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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 computationFri, 04 Dec 2015 13:13:39 +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/Dec/04/t1449235183y5js6t9664enpoj.htm/, Retrieved Thu, 16 May 2024 11:48:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285134, Retrieved Thu, 16 May 2024 11:48:07 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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-       [Paired and Unpaired Two Samples Tests about the Mean] [Unnpaired two sam...] [2015-12-04 13:13:39] [ff6d1090be03ecb1ea559b1add2eb09a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
386 403
359 436
407 420
387 408
349 401
358 401
397 394
375 396
332 346
386 417
391 374
399 394
374 415
370 363
370 376
244 414
430 379
416 412
367 412
376 379
376 472
438 439
249 409
385 419
393 417
396 413
412 388
394 409
270 416
383 440
407 416
417 403
366 395
405 404
374 398
394 402
403 418
368 446
395 449
353 389
373 395
371 377
326 381
359 388
385 222
376 400
363 378
351 393
357 380
307 376
378 427
354 365

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285134&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285134&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'Gwilym Jenkins' @ jenkins.wessa.net






Two Sample t-test (unpaired)
Mean of Sample 1399.307692307692
Mean of Sample 2372.134615384615
t-stat3.7938841987451
df102
p-value0.000125856958229604
H0 value0
Alternativegreater
CI Level0.95
CI[15.2840991469808,Inf]
F-test to compare two variances
F-stat0.79891876909541
df51
p-value0.425532099699096
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.458599417440592,1.39178371218845]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 399.307692307692 \tabularnewline
Mean of Sample 2 & 372.134615384615 \tabularnewline
t-stat & 3.7938841987451 \tabularnewline
df & 102 \tabularnewline
p-value & 0.000125856958229604 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & greater \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [15.2840991469808,Inf] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.79891876909541 \tabularnewline
df & 51 \tabularnewline
p-value & 0.425532099699096 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.458599417440592,1.39178371218845] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285134&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]399.307692307692[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]372.134615384615[/C][/ROW]
[ROW][C]t-stat[/C][C]3.7938841987451[/C][/ROW]
[ROW][C]df[/C][C]102[/C][/ROW]
[ROW][C]p-value[/C][C]0.000125856958229604[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]greater[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][15.2840991469808,Inf][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.79891876909541[/C][/ROW]
[ROW][C]df[/C][C]51[/C][/ROW]
[ROW][C]p-value[/C][C]0.425532099699096[/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][0.458599417440592,1.39178371218845][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285134&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 1399.307692307692
Mean of Sample 2372.134615384615
t-stat3.7938841987451
df102
p-value0.000125856958229604
H0 value0
Alternativegreater
CI Level0.95
CI[15.2840991469808,Inf]
F-test to compare two variances
F-stat0.79891876909541
df51
p-value0.425532099699096
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.458599417440592,1.39178371218845]






Welch Two Sample t-test (unpaired)
Mean of Sample 1399.307692307692
Mean of Sample 2372.134615384615
t-stat3.7938841987451
df100.741284878221
p-value0.000126622244198244
H0 value0
Alternativegreater
CI Level0.95
CI[15.2827374253425,Inf]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 399.307692307692 \tabularnewline
Mean of Sample 2 & 372.134615384615 \tabularnewline
t-stat & 3.7938841987451 \tabularnewline
df & 100.741284878221 \tabularnewline
p-value & 0.000126622244198244 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & greater \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [15.2827374253425,Inf] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285134&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]399.307692307692[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]372.134615384615[/C][/ROW]
[ROW][C]t-stat[/C][C]3.7938841987451[/C][/ROW]
[ROW][C]df[/C][C]100.741284878221[/C][/ROW]
[ROW][C]p-value[/C][C]0.000126622244198244[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]greater[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][15.2827374253425,Inf][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285134&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285134&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 1399.307692307692
Mean of Sample 2372.134615384615
t-stat3.7938841987451
df100.741284878221
p-value0.000126622244198244
H0 value0
Alternativegreater
CI Level0.95
CI[15.2827374253425,Inf]






Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)
W2053
p-value2.62058445974213e-06
H0 value0
Alternativegreater
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0192307692307692
p-value0.980952962360203
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.173076923076923
p-value0.21062156056042

\begin{tabular}{lllllllll}
\hline
Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired) \tabularnewline
W & 2053 \tabularnewline
p-value & 2.62058445974213e-06 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & greater \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.0192307692307692 \tabularnewline
p-value & 0.980952962360203 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.173076923076923 \tabularnewline
p-value & 0.21062156056042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285134&T=3

[TABLE]
[ROW][C]Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]2053[/C][/ROW]
[ROW][C]p-value[/C][C]2.62058445974213e-06[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]greater[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributions of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.0192307692307692[/C][/ROW]
[ROW][C]p-value[/C][C]0.980952962360203[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.173076923076923[/C][/ROW]
[ROW][C]p-value[/C][C]0.21062156056042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285134&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285134&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 Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)
W2053
p-value2.62058445974213e-06
H0 value0
Alternativegreater
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0192307692307692
p-value0.980952962360203
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.173076923076923
p-value0.21062156056042


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = 0.95 ; par4 = less ; par5 = unpaired ; par6 = 0 ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = 0.95 ; par4 = greater ; par5 = unpaired ; par6 = 0 ;
R code (references can be found in the software module):
par6 <- '0'
par5 <- 'unpaired'
par4 <- 'greater'
par3 <- '0.95'
par2 <- '1'
par1 <- '2'
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')