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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 computationThu, 04 Dec 2014 13:58:09 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/04/t14177017282h28xp5dbylcfnv.htm/, Retrieved Thu, 16 May 2024 21:55:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263284, Retrieved Thu, 16 May 2024 21:55:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

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-       [Paired and Unpaired Two Samples Tests about the Mean] [] [2014-12-04 13:58:09] [18673d63f90870b9c004059cd6229007] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.5	0.5
2.5	7.5
6	9
6.5	9.5
1	8.5
1	7
5.5	8
8.5	10
6.5	7
4.5	8.5
2	9
5	9.5
0.5	4
5	6
5	8
2.5	5.5
5	9.5
5.5	7.5
3.5	7
3	7.5
4	8
0.5	7
6.5	7
4.5	6
7.5	10
5.5	2.5
4	9
7.5	8
7	6
4	8.5
5.5	6
2.5	9
5.5	8
0.5	8
3.5	9
2.5	5.5
4.5	5
4.5	7
4.5	5.5
6	9
2.5	2
5	8.5
0	9
5	8.5
6.5	9
5	7.5
6	10
4.5	9
5.5	7.5
1	6
7.5	10.5
6	8.5
5	8
1	10
5	10.5
6.5	6.5
7	9.5
4.5	8.5
0	7.5
8.5	5
3.5	8
7.5	10
3.5	7
6	7.5
1.5	7.5
9	9.5
3.5	6
3.5	10
4	7
6.5	3
7.5	6
6	7
5	10
5.5	7
3.5	3.5
7.5	8
1	10
6.5	5.5
6.5	6
6.5	6.5
7	6.5
3.5	8.5
1.5	4
4	9.5
7.5	8
4.5	8.5
0	5.5
3.5	7
5.5	9
5	8
4.5	10
2.5	8
7.5	6
7	8
0	5
4.5	9
3	4.5
1.5	8.5
3.5	7
2.5	9.5
5.5	8.5
8	7.5
1	7.5
5	5
4.5	7
3	8
3	5.5
8	8.5
2.5	7.5
7	9.5
0	7
1	8
3.5	8.5
5.5	3.5
5.5	6.5
NA	6.5
NA	10.5
NA	8.5
NA	8
NA	10
NA	10
NA	9.5
NA	9
NA	10
NA	7.5
NA	4.5
NA	4.5
NA	0.5
NA	6.5
NA	4.5
NA	5.5
NA	5
NA	6
NA	4
NA	8
NA	10.5
NA	8.5
NA	6.5
NA	8
NA	8.5
NA	5.5
NA	7
NA	5
NA	3.5
NA	5
NA	9
NA	8.5
NA	5
NA	9.5
NA	3
NA	1.5
NA	6
NA	0.5
NA	6.5
NA	7.5
NA	4.5
NA	8
NA	9
NA	7.5
NA	8.5
NA	7
NA	9.5
NA	6.5
NA	9.5
NA	6
NA	8
NA	9.5
NA	8
NA	8
NA	9
NA	5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263284&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263284&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ yule.wessa.net






Two Sample t-test (unpaired)
Mean of Sample 14.47391304347826
Mean of Sample 27.27777777777778
t-stat-10.774225847355
df284
p-value6.39283926251181e-23
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-3.31610508267213,-2.2916243859269]
F-test to compare two variances
F-stat1.14333291780865
df114
p-value0.426354235815717
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.820885410262745,1.61059028325578]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 4.47391304347826 \tabularnewline
Mean of Sample 2 & 7.27777777777778 \tabularnewline
t-stat & -10.774225847355 \tabularnewline
df & 284 \tabularnewline
p-value & 6.39283926251181e-23 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-3.31610508267213,-2.2916243859269] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 1.14333291780865 \tabularnewline
df & 114 \tabularnewline
p-value & 0.426354235815717 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.820885410262745,1.61059028325578] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263284&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]4.47391304347826[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]7.27777777777778[/C][/ROW]
[ROW][C]t-stat[/C][C]-10.774225847355[/C][/ROW]
[ROW][C]df[/C][C]284[/C][/ROW]
[ROW][C]p-value[/C][C]6.39283926251181e-23[/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][-3.31610508267213,-2.2916243859269][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]1.14333291780865[/C][/ROW]
[ROW][C]df[/C][C]114[/C][/ROW]
[ROW][C]p-value[/C][C]0.426354235815717[/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][0.820885410262745,1.61059028325578][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263284&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 14.47391304347826
Mean of Sample 27.27777777777778
t-stat-10.774225847355
df284
p-value6.39283926251181e-23
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-3.31610508267213,-2.2916243859269]
F-test to compare two variances
F-stat1.14333291780865
df114
p-value0.426354235815717
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.820885410262745,1.61059028325578]






Welch Two Sample t-test (unpaired)
Mean of Sample 14.47391304347826
Mean of Sample 27.27777777777778
t-stat-10.6335610666497
df233.400938016346
p-value8.60683139142399e-22
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-3.32336314039198,-2.28436632820705]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 4.47391304347826 \tabularnewline
Mean of Sample 2 & 7.27777777777778 \tabularnewline
t-stat & -10.6335610666497 \tabularnewline
df & 233.400938016346 \tabularnewline
p-value & 8.60683139142399e-22 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-3.32336314039198,-2.28436632820705] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263284&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]4.47391304347826[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]7.27777777777778[/C][/ROW]
[ROW][C]t-stat[/C][C]-10.6335610666497[/C][/ROW]
[ROW][C]df[/C][C]233.400938016346[/C][/ROW]
[ROW][C]p-value[/C][C]8.60683139142399e-22[/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][-3.32336314039198,-2.28436632820705][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263284&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 14.47391304347826
Mean of Sample 27.27777777777778
t-stat-10.6335610666497
df233.400938016346
p-value8.60683139142399e-22
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-3.32336314039198,-2.28436632820705]






Wicoxon rank sum test with continuity correction (unpaired)
W3431
p-value8.66495011031898e-21
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.501449275362319
p-value1.88737914186277e-15
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.0999237223493517
p-value0.498424428416041

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 3431 \tabularnewline
p-value & 8.66495011031898e-21 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.501449275362319 \tabularnewline
p-value & 1.88737914186277e-15 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.0999237223493517 \tabularnewline
p-value & 0.498424428416041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263284&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]3431[/C][/ROW]
[ROW][C]p-value[/C][C]8.66495011031898e-21[/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]0.501449275362319[/C][/ROW]
[ROW][C]p-value[/C][C]1.88737914186277e-15[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.0999237223493517[/C][/ROW]
[ROW][C]p-value[/C][C]0.498424428416041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263284&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:

Wicoxon rank sum test with continuity correction (unpaired)
W3431
p-value8.66495011031898e-21
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.501449275362319
p-value1.88737914186277e-15
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.0999237223493517
p-value0.498424428416041


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):
par6 <- '0.0'
par5 <- 'unpaired'
par4 <- 'two.sided'
par3 <- '0.95'
par2 <- '2'
par1 <- '1'
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)
a<-table.element(a,paste('Wicoxon rank sum test 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')