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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 computationSun, 22 Nov 2015 14:33:46 +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/2015/Nov/22/t14482028475acyzxogql6s21i.htm/, Retrieved Tue, 21 May 2024 23:44:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283811, Retrieved Tue, 21 May 2024 23:44:01 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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] [] [2015-11-22 14:33:46] [4bfd98e85da8d65970e2f1f883f9da72] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26 21 21
20 16 15
19 19 18
19 18 11
20 16 8
25 23 19
25 17 4
22 12 20
26 19 16
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26 27 23
21 17 11
13 8 9
26 25 24
20 26 5
22 13 15
14 19 5
21 15 19
7 5 6
23 16 13
17 14 11
25 24 17
25 24 17
19 9 5
20 19 9
23 19 15
22 25 17
22 19 17
21 18 20
15 15 12
20 12 7
22 21 16
18 12 7
20 15 14
28 28 24
22 25 15
18 19 15
23 20 10
20 24 14
25 26 18
26 25 12
15 12 9
17 12 9
23 15 8
21 17 18
13 14 10
18 16 17
19 11 14
22 20 16
16 11 10
24 22 19
18 20 10
20 19 14
24 17 10
14 21 4
22 23 19
24 18 9
18 17 12
21 27 16
23 25 11
17 19 18
22 22 11
24 24 24
21 20 17
22 19 18
16 11 9
21 22 19
23 22 18
22 16 12
24 20 23
24 24 22
16 16 14
16 16 14
21 22 16
26 24 23
15 16 7
25 27 10
18 11 12
23 21 12
20 20 12
17 20 17
25 27 21
24 20 16
17 12 11
19 8 14
20 21 13
15 18 9
27 24 19
22 16 13
23 18 19
16 20 13
19 20 13
25 19 13
19 17 14
19 16 12
26 26 22
21 15 11
20 22 5
24 17 18
22 23 19
20 21 14
18 19 15
18 14 12
24 17 19
24 12 15
22 24 17
23 18 8
22 20 10
20 16 12
18 20 12
25 22 20
18 12 12
16 16 12
20 17 14
19 22 6
15 12 10
19 14 18
19 23 18
16 15 7
17 17 18
28 28 9
23 20 17
25 23 22
20 13 11
17 18 15
23 23 17
16 19 15
23 23 22
11 12 9
18 16 13
24 23 20
23 13 14
21 22 14
16 18 12
24 23 20
23 20 20
18 10 8
20 17 17
9 18 9
24 15 18
25 23 22
20 17 10
21 17 13
25 22 15
22 20 18
21 20 18
21 19 12
22 18 12
27 22 20
24 20 12
24 22 16
21 18 16
18 16 18
16 16 16
22 16 13
20 16 17
18 17 13
20 18 17

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283811&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283811&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Two Sample t-test (paired)
Difference: Mean1 - Mean22.10493827160494
t-stat-13.432105132597
df161
p-value4.50382339668795e-28
H0 value6
Alternativetwo.sided
CI Level0.95
CI[1.53228049807096,2.67759604513891]
F-test to compare two variances
F-stat0.678766085046185
df161
p-value0.0144106285826109
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.497823877510296,0.925474688986562]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & 2.10493827160494 \tabularnewline
t-stat & -13.432105132597 \tabularnewline
df & 161 \tabularnewline
p-value & 4.50382339668795e-28 \tabularnewline
H0 value & 6 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [1.53228049807096,2.67759604513891] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.678766085046185 \tabularnewline
df & 161 \tabularnewline
p-value & 0.0144106285826109 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.497823877510296,0.925474688986562] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283811&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]2.10493827160494[/C][/ROW]
[ROW][C]t-stat[/C][C]-13.432105132597[/C][/ROW]
[ROW][C]df[/C][C]161[/C][/ROW]
[ROW][C]p-value[/C][C]4.50382339668795e-28[/C][/ROW]
[ROW][C]H0 value[/C][C]6[/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][1.53228049807096,2.67759604513891][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.678766085046185[/C][/ROW]
[ROW][C]df[/C][C]161[/C][/ROW]
[ROW][C]p-value[/C][C]0.0144106285826109[/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][0.497823877510296,0.925474688986562][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283811&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 - Mean22.10493827160494
t-stat-13.432105132597
df161
p-value4.50382339668795e-28
H0 value6
Alternativetwo.sided
CI Level0.95
CI[1.53228049807096,2.67759604513891]
F-test to compare two variances
F-stat0.678766085046185
df161
p-value0.0144106285826109
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.497823877510296,0.925474688986562]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean22.10493827160494
t-stat-13.432105132597
df161
p-value4.50382339668795e-28
H0 value6
Alternativetwo.sided
CI Level0.95
CI[1.53228049807096,2.67759604513891]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & 2.10493827160494 \tabularnewline
t-stat & -13.432105132597 \tabularnewline
df & 161 \tabularnewline
p-value & 4.50382339668795e-28 \tabularnewline
H0 value & 6 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [1.53228049807096,2.67759604513891] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283811&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]2.10493827160494[/C][/ROW]
[ROW][C]t-stat[/C][C]-13.432105132597[/C][/ROW]
[ROW][C]df[/C][C]161[/C][/ROW]
[ROW][C]p-value[/C][C]4.50382339668795e-28[/C][/ROW]
[ROW][C]H0 value[/C][C]6[/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][1.53228049807096,2.67759604513891][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283811&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 - Mean22.10493827160494
t-stat-13.432105132597
df161
p-value4.50382339668795e-28
H0 value6
Alternativetwo.sided
CI Level0.95
CI[1.53228049807096,2.67759604513891]






Wilcoxon Signed-Rank Test with continuity correction (paired)
W690.5
p-value5.96661086574072e-21
H0 value6
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.228395061728395
p-value0.00042753683763197
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.12962962962963
p-value0.131419728340629

\begin{tabular}{lllllllll}
\hline
Wilcoxon Signed-Rank Test with continuity correction (paired) \tabularnewline
W & 690.5 \tabularnewline
p-value & 5.96661086574072e-21 \tabularnewline
H0 value & 6 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.228395061728395 \tabularnewline
p-value & 0.00042753683763197 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.12962962962963 \tabularnewline
p-value & 0.131419728340629 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283811&T=3

[TABLE]
[ROW][C]Wilcoxon Signed-Rank Test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]690.5[/C][/ROW]
[ROW][C]p-value[/C][C]5.96661086574072e-21[/C][/ROW]
[ROW][C]H0 value[/C][C]6[/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]0.228395061728395[/C][/ROW]
[ROW][C]p-value[/C][C]0.00042753683763197[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.12962962962963[/C][/ROW]
[ROW][C]p-value[/C][C]0.131419728340629[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283811&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283811&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 Signed-Rank Test with continuity correction (paired)
W690.5
p-value5.96661086574072e-21
H0 value6
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.228395061728395
p-value0.00042753683763197
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.12962962962963
p-value0.131419728340629


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 6 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 6 ;
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')