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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_twosampletests_mean.wasp
Title produced by softwarePaired and Unpaired Two Samples Tests about the Mean
Date of computationWed, 21 Dec 2016 16:18:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t14823345912sp6x7qxr0uk7dk.htm/, Retrieved Tue, 07 May 2024 02:33:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302388, Retrieved Tue, 07 May 2024 02:33:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50

Tree of Dependent Computations

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-       [Paired and Unpaired Two Samples Tests about the Mean] [Unpaired Two Samp...] [2016-12-21 15:18:32] [bde5266f17215258f6d7c4cd7e531432] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302388&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302388&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Two Sample t-test (unpaired)
Mean of Sample 113.9940828402367
Mean of Sample 216.3668639053254
t-stat-9.44928611962282
df336
p-value6.00816897820134e-19
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.86672076310041,-1.87884136707711]
F-test to compare two variances
F-stat0.699730337078652
df168
p-value0.0211951730808414
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.516583701082409,0.9478087357427]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 13.9940828402367 \tabularnewline
Mean of Sample 2 & 16.3668639053254 \tabularnewline
t-stat & -9.44928611962282 \tabularnewline
df & 336 \tabularnewline
p-value & 6.00816897820134e-19 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-2.86672076310041,-1.87884136707711] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.699730337078652 \tabularnewline
df & 168 \tabularnewline
p-value & 0.0211951730808414 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.516583701082409,0.9478087357427] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302388&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]13.9940828402367[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]16.3668639053254[/C][/ROW]
[ROW][C]t-stat[/C][C]-9.44928611962282[/C][/ROW]
[ROW][C]df[/C][C]336[/C][/ROW]
[ROW][C]p-value[/C][C]6.00816897820134e-19[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][-2.86672076310041,-1.87884136707711][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.699730337078652[/C][/ROW]
[ROW][C]df[/C][C]168[/C][/ROW]
[ROW][C]p-value[/C][C]0.0211951730808414[/C][/ROW]
[ROW][C]H0 value[/C][C]1[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][0.516583701082409,0.9478087357427][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302388&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Two Sample t-test (unpaired)
Mean of Sample 113.9940828402367
Mean of Sample 216.3668639053254
t-stat-9.44928611962282
df336
p-value6.00816897820134e-19
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.86672076310041,-1.87884136707711]
F-test to compare two variances
F-stat0.699730337078652
df168
p-value0.0211951730808414
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.516583701082409,0.9478087357427]






Welch Two Sample t-test (unpaired)
Mean of Sample 113.9940828402367
Mean of Sample 216.3668639053254
t-stat-9.44928611962282
df325.831521888727
p-value6.8933375296191e-19
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.86677649089756,-1.87878563927996]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 13.9940828402367 \tabularnewline
Mean of Sample 2 & 16.3668639053254 \tabularnewline
t-stat & -9.44928611962282 \tabularnewline
df & 325.831521888727 \tabularnewline
p-value & 6.8933375296191e-19 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-2.86677649089756,-1.87878563927996] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302388&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]13.9940828402367[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]16.3668639053254[/C][/ROW]
[ROW][C]t-stat[/C][C]-9.44928611962282[/C][/ROW]
[ROW][C]df[/C][C]325.831521888727[/C][/ROW]
[ROW][C]p-value[/C][C]6.8933375296191e-19[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][-2.86677649089756,-1.87878563927996][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302388&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302388&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Welch Two Sample t-test (unpaired)
Mean of Sample 113.9940828402367
Mean of Sample 216.3668639053254
t-stat-9.44928611962282
df325.831521888727
p-value6.8933375296191e-19
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.86677649089756,-1.87878563927996]






Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)
W6280
p-value3.01073253586711e-19
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.443786982248521
p-value6.99440505513849e-15
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.136094674556213
p-value0.0874127742374106

\begin{tabular}{lllllllll}
\hline
Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired) \tabularnewline
W & 6280 \tabularnewline
p-value & 3.01073253586711e-19 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.443786982248521 \tabularnewline
p-value & 6.99440505513849e-15 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.136094674556213 \tabularnewline
p-value & 0.0874127742374106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302388&T=3

[TABLE]
[ROW][C]Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]6280[/C][/ROW]
[ROW][C]p-value[/C][C]3.01073253586711e-19[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributions of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.443786982248521[/C][/ROW]
[ROW][C]p-value[/C][C]6.99440505513849e-15[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.136094674556213[/C][/ROW]
[ROW][C]p-value[/C][C]0.0874127742374106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302388&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302388&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)
W6280
p-value3.01073253586711e-19
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.443786982248521
p-value6.99440505513849e-15
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.136094674556213
p-value0.0874127742374106


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.0 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #column number of first sample
par2 <- as.numeric(par2) #column number of second sample
par3 <- as.numeric(par3) #confidence (= 1 - alpha)
if (par5 == 'unpaired') paired <- FALSE else paired <- TRUE
par6 <- as.numeric(par6) #H0
z <- t(y)
if (par1 == par2) stop('Please, select two different column numbers')
if (par1 < 1) stop('Please, select a column number greater than zero for the first sample')
if (par2 < 1) stop('Please, select a column number greater than zero for the second sample')
if (par1 > length(z[1,])) stop('The column number for the first sample should be smaller')
if (par2 > length(z[1,])) stop('The column number for the second sample should be smaller')
if (par3 <= 0) stop('The confidence level should be larger than zero')
if (par3 >= 1) stop('The confidence level should be smaller than zero')
(r.t <- t.test(z[,par1],z[,par2],var.equal=TRUE,alternative=par4,paired=paired,mu=par6,conf.level=par3))
(v.t <- var.test(z[,par1],z[,par2],conf.level=par3))
(r.w <- t.test(z[,par1],z[,par2],var.equal=FALSE,alternative=par4,paired=paired,mu=par6,conf.level=par3))
(w.t <- wilcox.test(z[,par1],z[,par2],alternative=par4,paired=paired,mu=par6,conf.level=par3))
(ks.t <- ks.test(z[,par1],z[,par2],alternative=par4))
m1 <- mean(z[,par1],na.rm=T)
m2 <- mean(z[,par2],na.rm=T)
mdiff <- m1 - m2
newsam1 <- z[!is.na(z[,par1]),par1]
newsam2 <- z[,par2]+mdiff
newsam2 <- newsam2[!is.na(newsam2)]
(ks1.t <- ks.test(newsam1,newsam2,alternative=par4))
mydf <- data.frame(cbind(z[,par1],z[,par2]))
colnames(mydf) <- c('Variable 1','Variable 2')
bitmap(file='test1.png')
boxplot(mydf, notch=TRUE, ylab='value',main=main)
dev.off()
bitmap(file='test2.png')
qqnorm(z[,par1],main='Normal QQplot - Variable 1')
qqline(z[,par1])
dev.off()
bitmap(file='test3.png')
qqnorm(z[,par2],main='Normal QQplot - Variable 2')
qqline(z[,par2])
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Two Sample t-test (',par5,')',sep=''),2,TRUE)
a<-table.row.end(a)
if(!paired){
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 1',header=TRUE)
a<-table.element(a,r.t$estimate[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 2',header=TRUE)
a<-table.element(a,r.t$estimate[[2]])
a<-table.row.end(a)
} else {
a<-table.row.start(a)
a<-table.element(a,'Difference: Mean1 - Mean2',header=TRUE)
a<-table.element(a,r.t$estimate)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,'t-stat',header=TRUE)
a<-table.element(a,r.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'df',header=TRUE)
a<-table.element(a,r.t$parameter[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,r.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,r.t$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,r.t$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI Level',header=TRUE)
a<-table.element(a,attr(r.t$conf.int,'conf.level'))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI',header=TRUE)
a<-table.element(a,paste('[',r.t$conf.int[1],',',r.t$conf.int[2],']',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'F-test to compare two variances',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'F-stat',header=TRUE)
a<-table.element(a,v.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'df',header=TRUE)
a<-table.element(a,v.t$parameter[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,v.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,v.t$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,v.t$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI Level',header=TRUE)
a<-table.element(a,attr(v.t$conf.int,'conf.level'))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI',header=TRUE)
a<-table.element(a,paste('[',v.t$conf.int[1],',',v.t$conf.int[2],']',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Welch Two Sample t-test (',par5,')',sep=''),2,TRUE)
a<-table.row.end(a)
if(!paired){
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 1',header=TRUE)
a<-table.element(a,r.w$estimate[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 2',header=TRUE)
a<-table.element(a,r.w$estimate[[2]])
a<-table.row.end(a)
} else {
a<-table.row.start(a)
a<-table.element(a,'Difference: Mean1 - Mean2',header=TRUE)
a<-table.element(a,r.w$estimate)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,'t-stat',header=TRUE)
a<-table.element(a,r.w$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'df',header=TRUE)
a<-table.element(a,r.w$parameter[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,r.w$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,r.w$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,r.w$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI Level',header=TRUE)
a<-table.element(a,attr(r.w$conf.int,'conf.level'))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI',header=TRUE)
a<-table.element(a,paste('[',r.w$conf.int[1],',',r.w$conf.int[2],']',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
myWlabel <- 'Wilcoxon Signed-Rank Test'
if (par5=='unpaired') myWlabel = 'Wilcoxon Rank-Sum Test (Mann–Whitney U test)'
a<-table.element(a,paste(myWlabel,' with continuity correction (',par5,')',sep=''),2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'W',header=TRUE)
a<-table.element(a,w.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,w.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,w.t$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,w.t$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kolmogorov-Smirnov Test to compare Distributions of two Samples',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'KS Statistic',header=TRUE)
a<-table.element(a,ks.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,ks.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'KS Statistic',header=TRUE)
a<-table.element(a,ks1.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,ks1.t$p.value)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')