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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 computationTue, 01 Dec 2015 12:11:00 +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/2015/Dec/01/t1448972041xxr0j7kr50df4r5.htm/, Retrieved Thu, 31 Oct 2024 22:46:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284699, Retrieved Thu, 31 Oct 2024 22:46:49 +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] [two sample t-test] [2015-12-01 12:11:00] [002d4648fc88037d8570a4a28cacbbc2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.5 80.8 2.3
6.8 83.7 1.9
6.8 94.2 0.6
6.5 86.2 0.6
6.2 89 -0.4
6.2 94.7 -1.1
6.6 81.9 -1.7
6.7 80.2 -0.8
6.5 96.5 -1.2
6.4 95.6 -1
6.5 91.9 -0.1
6.8 89.9 0.3
7.1 86.5 0.6
7.2 94.6 0.7
7.1 107.1 1.7
7 98.3 1.8
6.9 94.6 2.3
6.9 111.1 2.5
7.4 91.7 2.6
7.3 91.3 2.3
7 110.7 2.9
6.8 106.4 3
6.5 105.1 2.9
6.4 102.6 3.1
6.3 97.5 3.2
6 103.7 3.4
5.9 124.5 3.5
5.7 103.8 3.4
5.7 111.8 3.4
5.7 108.4 3.7
6.2 91.7 3.8
6.4 100.9 3.6
6.2 114.6 3.6
6.2 106.6 3.6
6.1 103.5 3.9
6.1 101.3 3.5
6.2 97.6 3.7
6.1 100.7 3.7
6.1 118.2 3.4
6.2 98.6 3.2
6.2 101.5 2.8
6.2 109.8 2.3
6.4 96.8 2.3
6.4 97.2 2.9
6.4 107 2.8
6.7 111.3 2.8
6.9 104.6 2.3
7.1 98.7 2.2
7.3 97 1.5
7.2 95.5 1.2
7.1 107.7 1.1
6.9 106.9 1
6.8 105.5 1.2
6.7 110 1.6
7.2 103.4 1.5
7.2 92.8 1
7.1 109 0.9
7.1 115.1 0.6
7 105.4 0.8
7.1 102.3 1
7.3 100.4 1.1
7.2 103.3 1
7.1 111.3 0.9
7 109.9 0.6
6.9 106.7 0.4
7 114.3 0.3
7.5 101.5 0.3
7.6 92.5 0
7.5 119 -0.1
7.3 117 0.1
7.3 105.3 -0.1
7.4 105.5 -0.4
7.7 100.4 -0.7
7.8 98.6 -0.4
7.7 118.5 -0.4
7.5 110.1 0.3
7.3 102.8 0.6
7.3 116.5 0.6
7.6 100.5 0.5
7.6 96.8 0.9

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284699&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284699&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284699&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'Gwilym Jenkins' @ jenkins.wessa.net






Two Sample t-test (paired)
Difference: Mean1 - Mean2-95.1575
t-stat-91.1762875139516
df79
p-value8.26233910611708e-82
H0 value0
Alternativetwo.sided
CI Level0.9
CI[-96.8945461847405,-93.4204538152595]
F-test to compare two variances
F-stat0.00323829278490415
df79
p-value1.91613999456405e-76
H0 value1
Alternativetwo.sided
CI Level0.9
CI[0.00223153195889104,0.00469925609578702]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -95.1575 \tabularnewline
t-stat & -91.1762875139516 \tabularnewline
df & 79 \tabularnewline
p-value & 8.26233910611708e-82 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.9 \tabularnewline
CI & [-96.8945461847405,-93.4204538152595] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.00323829278490415 \tabularnewline
df & 79 \tabularnewline
p-value & 1.91613999456405e-76 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.9 \tabularnewline
CI & [0.00223153195889104,0.00469925609578702] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284699&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-95.1575[/C][/ROW]
[ROW][C]t-stat[/C][C]-91.1762875139516[/C][/ROW]
[ROW][C]df[/C][C]79[/C][/ROW]
[ROW][C]p-value[/C][C]8.26233910611708e-82[/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]0.9[/C][/ROW]
[ROW][C]CI[/C][C][-96.8945461847405,-93.4204538152595][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.00323829278490415[/C][/ROW]
[ROW][C]df[/C][C]79[/C][/ROW]
[ROW][C]p-value[/C][C]1.91613999456405e-76[/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]0.9[/C][/ROW]
[ROW][C]CI[/C][C][0.00223153195889104,0.00469925609578702][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284699&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284699&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 - Mean2-95.1575
t-stat-91.1762875139516
df79
p-value8.26233910611708e-82
H0 value0
Alternativetwo.sided
CI Level0.9
CI[-96.8945461847405,-93.4204538152595]
F-test to compare two variances
F-stat0.00323829278490415
df79
p-value1.91613999456405e-76
H0 value1
Alternativetwo.sided
CI Level0.9
CI[0.00223153195889104,0.00469925609578702]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean2-95.1575
t-stat-91.1762875139516
df79
p-value8.26233910611708e-82
H0 value0
Alternativetwo.sided
CI Level0.9
CI[-96.8945461847405,-93.4204538152595]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -95.1575 \tabularnewline
t-stat & -91.1762875139516 \tabularnewline
df & 79 \tabularnewline
p-value & 8.26233910611708e-82 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.9 \tabularnewline
CI & [-96.8945461847405,-93.4204538152595] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284699&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-95.1575[/C][/ROW]
[ROW][C]t-stat[/C][C]-91.1762875139516[/C][/ROW]
[ROW][C]df[/C][C]79[/C][/ROW]
[ROW][C]p-value[/C][C]8.26233910611708e-82[/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]0.9[/C][/ROW]
[ROW][C]CI[/C][C][-96.8945461847405,-93.4204538152595][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284699&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284699&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 - Mean2-95.1575
t-stat-91.1762875139516
df79
p-value8.26233910611708e-82
H0 value0
Alternativetwo.sided
CI Level0.9
CI[-96.8945461847405,-93.4204538152595]






Wilcoxon Signed-Rank Test with continuity correction (paired)
W0
p-value7.99671255833361e-15
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic1
p-value0
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.475
p-value2.89744097603517e-08

\begin{tabular}{lllllllll}
\hline
Wilcoxon Signed-Rank Test with continuity correction (paired) \tabularnewline
W & 0 \tabularnewline
p-value & 7.99671255833361e-15 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 1 \tabularnewline
p-value & 0 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.475 \tabularnewline
p-value & 2.89744097603517e-08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284699&T=3

[TABLE]
[ROW][C]Wilcoxon Signed-Rank Test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]0[/C][/ROW]
[ROW][C]p-value[/C][C]7.99671255833361e-15[/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]1[/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]0.475[/C][/ROW]
[ROW][C]p-value[/C][C]2.89744097603517e-08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284699&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284699&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)
W0
p-value7.99671255833361e-15
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic1
p-value0
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.475
p-value2.89744097603517e-08


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.90 ; par4 = two.sided ; par5 = paired ; par6 = 0.0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.90 ; 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 <- '0.90'
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)
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')