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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 computationThu, 11 Dec 2014 12:55:46 +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/2014/Dec/11/t1418302569qgndoeu5ymzkz6g.htm/, Retrieved Thu, 16 May 2024 16:58:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265944, Retrieved Thu, 16 May 2024 16:58:47 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

Tree of Dependent Computations

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-       [Paired and Unpaired Two Samples Tests about the Mean] [Two sample T-test PR] [2014-12-11 12:55:46] [d71ad52285d92a63edfc83f9fb1da7a1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.8 2
1.6 2.3
2.1 3.5
2.2 1.9
2.3 2.4
2.1 1.9
2.7 2.6
2.1 2.2
2.4 2.1
2.9 1.8
2.2 1.9
2.1 2
2.2 1.7
2.2 1.9
2.7 2
1.9 2.1
2.5 1.8
2.2 2.6
1.9 2.2
2.1 2.2
3.5 2.1
2.1 1.9
2.3 2
2.3 1.7
2.2 2.2
1.9 2.2
1.9 2.3
1.9 2.4
2.1 2.1
1.6 1.9
2 1.7
3.2 1.8
2.3 1.5
2.5 1.9
1.8 1.9
2.8 1.7
2.3 1.9
2 1.9
2.5 1.8
2.3 2.4
1.8 1.8
2.6 1.9
2 1.8
1.6 2.1
1.8 1.9
2.4 2.2
1.9 2
2.1 1.7
2.1 1.7
2.4 1.8
1.8 1.9
2.3 1.8
2.1 3
2.8 2
2 4
2.7 2
2.9 2
2 2
2.5 3
2.1 2
2.3 3
2.3 2
2 4
2.1 1
1 4
1 3
4 3
4 2
4 3
4 3
4 4
2 3
4 4
1 2
3 3
3 3
4 4
3 3
3 3
3 3
4 3
3 1
3 1
2 3
2 2
3 3
1 2
4 2
3 2
4 2
4 3
4 2
4 3
4 2
4 1
3 1
4 4
3 3
4 1
4 2
4 3
3 1
4 3
4 1
4 1
3 2
4 2
1 1
4 2
4 2
3 3
4 4
1 2
4 3
4 2
4 2
4 3
4 2
1 3
4 3
3 1
4 2
3 2
4 3
4 3
4 2
3 2
4 3
4 3
4 1
3 3
4 2
4 2
4 3
4 3
2 3
1 1
4 NA
2 NA
3 NA
4 NA
4 NA
3 NA
4 NA
4 NA
4 NA
2 NA
4 NA
2 NA
3 NA

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265944&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265944&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265944&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'Gertrude Mary Cox' @ cox.wessa.net






Two Sample t-test (unpaired)
Mean of Sample 12.84866666666667
Mean of Sample 22.27737226277372
t-stat5.68065236390786
df285
p-value3.3096126523122e-08
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.373343250375646,0.769245557410242]
F-test to compare two variances
F-stat1.64616409864609
df149
p-value0.00330187296459439
H0 value1
Alternativetwo.sided
CI Level0.95
CI[1.18193028265919,2.28697749238772]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 2.84866666666667 \tabularnewline
Mean of Sample 2 & 2.27737226277372 \tabularnewline
t-stat & 5.68065236390786 \tabularnewline
df & 285 \tabularnewline
p-value & 3.3096126523122e-08 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.373343250375646,0.769245557410242] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 1.64616409864609 \tabularnewline
df & 149 \tabularnewline
p-value & 0.00330187296459439 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [1.18193028265919,2.28697749238772] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265944&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]2.84866666666667[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]2.27737226277372[/C][/ROW]
[ROW][C]t-stat[/C][C]5.68065236390786[/C][/ROW]
[ROW][C]df[/C][C]285[/C][/ROW]
[ROW][C]p-value[/C][C]3.3096126523122e-08[/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][0.373343250375646,0.769245557410242][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]1.64616409864609[/C][/ROW]
[ROW][C]df[/C][C]149[/C][/ROW]
[ROW][C]p-value[/C][C]0.00330187296459439[/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][1.18193028265919,2.28697749238772][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265944&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265944&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 12.84866666666667
Mean of Sample 22.27737226277372
t-stat5.68065236390786
df285
p-value3.3096126523122e-08
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.373343250375646,0.769245557410242]
F-test to compare two variances
F-stat1.64616409864609
df149
p-value0.00330187296459439
H0 value1
Alternativetwo.sided
CI Level0.95
CI[1.18193028265919,2.28697749238772]






Welch Two Sample t-test (unpaired)
Mean of Sample 12.84866666666667
Mean of Sample 22.27737226277372
t-stat5.74405690496389
df278.257353369301
p-value2.41976338837133e-08
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.375508060789264,0.767080746996624]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 2.84866666666667 \tabularnewline
Mean of Sample 2 & 2.27737226277372 \tabularnewline
t-stat & 5.74405690496389 \tabularnewline
df & 278.257353369301 \tabularnewline
p-value & 2.41976338837133e-08 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.375508060789264,0.767080746996624] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265944&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]2.84866666666667[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]2.27737226277372[/C][/ROW]
[ROW][C]t-stat[/C][C]5.74405690496389[/C][/ROW]
[ROW][C]df[/C][C]278.257353369301[/C][/ROW]
[ROW][C]p-value[/C][C]2.41976338837133e-08[/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][0.375508060789264,0.767080746996624][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265944&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265944&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 12.84866666666667
Mean of Sample 22.27737226277372
t-stat5.74405690496389
df278.257353369301
p-value2.41976338837133e-08
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.375508060789264,0.767080746996624]






Wicoxon rank sum test with continuity correction (unpaired)
W14047.5
p-value5.67894933600689e-08
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.321411192214112
p-value7.51851610969467e-07
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.267639902676399
p-value7.0153266826356e-05

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 14047.5 \tabularnewline
p-value & 5.67894933600689e-08 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.321411192214112 \tabularnewline
p-value & 7.51851610969467e-07 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.267639902676399 \tabularnewline
p-value & 7.0153266826356e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265944&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]14047.5[/C][/ROW]
[ROW][C]p-value[/C][C]5.67894933600689e-08[/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]0.321411192214112[/C][/ROW]
[ROW][C]p-value[/C][C]7.51851610969467e-07[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.267639902676399[/C][/ROW]
[ROW][C]p-value[/C][C]7.0153266826356e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265944&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265944&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)
W14047.5
p-value5.67894933600689e-08
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.321411192214112
p-value7.51851610969467e-07
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.267639902676399
p-value7.0153266826356e-05


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; 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')