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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 computationFri, 28 Oct 2011 07:41:35 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/28/t1319802297rnpw29ra3gt70x9.htm/, Retrieved Tue, 10 Feb 2026 09:25:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=137658, Retrieved Tue, 10 Feb 2026 09:25:08 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact450

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Paired and Unpaired Two Samples Tests about the Mean] [treatment A] [2011-10-28 10:53:52] [380049693c521f4999989215fb37aeca]
- R  D    [Paired and Unpaired Two Samples Tests about the Mean] [Treatment T] [2011-10-28 11:41:35] [1b6261517283a6546869240081f8d68e] [Current]
-    D      [Paired and Unpaired Two Samples Tests about the Mean] [Treatment S] [2011-10-28 12:09:01] [380049693c521f4999989215fb37aeca]
-    D        [Paired and Unpaired Two Samples Tests about the Mean] [Treatment S] [2011-10-28 12:48:58] [380049693c521f4999989215fb37aeca]
-    D          [Paired and Unpaired Two Samples Tests about the Mean] [Treatment E] [2011-10-28 12:51:12] [380049693c521f4999989215fb37aeca]
-    D            [Paired and Unpaired Two Samples Tests about the Mean] [Treatment T] [2011-10-28 12:53:01] [380049693c521f4999989215fb37aeca]
-  M                [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 22:19:04] [46d7ccc24e5d35a2decd922dfb3b3a39]
- R               [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 18:06:11] [0748461f029d231b348d2f525a63e360]
- R  D              [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 18:15:32] [0748461f029d231b348d2f525a63e360]
- R  D              [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 18:18:13] [0748461f029d231b348d2f525a63e360]
-                 [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 22:11:13] [46d7ccc24e5d35a2decd922dfb3b3a39]
-               [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 22:14:35] [46d7ccc24e5d35a2decd922dfb3b3a39]
-             [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 22:02:20] [46d7ccc24e5d35a2decd922dfb3b3a39]
- R         [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-03 11:32:35] [0748461f029d231b348d2f525a63e360]
- R  D      [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-03 12:15:41] [0748461f029d231b348d2f525a63e360]
-           [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-11-08 21:57:59] [46d7ccc24e5d35a2decd922dfb3b3a39]
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Dataset

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





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137658&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137658&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Two Sample t-test (paired)
Difference: Mean1 - Mean2-0.108108108108108
t-stat-1.27558560828656
df36
p-value0.210271903264746
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.27999261675031,0.063776400534094]
F-test to compare two variances
F-stat1.08974358974359
df36
p-value0.79794763479162
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.561111459186031,2.11640855296368]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -0.108108108108108 \tabularnewline
t-stat & -1.27558560828656 \tabularnewline
df & 36 \tabularnewline
p-value & 0.210271903264746 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.27999261675031,0.063776400534094] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 1.08974358974359 \tabularnewline
df & 36 \tabularnewline
p-value & 0.79794763479162 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.561111459186031,2.11640855296368] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137658&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-0.108108108108108[/C][/ROW]
[ROW][C]t-stat[/C][C]-1.27558560828656[/C][/ROW]
[ROW][C]df[/C][C]36[/C][/ROW]
[ROW][C]p-value[/C][C]0.210271903264746[/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][-0.27999261675031,0.063776400534094][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]1.08974358974359[/C][/ROW]
[ROW][C]df[/C][C]36[/C][/ROW]
[ROW][C]p-value[/C][C]0.79794763479162[/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][0.561111459186031,2.11640855296368][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137658&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 (paired)
Difference: Mean1 - Mean2-0.108108108108108
t-stat-1.27558560828656
df36
p-value0.210271903264746
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.27999261675031,0.063776400534094]
F-test to compare two variances
F-stat1.08974358974359
df36
p-value0.79794763479162
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.561111459186031,2.11640855296368]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean2-0.108108108108108
t-stat-1.27558560828656
df36
p-value0.210271903264746
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.27999261675031,0.063776400534094]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -0.108108108108108 \tabularnewline
t-stat & -1.27558560828656 \tabularnewline
df & 36 \tabularnewline
p-value & 0.210271903264746 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.27999261675031,0.063776400534094] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137658&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-0.108108108108108[/C][/ROW]
[ROW][C]t-stat[/C][C]-1.27558560828656[/C][/ROW]
[ROW][C]df[/C][C]36[/C][/ROW]
[ROW][C]p-value[/C][C]0.210271903264746[/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][-0.27999261675031,0.063776400534094][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137658&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137658&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 (paired)
Difference: Mean1 - Mean2-0.108108108108108
t-stat-1.27558560828656
df36
p-value0.210271903264746
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.27999261675031,0.063776400534094]






Wicoxon rank sum test with continuity correction (paired)
W16.5
p-value0.227272320646642
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.108108108108108
p-value0.982068356359166
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.540540540540541
p-value4.03603120738838e-05

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (paired) \tabularnewline
W & 16.5 \tabularnewline
p-value & 0.227272320646642 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.108108108108108 \tabularnewline
p-value & 0.982068356359166 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.540540540540541 \tabularnewline
p-value & 4.03603120738838e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137658&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]16.5[/C][/ROW]
[ROW][C]p-value[/C][C]0.227272320646642[/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]0.108108108108108[/C][/ROW]
[ROW][C]p-value[/C][C]0.982068356359166[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.540540540540541[/C][/ROW]
[ROW][C]p-value[/C][C]4.03603120738838e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137658&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137658&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 (paired)
W16.5
p-value0.227272320646642
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.108108108108108
p-value0.982068356359166
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.540540540540541
p-value4.03603120738838e-05


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 0.0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; 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)
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')