Type: Package
Title: Sample Variance Plots (Sv-Plots)
Version: 0.1.0
Author: Uditha Amarananda Wijesuriya <u.wijesuriya@usi.edu>
Maintainer: Uditha Amarananda Wijesuriya <u.wijesuriya@usi.edu>
Description: Two versions of sample variance plots, Sv-plot1 and Sv-plot2, will be provided illustrating the squared deviations from sample variance. Besides indicating the contribution of squared deviations for the sample variability, these plots are capable of detecting characteristics of the distribution such as symmetry, skewness and outliers. A remarkable graphical method based on Sv-plot2 can determine the decision on testing hypotheses over one or two population means. In sum, Sv-plots will be appealing visualization tools. Complete description of this methodology can be found in the article, Wijesuriya (2020) <doi:10.1080/03610918.2020.1851716>.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.1.1
Depends: R (≥ 3.0.2)
Imports: ggplot2
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown, stats
Config/testthat/edition: 3
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2021-04-06 15:55:07 UTC; uwijesuriy
Repository: CRAN
Date/Publication: 2021-04-07 08:40:02 UTC

Creates Sv-plot1, the first version of the sample variance plots.

Description

Sv-plot1 identifies the characteristics of the distribution illustrating squared deviations in the sample variance by squares for each data value.

Usage

svplot1(X,title="Sv-plot1",xlab="x",lbcol="grey5",lscol="grey60",
              rbcol="grey45",rscol="grey75",...)

Arguments

X

an n by 1 matrix, equivalently, a column vector of length n, where n is number of observations.

title

title of the plot, Sv-plot1 by default.

xlab

x-axis label, x by default.

lbcol

left bound color, grey5 by default.

lscol

left square color, grey60 by default.

rbcol

right bound color, grey45 by default.

rscol

right square color, grey75 by default.

...

other graphical parameters.

Value

Sv-plot1

References

Wijesuriya, U. A. (2020). Sv-plots for identifying characteristics of the distribution and testing hypotheses. Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2020.1851716.

Examples

   set.seed(0)
   X1 <- matrix(rnorm(50,mean=2,sd=5))
   svplot1(X1)

   X2 <- matrix(rf(50,df1=10,df2=5))
   svplot1(X2)

   X3 <- matrix(rbeta(50,shape1=10,shape2=2))
   svplot1(X3,title="",lbcol="blue",lscol="blue",rbcol="red",rscol="grey75")

Creates Sv-plot2, the second version of the sample variance plots.

Description

Sv-plot2 identifies the characteristics of the distribution illustrating squared deviation values in the sample variance against each data value.

Usage

svplot2(X,title="Sv-plot2",xlab="x",lbcol="grey5", lsdcol="grey60",
             rbcol="grey45",rsdcol="grey75",...)

Arguments

X

an n by 1 matrix, equivalently, a column vector of length n, where n is number of observations.

title

title of the plot, Sv-plot2 by default.

xlab

x-axis label, x by default.

lbcol

left bound color, grey5 by default.

lsdcol

left squared deviation color, grey60 by default.

rbcol

right bound color, grey45 by default.

rsdcol

right squared deviation color, grey75 by default.

...

other graphical parameters.

Value

Sv-plot2

References

Wijesuriya, U. A. (2020). Sv-plots for identifying characteristics of the distribution and testing hypotheses. Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2020.1851716.

Examples

   set.seed(0)
   X1 <- matrix(rnorm(50,mean=2,sd=5))
   svplot2(X1)

   X2 <- matrix(rf(50,df1=10,df2=5))
   svplot2(X2)

   X3 <- matrix(rbeta(50,shape1=10,shape2=2))
   svplot2(X3,lbcol="blue",lsdcol="blue",rbcol="red",rsdcol="red")

Tests the hypothesis over population mean based on one sample by Sv-plot2.

Description

Decision on hypothesis testing over single mean is made by graphing sample and population Sv-plot2s along with the threshold line. If the intersection point of two Sv-plot2s locates on or above the threshold line, the null hypothesis is rejected at specified significance level, otherwise, failed to reject.

Usage

test1mu(X,mu0=3.5,alpha=0.05,unkwnsigma=TRUE,sigma=NULL,xlab="x",
               title="Single mean: Hypothesis testing by Sv-plot2",
               samcol="grey5",popcol="grey45",thrcol="black",...)

Arguments

X

an n by 1 matrix, equivalently, a column vector of length n, where n is number of observations.

mu0

hypothesized population mean, mu0=3.5 by default.

alpha

significance level, alpha=0.05 by default.

unkwnsigma

population standard deviation is unknown, TRUE by default.

sigma

population standard deviation, NULL by default.

xlab

x-axis label, x by default.

title

title of the plot, Single mean: Hypothesis testing by Sv-plot2 by default.

samcol

sample Sv-plot2 color, grey5 by default.

popcol

sample Sv-plot2 color, grey45 by default.

thrcol

threshold color, black by default.

...

other graphical parameters.

Value

Decision on testing hypotheses over single population mean by Sv-plot2.

References

Wijesuriya, U. A. (2020). Sv-plots for identifying characteristics of the distribution and testing hypotheses. Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2020.1851716.

Examples

   set.seed(5)
   X=matrix(rnorm(20,mean=3,sd=2))
   test1mu(X,mu0=3.5,alpha=0.05,unkwnsigma=TRUE,sigma=NULL,xlab="x",
           title="Single mean: Hypothesis testing by Sv-plot2",
           samcol="grey5",popcol="grey45",thrcol="black")

Tests the hypothesis over population mean based on one sample summary statistics by Sv-plot2.

Description

Decision on hypothesis testing over single mean is made by graphing sample and population Sv-plot2s along with the threshold line. Intersecting Sv-plots on or above the horizontal line concludes the alternative hypothesis.

Usage

test1musm(n=20,xbar=3,s=2,mu0=4.5,alpha=0.05,
                 unkwnsigma=TRUE,sigma=NULL,xlab="x",
                 title="Single mean summary: Hypothesis testing by Sv-plot2",
                 samcol="grey5",popcol="grey45",thrcol="black",...)

Arguments

n

sample size, n=20 by default.

xbar

sample average, xbar=3 by default.

s

sample standard deviation, s=2 by default.

mu0

hypothesized population mean, mu0=4.5 by default.

alpha

significance level, alpha=0.05 by default.

unkwnsigma

population standard deviation is unknown, TRUE by default.

sigma

population standard deviation, NULL by default.

xlab

x-axis label, x by default.

title

title of the plot, Single mean: Hypothesis testing by Sv-plot2 by default by default.

samcol

sample Sv-plot2 color, grey5 by default.

popcol

sample Sv-plot2 color, grey45 by default.

thrcol

threshold color, black.

...

other graphical parameters.

Value

Decision on testing hypotheses over single population mean by Sv-plot2.

References

Wijesuriya, U. A. (2020). Sv-plots for identifying characteristics of the distribution and testing hypotheses. Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2020.1851716.

Examples

 ## For summary data
    test1musm(n=20,xbar=3,s=2,mu0=4.5,alpha=0.05, unkwnsigma=TRUE,sigma=NULL,xlab="x",
    title="Single mean summary: Hypothesis testing by Sv-plot2",
    samcol="grey5",popcol="grey45",thrcol="black")

Tests the hypothesis over two population means based on two samples by Sv-plot2.

Description

Decision on hypothesis testing over two means is made by graphing two sample Sv-plot2s along with the threshold line. If the intersection point of two Sv-plot2s locates on or above the threshold line, the null hypothesis is rejected at specified significance level, otherwise, failed to reject.

Usage

test2mu(X1,X2,paired=FALSE,eqlvar=FALSE,unkwnsigmas=TRUE,
               sigma1=NULL,sigma2=NULL,alpha=0.05,xlab="x",
               title="Two means: Hypothesis testing by Sv-plot2",
               sam1col="grey5",sam2col="grey45",thrcol="black",...)

Arguments

X1

an n1 by 1 matrix, equivalently, a column vector of length n1, where n1 is number of observations.

X2

an n2 by 1 matrix, equivalently, a column vector of length n2, where n2 is number of observations.

paired

for dependent samples TRUE, FALSE by default.

eqlvar

population variances are equal, FALSE by default.

unkwnsigmas

population standard deviations are unknown, TRUE by default.

sigma1

population1 standard deviation, NULL by default.

sigma2

population2 standard deviation, NULL by default.

alpha

significance level, alpha=0.05 by default.

xlab

x-axis label, x by default.

title

title of the plot, Two means: Hypothesis testing by Sv-plot2 by default.

sam1col

sample1 Sv-plot2 color, grey5 by default.

sam2col

sample2 Sv-plot2 color, grey45 by default.

thrcol

threshold color, black by default.

...

other graphical parameters.

Value

Decision on testing hypotheses over two population means by Sv-plot2.

References

Wijesuriya, U. A. (2020). Sv-plots for identifying characteristics of the distribution and testing hypotheses. Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2020.1851716.

Examples

set.seed(5)
test2mu(X1=matrix(rnorm(10,mean=3,sd=2)),X2=matrix(rnorm(20,mean=4,sd=2.5)),
       paired=FALSE,eqlvar=FALSE,unkwnsigmas=TRUE,
       sigma1=NULL,sigma2=NULL,alpha=0.05,
       sam1col="grey5",sam2col="grey45",thrcol="black")

test2mu(X1=matrix(rnorm(10,mean=3,sd=2)),X2=matrix(rnorm(20,mean=4,sd=2.5)),
       paired=FALSE,eqlvar=TRUE,unkwnsigmas=TRUE,
       sigma1=NULL,sigma2=NULL,alpha=0.05,
       sam1col="grey5",sam2col="grey45",thrcol="black")

test2mu(X1=matrix(rnorm(50,mean=3,sd=2)),X2=matrix(rnorm(30,mean=4,sd=2.5)),
       xlab="x",title="Two means: Hypothesis testing by Sv-plot2",
       paired=FALSE,eqlvar=FALSE,unkwnsigmas=TRUE,
       sigma1=NULL,sigma2=NULL,alpha=0.05,
       sam1col="grey5",sam2col="grey45",thrcol="black")

test2mu(X1=matrix(rnorm(50,mean=3,sd=2)),X2=matrix(rnorm(30,mean=4,sd=2.5)),
       paired=FALSE,eqlvar=FALSE,unkwnsigmas=FALSE,
       sigma1=2,sigma2=4.920782,alpha=0.05,
       sam1col="grey5",sam2col="grey45",thrcol="black")

X1=matrix(rnorm(10,mean=3,sd=2))
X2=2*X1
test2mu(X1,X2,
       paired=TRUE,eqlvar=FALSE,unkwnsigmas=TRUE,
       sigma1=NULL,sigma2=NULL,alpha=0.05,
       sam1col="blue",sam2col="red",thrcol="black")

Tests the hypothesis over two population means based on two samples summary statistics by Sv-plot2.

Description

Decision on hypothesis testing over two means is made by graphing two sample Sv-plot2s along with the threshold line. Intersecting Sv-plots on or above the horizontal line concludes the alternative hypothesis.

Usage

test2musm(n1=20,n2=25,xbar1=3,xbar2=4,s1=1,s2=1.5,
                 paired=FALSE,eqlvar=FALSE,unkwnsigmas=TRUE,
                 sigma1=NULL,sigma2=NULL,sdevdif=NULL,alpha=0.05,
                 xlab="x",title="Two means summary: Hypothesis testing by Sv-plot2",
                 sam1col="grey5",sam2col="grey45",thrcol="black",...)

Arguments

n1

sample1 size, n1=20 by default.

n2

sample2 size, n2=25 by default.

xbar1

sample1 average, xbar1=3 by default.

xbar2

sample2 average, xbar2=4 by default.

s1

sample1 standard deviation, s1=1 by default.

s2

sample2 standard deviation, s2=1.5 by default.

paired

for dependent samples TRUE, FALSE by default.

eqlvar

population variances are equal, FALSE by default.

unkwnsigmas

population standard deviations are unknown, TRUE by default.

sigma1

population1 standard deviation, NULL by default.

sigma2

population2 standard deviation, NULL by default.

sdevdif

standard deviation of the differences, NULL by default.

alpha

significance level, alpha=0.05 by default.

xlab

x-axis label, x by default.

title

title of the plot, Two means: Hypothesis testing by Sv-plot2 by default.

sam1col

sample1 Sv-plot2 color, grey5 by default.

sam2col

sample2 Sv-plot2 color, grey45 by default.

thrcol

threshold color, black by default.

...

other graphical parameter.

Value

Decision on testing hypotheses over two population means by Sv-plot2.

References

Wijesuriya, U. A. (2020). Sv-plots for identifying characteristics of the distribution and testing hypotheses. Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2020.1851716.

Examples

 ## For summary data
test2musm(n1=20,n2=25,xbar1=3,xbar2=4,s1=1,s2=1.5,
         paired=FALSE,eqlvar=FALSE,unkwnsigmas=TRUE,
         sigma1=NULL,sigma2=NULL,sdevdif=NULL,alpha=0.05,
         xlab="x",title="Two means summary: Hypothesis testing by Sv-plot2",
         sam1col="grey5",sam2col="grey45",thrcol="black")

test2musm(n1=20,n2=25,xbar1=3,xbar2=4,s1=1.5,s2=1.5,
        paired=FALSE,eqlvar=TRUE,unkwnsigmas=TRUE,
        sigma1=NULL,sigma2=NULL,sdevdif=NULL,alpha=0.05,
        xlab="x",title="Two means summary: Hypothesis testing by Sv-plot2",
        sam1col="grey5",sam2col="grey45",thrcol="black")

test2musm(n1=50,n2=35,xbar1=3,xbar2=4,s1=1,s2=1.5,
         paired=FALSE,eqlvar=FALSE,unkwnsigmas=TRUE,
         sigma1=NULL,sigma2=NULL,sdevdif=NULL,alpha=0.05,
         xlab="x",title="Two means summary: Hypothesis testing by Sv-plot2",
         sam1col="grey5",sam2col="grey45",thrcol="black")

test2musm(n1=50,n2=35,xbar1=3,xbar2=4,s1=1,s2=1.5,
         paired=FALSE,eqlvar=FALSE,unkwnsigmas=FALSE,
         sigma1=2,sigma2=3,sdevdif=NULL,alpha=0.05,
         xlab="x",title="Two means summary: Hypothesis testing by Sv-plot2",
         sam1col="grey5",sam2col="grey45",thrcol="black")

test2musm(n1=20,n2=20,xbar1=3,xbar2=4,s1=1,s2=1.5,
         paired=TRUE,eqlvar=FALSE,unkwnsigmas=TRUE,
         sigma1=NULL,sigma2=NULL,sdevdif=2,alpha=0.05,
         xlab="x",title="Two means summary: Hypothesis testing by Sv-plot2",
         sam1col="grey45",sam2col="grey5",thrcol="black")