Title: | 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. |
Authors: | Stephane Champely <[email protected]> |
Maintainer: | Stephane Champely <[email protected]> |
License: | GPL (>= 2) |
Version: | 1.1.1 |
Built: | 2024-12-19 06:56:41 UTC |
Source: | CRAN |
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.
The DESCRIPTION file:
Package: | PairedData |
Type: | Package |
Title: | Paired Data Analysis |
Version: | 1.1.1 |
Date: | 2018-06-02 |
Author: | Stephane Champely <[email protected]> |
Maintainer: | Stephane Champely <[email protected]> |
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. |
License: | GPL (>= 2) |
Depends: | methods,graphics,MASS,gld,mvtnorm,lattice,ggplot2 |
Collate: | global1.R ClassP1.R |
Packaged: | 2018-06-02 14:53:04 UTC; STEPHANE.CHAMPELY |
NeedsCompilation: | no |
Repository: | CRAN |
Date/Publication: | 2018-06-02 22:57:15 UTC |
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
Stephane Champely <[email protected]>
Maintainer: Stephane Champely <[email protected]>
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.
data(Anorexia)
data(Anorexia)
A dataframe with 17 rows and 2 numeric columns:
[,1] | Prior | numeric | weight (lbs) before therapy |
[,2] | Post | numeric | weight (lbs) after therapy |
Hand, D.J., McConway, K., Lunn, D. & Ostrowki, editors (1993) A Handbook of Small Data Sets. Number 232, 285. Chapman & Hall: New-York.
Pruzek & Helmreich (2009) Enhancing dependent sample analysis with graphics. Journal of Statistics Education, 17 (1).
anorexia in MASS
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))
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))
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.
data(anscombe2)
data(anscombe2)
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.
S. Champely, CRIS, Lyon 1 University, FRANCE
F. Anscombe, Graphs in statistical analysis. The American Statistican, 27, 17-21.
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"))
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"))
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.
data(Barley)
data(Barley)
A dataframe with 17 rows and 3 columns:
[,1] | Farm | factor | |
[,2] | Glabron | numeric | yields (bushels per acre) |
[,3] | Velvet | numeric | yields |
Leonard, W.H. & Clark, A.G. (1939) Field Plot Techniques. Burgess: Minneapolis.
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.
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)))
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)))
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.
data(Blink)
data(Blink)
A dataframe with 12 rows and 3 columns:
[,1] | Subject | factor | |
[,2] | Straight | numeric | blink rate in first condition |
[,3] | Oscillating | numeric | blink rate in second condition |
Wetherhill, G.B. (1972) Elementary Statistical Methods, 2nd ed Chapman and Hall: London.
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.
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))
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))
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.
data(Blink2)
data(Blink2)
A dataframe with 12 rows and 4 columns:
[,1] | Subject | factor | |
[,2] | Resting | numeric | blink rate in pre-experimental condition |
[,3] | Straight | numeric | blink rate in first condition |
[,4] | Oscillating | numeric | blink rate in second condition |
Drew, G.C. (1951) Variations in blink-rate during visual-motor tasks. Quarterly Journal of Experimental Psychology, 3, 73-88.
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.
Blink
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.
data(BloodLead)
data(BloodLead)
A dataframe with 33 rows and 3 columns:
[,1] | Pair | factor | matched pair of chidren |
[,2] | Exposed | numeric | blood lead levels (mg/dl) for exposed children |
[,3] | Control | numeric | blood lead levels for controls |
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.
Pruzek, R.M. & Helmreich, J.E. (2009) Enhancing dependent sample analysis with graphics. Journal of Statistics Education, 17 (1).
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))
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))
Robust test of scale for paired samples based on the mean absolute deviations.
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, ...)
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, ...)
x |
first sample or object of class paired. |
y |
second sample. |
alternative |
alternative hypothesis. |
omega |
a priori ratio of means absolute deviations. |
conf.level |
confidence level. |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the following components:
statistic |
the value of the z-statistic. |
p.value |
the p-value for the test. |
conf.int |
a confidence interval for the ratio of means absolute deviations appropriate to the specified alternative hypothesis. |
estimate |
the estimated means absolute deviations. |
null.value |
the specified hypothesized value of the ratio of means absolute deviations. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
Stephane CHAMPELY
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.
Var.test, grambsch.Var.test
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)
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)
This dataset presents 10 paired data corresponding to the weights of chicks, two from ten families, reared in confinement or on open range.
data(ChickWeight)
data(ChickWeight)
A dataframe with 10 rows and 3 columns:
[,1] | Chicks | factor | |
[,2] | Confinement | numeric | chick weight (ounces) |
[,3] | OpenRange | numeric | chick weight |
Paterson, D.D. (1939) Statistical Techniques in Agricultural Research. McGrw-Hill: New-York.
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.
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))
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))
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).
data(Corn)
data(Corn)
A dataframe with 15 rows and 4 columns:
[,1] | pair | numeric | |
[,2] | pot | numeric | |
[,3] | Crossed | numeric | plant height (inches) |
[,4] | Self | numeric | plant height |
Darwin, C. (1876). The Effect of Cross- and Self-fertilization in the Vegetable Kingdom, 2nd Ed. London: John Murray.
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
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))
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))
This dataset presents for teaching purposes 50 paired datasets available in different R packages.
data(Datalcoholic)
data(Datalcoholic)
A dataframe with 4 columns.
[,1] | Dataset | name of the dataset |
[,2] | Package | name of the package |
[,3] | Topic | corresponding discipline (marketing, medicine...) |
[,4] | NumberPairs | size of the (paired) sample |
data(Datalcoholic) show(Datalcoholic)
data(Datalcoholic) show(Datalcoholic)
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
## S4 method for signature 'paired' effect.size(object,tr=0.2)
## S4 method for signature 'paired' effect.size(object,tr=0.2)
object |
an object of class paired |
tr |
percentage of trimming |
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:
Average |
Numerator is the difference in (trimmed) means, denominator is the average of the two (winsorised and rescaled to be consistent with the standard deviation when the distribution is normal) standard deviations |
Single (x) |
Denominator is the (winsorised and rescaled) standard deviation of the first sample |
Single (y) |
Denominator is the (winsorised and rescaled) standard deviation of the second sample |
Difference |
Numerator is the (trimmed) mean and denominator the (winsorised and rescaled) standard deviation of the differences (x-y) |
Stephane CHAMPELY
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.
z<-rnorm(20) x<-rnorm(20)+z y<-rnorm(20)+z+1 p<-paired(x,y) effect.size(p)
z<-rnorm(20) x<-rnorm(20)+z y<-rnorm(20)+z+1 p<-paired(x,y) effect.size(p)
This dataset gives the same measurements of muscle activation (EMG) in 3 days corresponding to a reproductibility study for 18 tennis players.
data(GDO)
data(GDO)
A dataframe with 18 rows and 4 columns.
[,1] | Subject | factor | anonymous subjects |
[,2] | Day1 | numeric | measurement first day |
[,3] | Day2 | numeric | measurement second day |
[,4] | Day3 | numeric | measurement third day |
Private communication. Samuel Rota, CRIS, Lyon 1 University, FRANCE
packages: agreement, irr and MethComp.
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)
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)
This dataset presents 9 paired data corresponding to the grain yields of Great Northern and Big Four oats grown in "adjacent" plots.
data(Grain)
data(Grain)
A dataframe with 9 rows and 3 columns:
[,1] | Year | factor | |
[,2] | GreatNorthern | numeric | grain yield (bushels per acre) |
[,3] | BigFour | numeric | grain yield |
LeClerg, E.L., Leonard, W.H. & Clark, A.G. (1962) Field Plot Technique. Burgess: Minneapolis.
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.
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"))
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"))
This dataset presents 6 paired data corresponding to the grain yields of two wheat varieties grown on pairs of plots.
data(Grain2)
data(Grain2)
A dataframe with 6 rows and 3 columns:
[,1] | Plot | factor | |
[,2] | Variety_1 | numeric | grain yield (bushels per acre) |
[,3] | Variety_2 | numeric | grain yield |
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.
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.
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)
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)
Robust test of scale for paired samples.
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, ...)
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, ...)
x |
first sample or an object of class paired. |
y |
second sample. |
alternative |
alternative hypothesis. |
... |
further arguments to be passed to or from methods. |
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.
A list with class "htest" containing the following components:
statistic |
the value of the F-statistic. |
p.value |
the p-value for the test. |
null.value |
the specified hypothesized value of the ratio of variances (=1!) |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
Stephane CHAMPELY
Grambsch,P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.
Var.test, bonettseier.Var.test
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)
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)
This dataset presents paired data corresponding to the percentage of solids recorded in the shaded and exposed halves of 25 grapefruits.
data(GrapeFruit)
data(GrapeFruit)
A dataframe with 25 rows and 3 columns:
[,1] | Fruit | numeric | |
[,2] | Shaded | numeric | percentage of solids in grapefruit |
[,3] | Exposed | numeric | percentage of solids |
Croxton, F.E. & Coxden, D.J. (1955) Applied Genral Statistics, 2nd ed. Chapman and Hall, London.
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.
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))
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))
This dataset gives the actual and motor imaginary performances (time) in horse-riding for 8 beginners.
data(HorseBeginners)
data(HorseBeginners)
A dataframe with 8 rows and 3 columns.
[,1] | Subject | factor | Anonymous subjects |
[,2] | Actual | numeric | Actual performance (sec.) |
[,3] | Imaginary | numeric | Imaginary performance (sec.) |
Private communication. Aymeric Guillot, CRIS, Lyon 1 University, FRANCE.
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.
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)))
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)))
This dataset gives the speed measurement (m/sec) for seven iceskating dancers using the return leg in flexion or in extension.
data(IceSkating)
data(IceSkating)
A dataframe with 7 rows and 3 columns.
[,1] | Subject | factor | anonymous subjects |
[,2] | Extension | numeric | speed when return leg in extension (m/sec) |
[,3] | Flexion | numeric | speed when return leg in flexion (m/sec) |
Private communication. Karine Monteil, CRIS, Lyon 1 University, FRANCE.
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.
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)))
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)))
Robust test of scale for paired samples based on absolute deviations from the trimmed means (or medians), called Imam test in Wilcox (1989).
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, ...)
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, ...)
x |
first sample or object of class paired. |
y |
second sample. |
alternative |
alternative hypothesis. |
mu |
the location parameter mu. |
conf.level |
confidence level. |
location |
location parameter for centering: trimmed mean or median. |
tr |
percentage of trimming. |
... |
further arguments to be passed to or from methods. |
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.
A list with class "htest" containing the components of a paired t test.
Stephane CHAMPELY
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.
Var.test, grambsch.Var.test
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)
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)
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).
data(Iron)
data(Iron)
A dataframe with 10 rows and 3 columns:
[,1] | Compound | factor | |
[,2] | Method_A | numeric | percentage of iron |
[,3] | Method_B | numeric | percentage of iron |
Chatfield, C. (1978) Statistics for Technology: A Course in Applied Statistics, 2nd ed. Chapman and Hall: London.
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.
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))
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))
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).
data(lambda.table)
data(lambda.table)
A dataframe with 8 rows (distributions) and 4 columns (parameters).
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.
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).
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, ...)
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, ...)
x |
first sample or object of class paired. |
y |
second sample. |
alternative |
alternative hypothesis. |
mu |
the location parameter mu. |
conf.level |
confidence level. |
location |
location parameter for centering: trimmed mean or median. |
tr |
percentage of trimming. |
... |
further arguments to be passed to or from methods. |
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.
A list with class "htest" containing the components of a paired t test.
Stephane CHAMPELY
Wilcox, R.R. (1989) Comparing the variances of dependent groups. Psychometrika, 54, 305-315.
Var.test, grambsch.Var.test
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)
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)
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.
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, ...)
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, ...)
x |
first sample or object of class paired. |
y |
second sample. |
alternative |
alternative hypothesis. |
method |
a character string indicating which correlation coefficient is to be used for the test. One of "spearman", "kendall", or "pearson", can be abbreviated. |
exact |
a logical indicating whether an exact p-value should be computed. |
conf.level |
confidence level. |
continuity |
logical: if true, a continuity correction is used for Spearman's rho when not computed exactly. |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the components of a (Spearman) correlation test.
Stephane CHAMPELY
McCulloch, C.E. (1987) Tests for equality of variances for paired data. Communications in Statistics - Theory and Methods, 16, 1377-1391.
Var.test, grambsch.Var.test
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)
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)
This dataset presents 20 paired data corresponding to the percentage of fat in samples of meat using two different methods: AOAC and Babcock.
data(Meat)
data(Meat)
A dataframe with 20 rows and 3 columns:
[,1] | AOAC | numeric | percentage of fat |
[,2] | Babcock | numeric | percentage of fat |
[,3] | MeatType | factor | meat type |
Tippett, L.H.C. (1952) Technological Applications of Statistics. Williams and Norgate: London.
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.
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))
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))
This function creates objects of class paired
paired(x, y)
paired(x, y)
x |
first vector. |
y |
second vector. |
The two vectors must share the same class. Moreover, for vectors of class factor, they must have the same levels.
An object of class paired.
Stephane Champely
x<-rnorm(15) y<-rnorm(15) p1<-paired(x,y) show(p1) data(IceSkating) p2<-with(IceSkating,paired(Extension,Flexion)) show(p2)
x<-rnorm(15) y<-rnorm(15) p1<-paired(x,y) show(p1) data(IceSkating) p2<-with(IceSkating,paired(Extension,Flexion)) show(p2)
"paired"
An object of class paired is a dataframe with two columns sharing the same class (usually numeric).
Objects can be created by calls of the form new("paired", ...)
.
.Data
:Object of class "list"
~~
names
:Object of class "character"
~~
row.names
:Object of class "data.frameRowLabels"
~~
.S3Class
:Object of class "character"
~~
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.
signature(object = "paired")
: ...
signature(object = "paired")
: ...
signature(object = "paired")
: ...
Stephane Champely
data(IceSkating) p<-with(IceSkating,paired(Extension,Flexion)) show(p) plot(p) summary(p) effect.size(p)
data(IceSkating) p<-with(IceSkating,paired(Extension,Flexion)) show(p) plot(p) summary(p) effect.size(p)
Produce a Bland-Altman plot for paired data, including a confidence region for the mean of the differences.
paired.plotBA(df, condition1, condition2, groups = NULL, facet = TRUE, ...)
paired.plotBA(df, condition1, condition2, groups = NULL, facet = TRUE, ...)
df |
a data.frame. |
condition1 |
name of the variable corresponding to the first sample. |
condition2 |
name of the variable corresponding to the first sample. |
groups |
name of the variable corresponding to the groups (optional). |
facet |
faceting or grouping strategy for plotting? |
... |
arguments to be passed to methods |
a graphical object of class ggplot.
Stephane CHAMPELY
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.
tmd
data(PrisonStress) paired.plotBA(PrisonStress,"PSSbefore","PSSafter") # Extending the resulting ggplot object by faceting paired.plotBA(PrisonStress,"PSSbefore","PSSafter")+facet_grid(~Group)
data(PrisonStress) paired.plotBA(PrisonStress,"PSSbefore","PSSafter") # Extending the resulting ggplot object by faceting paired.plotBA(PrisonStress,"PSSbefore","PSSafter")+facet_grid(~Group)
Produce a squared scatterplot for paired data (same units for both axes), including the first bisector line for reference.
paired.plotCor(df, condition1, condition2, groups = NULL, facet = TRUE, ...)
paired.plotCor(df, condition1, condition2, groups = NULL, facet = TRUE, ...)
df |
a data.frame. |
condition1 |
name of the variable corresponding to the first sample. |
condition2 |
name of the variable corresponding to the first sample. |
groups |
name of the variable corresponding to the groups (optional). |
facet |
faceting or grouping strategy for plotting? |
... |
arguments to be passed to methods |
a graphical object of class ggplot.
Stephane CHAMPELY
data(PrisonStress) paired.plotCor(PrisonStress,"PSSbefore","PSSafter") # Changing the theme of the ggplot object paired.plotCor(PrisonStress,"PSSbefore","PSSafter")+theme_bw()
data(PrisonStress) paired.plotCor(PrisonStress,"PSSbefore","PSSafter") # Changing the theme of the ggplot object paired.plotCor(PrisonStress,"PSSbefore","PSSafter")+theme_bw()
Produce a parallel lines plot for paired data.
paired.plotMcNeil(df, condition1, condition2, groups = NULL, subjects,facet = TRUE, ...)
paired.plotMcNeil(df, condition1, condition2, groups = NULL, subjects,facet = TRUE, ...)
df |
a data frame. |
condition1 |
name of the variable corresponding to the second sample. |
condition2 |
name of the variable corresponding to the first sample. |
groups |
names of the variable corresponding to groups (optional). |
subjects |
names of the variable corresponding to subjects. |
facet |
faceting or grouping strategy for plotting? |
... |
further arguments to be passed to methods. |
a graphical object of class ggplot.
Stephane CHAMPELY
McNeil, D.R. (1992) On graphing paired data. The American Statistician, 46 :307-310.
plotBA
data(PrisonStress) paired.plotMcNeil(PrisonStress,"PSSbefore","PSSafter",subjects="Subject")
data(PrisonStress) paired.plotMcNeil(PrisonStress,"PSSbefore","PSSafter",subjects="Subject")
Produce a profile plot or before-after plot or 1-1 plot for paired data.
paired.plotProfiles(df, condition1, condition2, groups = NULL,subjects, facet = TRUE, ...)
paired.plotProfiles(df, condition1, condition2, groups = NULL,subjects, facet = TRUE, ...)
df |
a data frame. |
condition1 |
name of the variable corresponding to the second sample. |
condition2 |
name of the variable corresponding to the first sample. |
groups |
names of the variable corresponding to groups (optional). |
subjects |
names of the variable corresponding to subjects. |
facet |
faceting or grouping strategy for plotting? |
... |
further arguments to be passed to methods. |
a graphical object of class ggplot.
Stephane CHAMPELY
Cox, N.J. (2004) Speaking data: graphing agreement and disagreement. The Stata Journal, 4, 329-349.
plotBA,plotMcNeil
data(PrisonStress) paired.plotProfiles(PrisonStress,"PSSbefore","PSSafter",subjects="Subject",groups="Group") # Changing the line colour paired.plotProfiles(PrisonStress,"PSSbefore","PSSafter")+geom_line(colour="red")
data(PrisonStress) paired.plotProfiles(PrisonStress,"PSSbefore","PSSafter",subjects="Subject",groups="Group") # Changing the line colour paired.plotProfiles(PrisonStress,"PSSbefore","PSSafter")+geom_line(colour="red")
plot
~~ Plot an object of class paired.
## S4 method for signature 'paired' plot(x, groups=NULL,subjects=NULL, facet=TRUE,type=c("correlation","BA","McNeil","profile"),...)
## S4 method for signature 'paired' plot(x, groups=NULL,subjects=NULL, facet=TRUE,type=c("correlation","BA","McNeil","profile"),...)
x |
a paired object created by the
|
groups |
a factor (optional). |
subjects |
subjects name. |
facet |
faceting or grouping strategy for plotting? |
type |
type of the plot (correlation, Bland-Altman, McNeil or profile plot). |
... |
arguments to be passed to methods. |
an graphical object of class ggplot.
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()
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()
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.
data(PrisonStress)
data(PrisonStress)
A dataframe with 26 rows and 4 columns.
[,1] | Subject | factor | anonymous subjects |
[,2] | Group | factor | sport or control |
[,3] | PSSbefore | numeric | stress measurement before training |
[,4] | PSSafter | numeric | stress measurement after training |
Private communication. Charlotte Verdot, CRIS, Lyon 1 University, FRANCE
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.
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$Group,2) aovJail<-aov(PSS~Condition*Time+Error(Subject)) summary(aovJail)
data(PrisonStress) # The two groups are not randomized! # The control group is less stressed before the experiment with(PrisonStress,boxplot(PSSbefore~Group,ylab="Stress at the eginning of the study")) # But more stressed at the end! with(PrisonStress,boxplot(PSSafter~Group,ylab="22 weeks later")) # So the effects of physical training seems promising with(PrisonStress,plot(paired(PSSbefore,PSSafter),groups=Group,type="BA",facet=FALSE)) # Testing using gain scores analysis difference<-PrisonStress$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)
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.
rpaired.contaminated(n, d1 = c(0.1, 10, 1), d2 = c(0.1, 10, 1), r = 0.5)
rpaired.contaminated(n, d1 = c(0.1, 10, 1), d2 = c(0.1, 10, 1), r = 0.5)
n |
sample size. |
d1 |
vector of 3 parameters for the first contaminated normal distribution (eps,K,sigma). |
d2 |
vector of 3 parameters for the second contaminated normal distribution. |
r |
correlation. |
An object of class paired.
Stephane CHAMPELY
Grambsch, P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.
rpaired.gld
rpaired.contaminated(n=30,r=0.25)
rpaired.contaminated(n=30,r=0.25)
Simulate paired data with a given correlation (Kendall's tau=(2/pi)arcsine(r)) and marginals being Generalized Tukey-Lambda (G-TL) distributions.
rpaired.gld(n, d1=c(0.000,0.1974,0.1349,0.1349), d2=c(0.000,0.1974,0.1349,0.1349), r)
rpaired.gld(n, d1=c(0.000,0.1974,0.1349,0.1349), d2=c(0.000,0.1974,0.1349,0.1349), r)
n |
sample size. |
d1 |
vector of four parameters for the first G-TL distribution. |
d2 |
vector of four parameters for the second G-TL distribution. |
r |
correlation. |
An object of class paired.
Stephane CHAMPELY
Grambsch, P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.
rpaired.contaminated
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)
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)
This dataset gives the ratings on a continuous ten-points scale of two experts about 93 actions during several rugby union matches.
data(Rugby)
data(Rugby)
A dataframe with 93 rows and 3 columns.
[,1] | EXPERT.1 | numeric | First expert ratings |
[,2] | EXPERT.2 | numeric | Second expert ratings |
[,3] | Actions | factor | Subject label |
Private communication. Mickael Campo, CRIS, Lyon 1 University, FRANCE.
data(Rugby) with(Rugby,plot(paired(EXPERT.1,EXPERT.2))) with(Rugby,plot(paired(EXPERT.1,EXPERT.2),type="BA"))
data(Rugby) with(Rugby,plot(paired(EXPERT.1,EXPERT.2))) with(Rugby,plot(paired(EXPERT.1,EXPERT.2),type="BA"))
Robust test of scale for paired samples based on the absolute deviations from the trimmed means (or medians).
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, ...)
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, ...)
x |
first sample or object of class paired. |
y |
second sample. |
alternative |
alternative hypothesis. |
mu |
the location parameter mu. |
exact |
a logical indicating whether an exact p-value should be computed. |
correct |
a logical indicating whether to apply continuity correction in the normal approximation for the p-value. |
conf.int |
a logical indicating whether a confidence interval should be computed. |
conf.level |
confidence level. |
location |
location parameter for centering: trimmed mean or median. |
tr |
percentage of trimming. |
... |
further arguments to be passed to or from methods. |
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.
A list with class "htest" containing the components of a wilcoxon signed-rank test.
Stephane CHAMPELY
Sandvik, L. and Olsson, B. (1982) A nearly distribution-free test for comparing dispersion in paired samples. Biometrika, 69, 484-485.
Var.test, grambsch.Var.test
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")
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")
This dataset presents 8 paired data corresponding to log coliform densities per ml for 2 sewage chlorination methods on each of 8 days.
data(Sewage)
data(Sewage)
A dataframe with 8 rows and 3 columns:
[,1] | Day | numeric | |
[,2] | Method_A | numeric | log density |
[,3] | Method_B | numeric | log density |
Wetherill, G.B. (1972) Elementary Statistical Methods, 2nd ed. Chapman and Hall: London.
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.
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))
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))
This dataset gives the flexibility for the right and left shoulders in 15 swimmers and 15 sedentary people.
data(Shoulder)
data(Shoulder)
A dataframe with 30 rows and 4 columns.
[,1] | Subject | factor | anonymous subjects |
[,2] | Group | factor | swimmer or control |
[,3] | Right | numeric | right shoulder flexibility (deg.) |
[,4] | Left | numeric | left shoulder flexibility (deg.) |
Private communication. Karine Monteil, CRIS, Lyon 1 University, FRANCE.
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.
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"))
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"))
This dataset gives the actual and motor imaginary performances (time) in ski for 12 experts.
data(SkiExperts)
data(SkiExperts)
A dataframe with 12 rows and 3 columns.
[,1] | Subject | factor | anonymous subjects |
[,2] | Actual | numeric | actual performance (sec.) |
[,3] | Imaginary | numeric | imaginary performance (sec.) |
Private communication. Aymeric Guillot, CRIS, Lyon 1 University, FRANCE.
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.
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)))
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)))
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.
data(Sleep)
data(Sleep)
A dataframe with 10 rows and 2 columns:
[,1] | Dextro | numeric | sleep hour gain |
[,2] | Laevo | numeric | sleep hour gain |
Fisher, R.A. (1925) Statistical Metods for Research Workers. Oliver and Boyd: Edinburgh.
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.
Draw a sliding square plot for paired data which mixes the usual scatterplot with the tukey mean-difference plot.
## S4 method for signature 'paired' slidingchart(object,...)
## S4 method for signature 'paired' slidingchart(object,...)
object |
an object of class paired. |
... |
arguments to be passed to methods. |
Stephane CHAMPELY
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.
plot
data(PrisonStress) with(PrisonStress,slidingchart(paired(PSSbefore,PSSafter)))
data(PrisonStress) with(PrisonStress,slidingchart(paired(PSSbefore,PSSafter)))
Classical and robust statistics (location, scale and correlation) for paired samples.
## S4 method for signature 'paired' summary(object,tr=0.2)
## S4 method for signature 'paired' summary(object,tr=0.2)
object |
an object of class paired. |
tr |
percenatge of trimming. |
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.
n |
sample size. |
mean |
mean. |
median |
median. |
trim |
trimmed mean (tr=0.2) |
sd |
standard deviation. |
IQR |
interquartile range (standardised to be consistent with the sd in the normal case) |
median ad |
median of absolute deviations (standardised) |
mean ad |
mean of absolute deviations (standardised) |
sd(w) |
winsorised standard deviation (tr=0.2 and standardised) |
min |
minimum value. |
max |
maximum value. |
Stephane CHAMPELY
z<-rnorm(20) x<-rnorm(20)+z y<-rnorm(20)+z+1 p<-paired(x,y) summary(p)
z<-rnorm(20) x<-rnorm(20)+z y<-rnorm(20)+z+1 p<-paired(x,y) summary(p)
A method designed for objects of class paired.
## S3 method for class 'paired' t.test(x, ...)
## S3 method for class 'paired' t.test(x, ...)
x |
An object of class paired. |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the following components:
statistic |
the value of the t-statistic. |
parameter |
the degrees of freedom for the t-statistic. |
p.value |
the p-value for the test. |
conf.int |
a confidence interval for the mean appropriate to the specified alternative hypothesis. |
estimate |
the estimated difference in mean. |
null.value |
the specified hypothesized value of mean difference. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed (always paired here) |
data.name |
a character string giving the name(s) of the data. |
Stephane Champely
yuen.t.test
data(PrisonStress) with(PrisonStress,t.test(paired(PSSbefore,PSSafter)))
data(PrisonStress) with(PrisonStress,t.test(paired(PSSbefore,PSSafter)))
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.
data(Tobacco)
data(Tobacco)
A dataframe with 8 rows and 3 columns:
[,1] | Plant | factor | |
[,2] | Preparation_1 | numeric | number of lesions |
[,3] | Preparation_2 | numeric | number of lesions |
Snedecor, G.W. and Cochran, W.G. (1967) Statistical Methods, 6th ed. Iowa State University Press: Ames.
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.
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")
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")
Classical tests of variance for one-sample, two-independent samples or paired samples.
## 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,...)
## 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,...)
x |
first sample or an object of class paired or an object of class lm. |
y |
second sample or an object of class lm. |
ratio |
a priori ratio of variances (two-samples) or variance (one-sample). |
alternative |
alternative hypothesis. |
paired |
independent (the default) or paired samples. |
conf.level |
confidence level. |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the following components:
statistic |
the value of the X-squared statistic (one-sample) or F-statistic (two-samples). |
parameter |
the degrees of freedom for the statistic. |
p.value |
the p-value for the test. |
conf.int |
a confidence interval for the parameter appropriate to the specified alternative hypothesis. |
estimate |
the estimated variance(s). |
null.value |
the specified hypothesized value of the parameter. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
Stephane CHAMPELY
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.
bonettseier.Var.test, grambsch.Var.test
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$Imaginary,paired=TRUE) p<-with(HorseBeginners,paired(Actual,Imaginary)) Var.test(p)
data(HorseBeginners) #one sample test Var.test(HorseBeginners$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)
A method designed for objects of class paired.
## S3 method for class 'paired' wilcox.test(x, ...)
## S3 method for class 'paired' wilcox.test(x, ...)
x |
An object of class paired. |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the following components:
statistic |
the value of V statistic. |
parameter |
the parameter(s) for the exact distribution of the test statistic. |
p.value |
the p-value for the test. |
null.value |
the true location shift mu. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed (always paired here) |
data.name |
a character string giving the name(s) of the data. |
conf.int |
a confidence interval for the location parameter. (Only present if argument conf.int = TRUE.) |
estimate |
an estimate of the location parameter. (Only present if argument conf.int = TRUE.) |
Stephane Champely
yuen.test
data(PrisonStress) with(PrisonStress,wilcox.test(PSSbefore,PSSafter)) with(PrisonStress,wilcox.test(PSSbefore,PSSafter,paired=TRUE)) with(PrisonStress,wilcox.test(paired(PSSbefore,PSSafter)))
data(PrisonStress) with(PrisonStress,wilcox.test(PSSbefore,PSSafter)) with(PrisonStress,wilcox.test(PSSbefore,PSSafter,paired=TRUE)) with(PrisonStress,wilcox.test(paired(PSSbefore,PSSafter)))
Test for association between paired samples, using winsorized correlation coefficient.
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"), ...)
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"), ...)
x |
an object of class paired or the first variable. |
y |
second variable. |
tr |
percentage of winsorizing. |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the following components:
statistic |
the value of the t-statistic. |
parameter |
the degrees of freedom for the t-statistic. |
p.value |
the p-value for the test. |
estimate |
the winsorized correlation. |
null.value |
the specified hypothesized value of the winsorized correlation (=0). |
alternative |
a character string describing the alternative hypothesis. |
data.name |
a character string giving the name(s) of the data. |
Stephane Champely
cor.test
data(PrisonStress) with(PrisonStress,winsor.cor.test(PSSbefore,PSSafter)) with(PrisonStress,winsor.cor.test(paired(PSSbefore,PSSafter)))
data(PrisonStress) with(PrisonStress,winsor.cor.test(PSSbefore,PSSafter)) with(PrisonStress,winsor.cor.test(paired(PSSbefore,PSSafter)))
Yuen's test for one, two or paired samples.
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, ...)
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, ...)
x |
first sample or object of class paired. |
y |
second sample. |
tr |
percentage of trimming. |
alternative |
alternative hypothesis. |
mu |
a number indicating the true value of the trimmed mean (or difference in trimmed means if you are performing a two sample test). |
paired |
a logical indicating whether you want a paired yuen's test. |
conf.level |
confidence level. |
formula |
a formula of the form y ~ f where y is a numeric variable giving the data values and f a factor with TWO levels giving the corresponding groups. |
data |
an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula). |
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action"). |
... |
further arguments to be passed to or from methods. |
A list with class "htest" containing the following components:
statistic |
the value of the t-statistic. |
parameter |
the degrees of freedom for the t-statistic. |
p.value |
the p-value for the test. |
conf.int |
a confidence interval for the trimmed mean appropriate to the specified alternative hypothesis. |
estimate |
the estimated trimmed mean or difference in trimmed means depending on whether it was a one-sample test or a two-sample test. |
null.value |
the specified hypothesized value of the trimmed mean or trimmed mean difference depending on whether it was a one-sample test or a two-sample test. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
Stephane CHAMPELY, but some part are mere copy of the code of Wilcox (WRS)
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.
t.test
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)
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)