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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 computationSat, 13 Dec 2014 14:06:32 +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/13/t1418479953ry3frteq6yntc87.htm/, Retrieved Fri, 01 Nov 2024 00:09:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267106, Retrieved Fri, 01 Nov 2024 00:09:27 +0000
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Estimated Impact102

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.0	0.5
4.1	7.5
4.8	9
5.1	9.5
7.6	8.5
3.1	7
8.1	8
6.3	10
7.9	7
3.8	8.5
6.8	9
2.6	9.5
4.4	4
3.9	6
4.4	8
5.0	5.5
6.0	9.5
3.6	7.5
3.9	7
6.9	7.5
3.7	8
3.5	7
4.1	7
4.3	6
4.1	10
2.5	2.5
6.2	9
5.3	8
5.4	6
4.1	8.5
4.3	6
5.0	9
5.0	8
5.9	9
3.7	5.5
4.0	7
4.8	5.5
5.7	9
4.4	2
4.3	8.5
5.2	9
6.2	8.5
3.4	9
4.7	7.5
5.7	10
4.9	9
6.6	7.5
4.5	6
5.8	10.5
4.5	8.5
5.6	8
1.5	10
7.8	10.5
3.5	6.5
6.3	9.5
3.4	8.5
5.4	7.5
4.7	5
4.3	8
5.1	10
5.4	7
5.2	7.5
5.1	7.5
5.4	9.5
4.6	6
6.0	10
5.1	7
4.2	3
6.4	6
5.1	7
5.8	10
4.8	7
4.2	3.5
5.8	8
4.6	10
4.8	5.5
3.8	6
3.2	6.5
3.9	6.5
4.3	8.5
3.9	4
4.5	9.5
5.2	8
4.9	8.5
5.7	5.5
4.3	7
4.0	9
4.2	8
6.9	10
3.7	8
4.3	6
4.9	8
4.5	5
4.2	9
2.6	4.5
4.1	8.5
6.7	9.5
6.6	8.5
3.4	7.5
3.7	7.5
4.6	5
6.3	7
6.6	8
4.3	5.5
5.0	8.5
4.3	9.5
3.7	7
6.6	8
4.7	8.5
3.1	3.5
3.2	6.5
3.7	6.5
5.6	10.5
4.3	8.5
4.0	8
4.4	10
5.2	10
5.2	9.5
3.3	9
6.1	10
3.3	7.5
4.4	4.5
2.3	4.5
2.7	0.5
3.7	6.5
5.1	4.5
3.9	5.5
3.4	5
4.9	6
4.1	4
4.1	8
7.9	10.5
5.5	6.5
5.7	8
5.3	8.5
4.8	5.5
5.6	7
3.8	5
4.2	3.5
5.1	5
5.3	9
5.1	8.5
5.3	5
5.9	9.5
3.3	3
3.9	1.5
5.5	6
4.2	0.5
3.8	6.5
5.0	7.5
4.4	4.5
4.3	8
5.1	9
4.3	7.5
5.0	8.5
3.5	7
4.2	9.5
3.2	6.5
3.1	9.5
2.0	6
4.7	8
6.0	9.5
4.1	8
4.3	8
5.7	9
3.6	5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267106&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267106&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Two Sample t-test (paired)
Difference: Mean1 - Mean2-2.59036144578313
t-stat-17.1187696299755
df165
p-value2.01839950734961e-38
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.88912870228214,-2.29159418928413]
F-test to compare two variances
F-stat0.312688830959845
df165
p-value3.86311692623955e-13
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.230208553195307,0.424720557294341]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -2.59036144578313 \tabularnewline
t-stat & -17.1187696299755 \tabularnewline
df & 165 \tabularnewline
p-value & 2.01839950734961e-38 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-2.88912870228214,-2.29159418928413] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.312688830959845 \tabularnewline
df & 165 \tabularnewline
p-value & 3.86311692623955e-13 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.230208553195307,0.424720557294341] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267106&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-2.59036144578313[/C][/ROW]
[ROW][C]t-stat[/C][C]-17.1187696299755[/C][/ROW]
[ROW][C]df[/C][C]165[/C][/ROW]
[ROW][C]p-value[/C][C]2.01839950734961e-38[/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][-2.88912870228214,-2.29159418928413][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.312688830959845[/C][/ROW]
[ROW][C]df[/C][C]165[/C][/ROW]
[ROW][C]p-value[/C][C]3.86311692623955e-13[/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][0.230208553195307,0.424720557294341][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267106&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 - Mean2-2.59036144578313
t-stat-17.1187696299755
df165
p-value2.01839950734961e-38
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.88912870228214,-2.29159418928413]
F-test to compare two variances
F-stat0.312688830959845
df165
p-value3.86311692623955e-13
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.230208553195307,0.424720557294341]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean2-2.59036144578313
t-stat-17.1187696299755
df165
p-value2.01839950734961e-38
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.88912870228214,-2.29159418928413]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -2.59036144578313 \tabularnewline
t-stat & -17.1187696299755 \tabularnewline
df & 165 \tabularnewline
p-value & 2.01839950734961e-38 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-2.88912870228214,-2.29159418928413] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267106&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-2.59036144578313[/C][/ROW]
[ROW][C]t-stat[/C][C]-17.1187696299755[/C][/ROW]
[ROW][C]df[/C][C]165[/C][/ROW]
[ROW][C]p-value[/C][C]2.01839950734961e-38[/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][-2.88912870228214,-2.29159418928413][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267106&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267106&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 - Mean2-2.59036144578313
t-stat-17.1187696299755
df165
p-value2.01839950734961e-38
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-2.88912870228214,-2.29159418928413]






Wicoxon rank sum test with continuity correction (paired)
W527.5
p-value8.42902373055074e-25
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.650602409638554
p-value0
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.265060240963855
p-value1.7218891706805e-05

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (paired) \tabularnewline
W & 527.5 \tabularnewline
p-value & 8.42902373055074e-25 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.650602409638554 \tabularnewline
p-value & 0 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.265060240963855 \tabularnewline
p-value & 1.7218891706805e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267106&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]527.5[/C][/ROW]
[ROW][C]p-value[/C][C]8.42902373055074e-25[/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]0.650602409638554[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.265060240963855[/C][/ROW]
[ROW][C]p-value[/C][C]1.7218891706805e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267106&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267106&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)
W527.5
p-value8.42902373055074e-25
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.650602409638554
p-value0
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.265060240963855
p-value1.7218891706805e-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):
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')