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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 computationMon, 15 Nov 2010 22:40:00 +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/2010/Nov/15/t1289860697oub2jos0wvh6jdx.htm/, Retrieved Sat, 27 Apr 2024 14:55:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95146, Retrieved Sat, 27 Apr 2024 14:55:54 +0000
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User-defined keywords
Estimated Impact131

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2	4	4	1
4	3	4	1
4	5	5	1
2	4	3	3
4	2	3	2
3	4	4	2
4	3	3	2
5	2	3	2
4	4	4	2
5	2	3	1
2	4	3	2
4	2	3	4
4	5	4	1
4	3	4	2
4	4	3	2
2	4	3	2
3	3	2	4
2	4	4	2
5	2	3	2
5	3	2	2
2	4	3	4
4	2	2	2
3	4	4	2
2	4	4	2
3	4	4	2
3	3	3	2
1	4	4	1
2	2	3	1
3	4	1	3
2	4	4	1
5	4	4	2
3	2	3	3
4	4	3	2
4	4	4	4
2	4	4	3
1	4	4	2
3	3	3	2
2	4	4	4
4	3	3	4
4	3	4	2
4	3	3	2
2	3	4	2
4	2	3	2
5	2	2	3
2	4	3	
3	2	4	2
1	4	4	1
2	4	3	2
3	3	3	2
2	4	4	2
4	4	4	1
2	3	3	2
4	1	2	3
2	4	4	2
2	4	4	4
2	2	3	2
5	2	2	2
3	4	4	3
4	4	3	2
2	3	3	2
2	3	4	2
4	1	3	2
4	4	4	2
2	2	3	2
3	4	4	2
1	5	4	2
4	3	4	2
3	3	3	2
2	2	3	2
1	4	3	2
4	2	4	3
3	2	3	3
4	2	2	2
2	4	4	4
2	5	4	1
2	4	4	3
2	2	3	2
1	5	5	1
3	2	3	2
5	3	2	3
4	4	3	2
2	3	3	2
5	2	4	1
2	3	4	2
2	4	3	2
5	1	2	2
4	2	4	3
4	2	4	4
3	3	3	3
1	3	4	4
4	2	3	3
4	2	2	2
3	4	3	3
5	3	3	3
3	3	3	3
2	4	4	3
3	4	4	2
5	2	4	3
4	2	3	2
2	4	4	1
4	3	4	2
4	2	3	4
2	4	4	2
3	3	3	2
2	3	4	1
4	4	4	3
2	3	3	2
5	4	3	4
2	3	3	2
4	3	3	2
3	3	3	3
4	2	2	2
4	2	4	4
5	1	2	3
4	2	3	3
4	3	3	2
5	3	3	3
3	3	4	3
3	3	4	2
3	2	3	2
2	4	4	1
3	2	3	2
2	3	3	2
2	3	3	2
1	4	4	1
3	3	2	2
3	3	4	1
2	3	3	4
2	4	3	3
3	4	4	3
3	3	4	1
2	4	4	2
1	5	3	1
4	2	2	2
2	4	4	3
2	4	2	2
3	3	3	4
4	3	4	4
4	4	3	1
4	3	3	4
2	2	3	
4	4	3	3
3	4	4	2
2	4	3	2
2	3	3	2
2	4	2	2
1	4	2	2
3	4	3	2
4	4	4	3
4	3	3	2
2	3	4	4
1	5	3	1

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 Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95146&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95146&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 Ronald Aylmer Fisher' @ 193.190.124.24






Two Sample t-test (unpaired)
Mean of Sample 12.64473684210526
Mean of Sample 22.82236842105263
t-stat-1.47912030601238
df302
p-value0.140150460011566
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.413956062897789,0.0586929050030526]
F-test to compare two variances
F-stat0.722231730275543
df151
p-value0.0464072436443135
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.524339464125045,0.994811010624998]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 2.64473684210526 \tabularnewline
Mean of Sample 2 & 2.82236842105263 \tabularnewline
t-stat & -1.47912030601238 \tabularnewline
df & 302 \tabularnewline
p-value & 0.140150460011566 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.413956062897789,0.0586929050030526] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.722231730275543 \tabularnewline
df & 151 \tabularnewline
p-value & 0.0464072436443135 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.524339464125045,0.994811010624998] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95146&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]2.64473684210526[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]2.82236842105263[/C][/ROW]
[ROW][C]t-stat[/C][C]-1.47912030601238[/C][/ROW]
[ROW][C]df[/C][C]302[/C][/ROW]
[ROW][C]p-value[/C][C]0.140150460011566[/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][-0.413956062897789,0.0586929050030526][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.722231730275543[/C][/ROW]
[ROW][C]df[/C][C]151[/C][/ROW]
[ROW][C]p-value[/C][C]0.0464072436443135[/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][0.524339464125045,0.994811010624998][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95146&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 (unpaired)
Mean of Sample 12.64473684210526
Mean of Sample 22.82236842105263
t-stat-1.47912030601238
df302
p-value0.140150460011566
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.413956062897789,0.0586929050030526]
F-test to compare two variances
F-stat0.722231730275543
df151
p-value0.0464072436443135
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.524339464125045,0.994811010624998]






Welch Two Sample t-test (unpaired)
Mean of Sample 12.64473684210526
Mean of Sample 22.82236842105263
t-stat-1.47912030601238
df294.343392484432
p-value0.140177553328489
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.413980798620476,0.0587176407257394]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 2.64473684210526 \tabularnewline
Mean of Sample 2 & 2.82236842105263 \tabularnewline
t-stat & -1.47912030601238 \tabularnewline
df & 294.343392484432 \tabularnewline
p-value & 0.140177553328489 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.413980798620476,0.0587176407257394] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95146&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]2.64473684210526[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]2.82236842105263[/C][/ROW]
[ROW][C]t-stat[/C][C]-1.47912030601238[/C][/ROW]
[ROW][C]df[/C][C]294.343392484432[/C][/ROW]
[ROW][C]p-value[/C][C]0.140177553328489[/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][-0.413980798620476,0.0587176407257394][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95146&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95146&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 (unpaired)
Mean of Sample 12.64473684210526
Mean of Sample 22.82236842105263
t-stat-1.47912030601238
df294.343392484432
p-value0.140177553328489
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.413980798620476,0.0587176407257394]






Wicoxon rank sum test with continuity correction (unpaired)
W10687.5
p-value0.239111592755362
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.105263157894737
p-value0.368814663974246
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.368421052631579
p-value2.19204321361133e-09

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 10687.5 \tabularnewline
p-value & 0.239111592755362 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.105263157894737 \tabularnewline
p-value & 0.368814663974246 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.368421052631579 \tabularnewline
p-value & 2.19204321361133e-09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95146&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]10687.5[/C][/ROW]
[ROW][C]p-value[/C][C]0.239111592755362[/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]0.105263157894737[/C][/ROW]
[ROW][C]p-value[/C][C]0.368814663974246[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.368421052631579[/C][/ROW]
[ROW][C]p-value[/C][C]2.19204321361133e-09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95146&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95146&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 (unpaired)
W10687.5
p-value0.239111592755362
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.105263157894737
p-value0.368814663974246
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.368421052631579
p-value2.19204321361133e-09


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 3 ; par2 = 4 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.0 ;
Parameters (R input):
par1 = 3 ; par2 = 4 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; 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')