sample trimmed t for unequal population variances. Biometrika, 61, 165-170.

See Also

t.test

Examples

z<-rnorm(20)
x<-rnorm(20)+z
y<-rnorm(20)+z+1

# two-sample test
yuen.t.test(x,y)

# one-sample test
yuen.t.test(y,mu=1,tr=0.25)

# paired-sample tests
yuen.t.test(x,y,paired=TRUE)

p<-paired(x,y)
yuen.t.test(p)