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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, 24 Nov 2014 10:01:34 +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/Nov/24/t1416823335jdgdc38lre2kxjf.htm/, Retrieved Sun, 19 May 2024 13:07:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258151, Retrieved Sun, 19 May 2024 13:07:05 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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-       [Paired and Unpaired Two Samples Tests about the Mean] [paper 7] [2014-11-24 10:01:34] [627bde65e5570be47fd7fc8a9f75ea40] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9	12.2
7.4	12.3
12.8	12.4
14.8	12.5
12.0	12.6
6.3	12.7
11.3	12.8
9.3	12.9
10.0	12.10
10.8	12.11
13.4	12.12
11.5	12.13
8.3	12.14
11.7	12.15
10.4	12.16
11.8	12.17
11.3	12.18
12.7	12.19
5.7	12.20
8.0	12.21
12.5	12.22
7.6	12.23
9.2	12.24
11.1	12.25
12.2	12.26
12.3	12.27
11.4	12.28
8.8	12.29
12.6	12.30
13.0	12.31
13.2	12.32
9.9	12.33
10.5	12.34
13.4	12.35
10.9	12.36
10.3	12.37
11.4	12.38
8.6	12.39
13.2	12.40
8.8	12.41
9.0	12.42
10.3	12.43
8.5	12.44
13.5	12.45
4.9	12.46
6.4	12.47
9.6	12.48
11.6	12.49
16.6	12.50
19.1	12.51
13.35	12.52
18.4	12.53
16.15	12.54
18.4	12.55
15.6	12.56
16.35	12.57
17.65	12.58
11.7	12.59
14.35	12.60
14.75	12.61
9.9	12.62
16.85	12.63
15.6	12.64
14.85	12.65
11.75	12.66
18.45	12.67
17.1	12.68
19.9	12.69
18.45	12.70
15	12.71
11.35	12.72
18.1	12.73
19.1	12.74
7.6	12.75
13.4	12.76
13.9	12.77
15.25	12.78
16.1	12.79
17.35	12.80
13.15	12.81
12.15	12.82
18.2	12.83
13.6	12.84
14.75	12.85
14.1	12.86
14.9	12.87
16.25	12.88
13.6	12.89
15.65	12.90
14.6	12.91
19.2	12.92
11.9	12.93
13.2	12.94
16.35	12.95
14.35	12.96
15.65	12.97
17.75	12.98
7.65	12.99
19.3	12.100
15.2	12.101
17.1	12.102
19.05	12.103
18.55	12.104
19.1	12.105
11.85	12.106
13.35	12.107
11.4	12.108
19.9	12.109
17.6	12.110
16.1	12.111
11.95	12.112
15.15	12.113
16.85	12.114
7.7	12.115
12.6	12.116
12.35	12.117
16.65	12.118
13.95	12.119
15.7	12.120
15.35	12.121
15.1	12.122
17.75	12.123
14.6	12.124
16.65	12.125
	12.126
	12.127
	12.128
	12.129
	12.130
	12.131
	12.132
	12.133
	12.134
	12.135
	12.136
	12.137
	12.138
	12.139
	12.140
	12.141
	12.142
	12.143
	12.144
	12.145
	12.146
	12.147
	12.148
	12.149
	12.150
	12.151
	12.152
	12.153
	12.154
	12.155
	12.156
	12.157
	12.158
	12.159
	12.160
	12.161
	12.162
	12.163
	12.164

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=258151&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=258151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258151&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 (unpaired)
Mean of Sample 113.1552147239264
Mean of Sample 212.1934355828221
t-stat3.7628541746137
df324
p-value0.000199358083597787
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.458937335377759,1.46462094683083]
F-test to compare two variances
F-stat8.49432745996265
df162
p-value0
H0 value1
Alternativetwo.sided
CI Level0.95
CI[6.2359659933476,11.5705568430052]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 13.1552147239264 \tabularnewline
Mean of Sample 2 & 12.1934355828221 \tabularnewline
t-stat & 3.7628541746137 \tabularnewline
df & 324 \tabularnewline
p-value & 0.000199358083597787 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.458937335377759,1.46462094683083] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 8.49432745996265 \tabularnewline
df & 162 \tabularnewline
p-value & 0 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [6.2359659933476,11.5705568430052] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258151&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]13.1552147239264[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]12.1934355828221[/C][/ROW]
[ROW][C]t-stat[/C][C]3.7628541746137[/C][/ROW]
[ROW][C]df[/C][C]324[/C][/ROW]
[ROW][C]p-value[/C][C]0.000199358083597787[/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][0.458937335377759,1.46462094683083][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]8.49432745996265[/C][/ROW]
[ROW][C]df[/C][C]162[/C][/ROW]
[ROW][C]p-value[/C][C]0[/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][6.2359659933476,11.5705568430052][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258151&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 113.1552147239264
Mean of Sample 212.1934355828221
t-stat3.7628541746137
df324
p-value0.000199358083597787
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.458937335377759,1.46462094683083]
F-test to compare two variances
F-stat8.49432745996265
df162
p-value0
H0 value1
Alternativetwo.sided
CI Level0.95
CI[6.2359659933476,11.5705568430052]






Welch Two Sample t-test (unpaired)
Mean of Sample 113.1552147239264
Mean of Sample 212.1934355828221
t-stat3.7628541746137
df199.621691000301
p-value0.00022077591809692
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.457759998404856,1.46579828380373]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 13.1552147239264 \tabularnewline
Mean of Sample 2 & 12.1934355828221 \tabularnewline
t-stat & 3.7628541746137 \tabularnewline
df & 199.621691000301 \tabularnewline
p-value & 0.00022077591809692 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.457759998404856,1.46579828380373] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258151&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]13.1552147239264[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]12.1934355828221[/C][/ROW]
[ROW][C]t-stat[/C][C]3.7628541746137[/C][/ROW]
[ROW][C]df[/C][C]199.621691000301[/C][/ROW]
[ROW][C]p-value[/C][C]0.00022077591809692[/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][0.457759998404856,1.46579828380373][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258151&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258151&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 113.1552147239264
Mean of Sample 212.1934355828221
t-stat3.7628541746137
df199.621691000301
p-value0.00022077591809692
H0 value0
Alternativetwo.sided
CI Level0.95
CI[0.457759998404856,1.46579828380373]






Wicoxon rank sum test with continuity correction (unpaired)
W15172.5
p-value0.0265328143799763
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.411042944785276
p-value2.19080309449282e-12
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.49079754601227
p-value0

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 15172.5 \tabularnewline
p-value & 0.0265328143799763 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.411042944785276 \tabularnewline
p-value & 2.19080309449282e-12 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.49079754601227 \tabularnewline
p-value & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258151&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]15172.5[/C][/ROW]
[ROW][C]p-value[/C][C]0.0265328143799763[/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]0.411042944785276[/C][/ROW]
[ROW][C]p-value[/C][C]2.19080309449282e-12[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.49079754601227[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258151&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258151&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)
W15172.5
p-value0.0265328143799763
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.411042944785276
p-value2.19080309449282e-12
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.49079754601227
p-value0


Figures (Output of Computation)

Input Parameters & R Code

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