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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_twosampletests_mean.wasp
Title produced by softwarePaired and Unpaired Two Samples Tests about the Mean
Date of computationThu, 25 Oct 2012 06:37:54 -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/2012/Oct/25/t1351161493a6kiq2vfpt0gvsv.htm/, Retrieved Tue, 10 Feb 2026 20:13:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=183491, Retrieved Tue, 10 Feb 2026 20:13:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact363

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] [WS5 - Task 3] [2012-10-25 10:37:54] [d0f95aac7f57db23d4da86d121b837fb] [Current]
- R P     [Paired and Unpaired Two Samples Tests about the Mean] [WS5 - Task 5.3] [2012-10-25 10:46:52] [1edfe4f7de973a74350ac08c1294a22c]
-  M        [Paired and Unpaired Two Samples Tests about the Mean] [WS5 taak5.3] [2012-10-29 08:14:15] [74be16979710d4c4e7c6647856088456]
- RMPD    [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 - Task 6] [2012-10-25 11:01:02] [1edfe4f7de973a74350ac08c1294a22c]
- R P       [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 - Task 6.1] [2012-10-25 11:02:27] [1edfe4f7de973a74350ac08c1294a22c]
-   P         [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 - Task 6.2] [2012-10-25 11:03:48] [1edfe4f7de973a74350ac08c1294a22c]
-  M            [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 taak 6.2] [2012-10-29 08:16:19] [74be16979710d4c4e7c6647856088456]
- R PD        [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 - Task 7.1] [2012-10-25 11:10:43] [1edfe4f7de973a74350ac08c1294a22c]
- R             [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 - Task 7.2] [2012-10-25 11:12:33] [1edfe4f7de973a74350ac08c1294a22c]
- RM D            [Two-Way ANOVA] [WS5 - Task 8] [2012-10-25 11:19:53] [1edfe4f7de973a74350ac08c1294a22c]
- RMP               [Two-Way ANOVA] [WS5 taak 8] [2012-10-29 08:19:11] [74be16979710d4c4e7c6647856088456]
-  MP             [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 taak 7.2] [2012-10-29 08:18:18] [74be16979710d4c4e7c6647856088456]
- RMP           [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 taak 7] [2012-10-29 08:17:26] [74be16979710d4c4e7c6647856088456]
-  M          [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [WS5 taak 6.1] [2012-10-29 08:15:20] [74be16979710d4c4e7c6647856088456]
- RM      [Paired and Unpaired Two Samples Tests about the Mean] [WS5 taak 3] [2012-10-29 08:11:07] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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1	0	0	1	2	'S'
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0	0	2	1	2	'S'
0	1	1	0	0	'S'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=183491&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=183491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=183491&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Two Sample t-test (paired)
Difference: Mean1 - Mean2-0.0571428571428571
t-stat-0.626947831813006
df34
p-value0.534881015733881
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.242370800813192,0.128085086527478]
F-test to compare two variances
F-stat0.993464052287582
df34
p-value0.984858744073723
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.501466047576137,1.96817078236551]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -0.0571428571428571 \tabularnewline
t-stat & -0.626947831813006 \tabularnewline
df & 34 \tabularnewline
p-value & 0.534881015733881 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.242370800813192,0.128085086527478] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.993464052287582 \tabularnewline
df & 34 \tabularnewline
p-value & 0.984858744073723 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.501466047576137,1.96817078236551] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=183491&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-0.0571428571428571[/C][/ROW]
[ROW][C]t-stat[/C][C]-0.626947831813006[/C][/ROW]
[ROW][C]df[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]0.534881015733881[/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][-0.242370800813192,0.128085086527478][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.993464052287582[/C][/ROW]
[ROW][C]df[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]0.984858744073723[/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][0.501466047576137,1.96817078236551][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=183491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=183491&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 - Mean2-0.0571428571428571
t-stat-0.626947831813006
df34
p-value0.534881015733881
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.242370800813192,0.128085086527478]
F-test to compare two variances
F-stat0.993464052287582
df34
p-value0.984858744073723
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.501466047576137,1.96817078236551]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean2-0.0571428571428571
t-stat-0.626947831813006
df34
p-value0.534881015733881
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.242370800813192,0.128085086527478]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -0.0571428571428571 \tabularnewline
t-stat & -0.626947831813006 \tabularnewline
df & 34 \tabularnewline
p-value & 0.534881015733881 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.242370800813192,0.128085086527478] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=183491&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-0.0571428571428571[/C][/ROW]
[ROW][C]t-stat[/C][C]-0.626947831813006[/C][/ROW]
[ROW][C]df[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]0.534881015733881[/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][-0.242370800813192,0.128085086527478][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=183491&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=183491&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 - Mean2-0.0571428571428571
t-stat-0.626947831813006
df34
p-value0.534881015733881
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.242370800813192,0.128085086527478]






Wicoxon rank sum test with continuity correction (paired)
W22
p-value0.565318637427207
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0571428571428571
p-value0.999999995591453
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.485714285714286
p-value0.000518798147327804

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (paired) \tabularnewline
W & 22 \tabularnewline
p-value & 0.565318637427207 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.0571428571428571 \tabularnewline
p-value & 0.999999995591453 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.485714285714286 \tabularnewline
p-value & 0.000518798147327804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=183491&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]22[/C][/ROW]
[ROW][C]p-value[/C][C]0.565318637427207[/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]0.0571428571428571[/C][/ROW]
[ROW][C]p-value[/C][C]0.999999995591453[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.485714285714286[/C][/ROW]
[ROW][C]p-value[/C][C]0.000518798147327804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=183491&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=183491&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)
W22
p-value0.565318637427207
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0571428571428571
p-value0.999999995591453
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.485714285714286
p-value0.000518798147327804


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 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')