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*The author of this computation has been verified*

R Software Module

rwasp_twosampletests_mean.wasp

Title produced by software

Paired and Unpaired Two Samples Tests about the Mean

Date of computation

Tue, 05 Dec 2017 19:49:04 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/05/t15125000168c1sw6hnjlrwsc6.htm/, Retrieved Tue, 14 May 2024 03:39:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308571, Retrieved Tue, 14 May 2024 03:39:04 +0000

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No (this computation is public)

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Estimated Impact

100

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308571&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308571&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308571&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Two Sample t-test (unpaired)
Mean of Sample 1	7.04020100502513
Mean of Sample 2	7.56275303643725
t-stat	-2.8839931951113
df	444
p-value	0.00411760403831991
H0 value	0
Alternative	two.sided
CI Level	0.95
CI	[-0.87864948384218,-0.166454578982062]
F-test to compare two variances
F-stat	0.83928907371866
df	198
p-value	0.198324157398695
H0 value	1
Alternative	two.sided
CI Level	0.95
CI	[0.644934364632108,1.09643216738001]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 7.04020100502513 \tabularnewline
Mean of Sample 2 & 7.56275303643725 \tabularnewline
t-stat & -2.8839931951113 \tabularnewline
df & 444 \tabularnewline
p-value & 0.00411760403831991 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.87864948384218,-0.166454578982062] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.83928907371866 \tabularnewline
df & 198 \tabularnewline
p-value & 0.198324157398695 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.644934364632108,1.09643216738001] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308571&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]7.04020100502513[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]7.56275303643725[/C][/ROW]
[ROW][C]t-stat[/C][C]-2.8839931951113[/C][/ROW]
[ROW][C]df[/C][C]444[/C][/ROW]
[ROW][C]p-value[/C][C]0.00411760403831991[/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][-0.87864948384218,-0.166454578982062][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.83928907371866[/C][/ROW]
[ROW][C]df[/C][C]198[/C][/ROW]
[ROW][C]p-value[/C][C]0.198324157398695[/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][0.644934364632108,1.09643216738001][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308571&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308571&T=1

As an alternative you can also use a QR Code:

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

Two Sample t-test (unpaired)
Mean of Sample 1	7.04020100502513
Mean of Sample 2	7.56275303643725
t-stat	-2.8839931951113
df	444
p-value	0.00411760403831991
H0 value	0
Alternative	two.sided
CI Level	0.95
CI	[-0.87864948384218,-0.166454578982062]
F-test to compare two variances
F-stat	0.83928907371866
df	198
p-value	0.198324157398695
H0 value	1
Alternative	two.sided
CI Level	0.95
CI	[0.644934364632108,1.09643216738001]

Welch Two Sample t-test (unpaired)
Mean of Sample 1	7.04020100502513
Mean of Sample 2	7.56275303643725
t-stat	-2.91130339953295
df	436.69851689237
p-value	0.00378351933272884
H0 value	0
Alternative	two.sided
CI Level	0.95
CI	[-0.875325144594678,-0.169778918229564]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 7.04020100502513 \tabularnewline
Mean of Sample 2 & 7.56275303643725 \tabularnewline
t-stat & -2.91130339953295 \tabularnewline
df & 436.69851689237 \tabularnewline
p-value & 0.00378351933272884 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.875325144594678,-0.169778918229564] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308571&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]7.04020100502513[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]7.56275303643725[/C][/ROW]
[ROW][C]t-stat[/C][C]-2.91130339953295[/C][/ROW]
[ROW][C]df[/C][C]436.69851689237[/C][/ROW]
[ROW][C]p-value[/C][C]0.00378351933272884[/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][-0.875325144594678,-0.169778918229564][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308571&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308571&T=2

As an alternative you can also use a QR Code:

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

Welch Two Sample t-test (unpaired)
Mean of Sample 1	7.04020100502513
Mean of Sample 2	7.56275303643725
t-stat	-2.91130339953295
df	436.69851689237
p-value	0.00378351933272884
H0 value	0
Alternative	two.sided
CI Level	0.95
CI	[-0.875325144594678,-0.169778918229564]

Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)
W	20005
p-value	0.000594870244975189
H0 value	0
Alternative	two.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic	0.170345655402519
p-value	0.00333649087262977
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic	0.170345655402519
p-value	0.00333649087262977

\begin{tabular}{lllllllll}
\hline
Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired) \tabularnewline
W & 20005 \tabularnewline
p-value & 0.000594870244975189 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.170345655402519 \tabularnewline
p-value & 0.00333649087262977 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.170345655402519 \tabularnewline
p-value & 0.00333649087262977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308571&T=3

[TABLE]
[ROW][C]Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]20005[/C][/ROW]
[ROW][C]p-value[/C][C]0.000594870244975189[/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]0.170345655402519[/C][/ROW]
[ROW][C]p-value[/C][C]0.00333649087262977[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.170345655402519[/C][/ROW]
[ROW][C]p-value[/C][C]0.00333649087262977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308571&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308571&T=3

As an alternative you can also use a 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)
W	20005
p-value	0.000594870244975189
H0 value	0
Alternative	two.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic	0.170345655402519
p-value	0.00333649087262977
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic	0.170345655402519
p-value	0.00333649087262977

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0 ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0 ;

R code (references can be found in the software module):

par6 <- '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)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code