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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 computationWed, 20 Nov 2013 10:25:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/20/t1384961353b10dnif8hwhf8zf.htm/, Retrieved Wed, 01 May 2024 17:44:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226644, Retrieved Wed, 01 May 2024 17:44:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

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] [WS7f] [2013-11-20 15:25:43] [38144ba7d4215ff1336c69b1a02252e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
53 32
83 51
66 42
67 41
76 46
78 47
53 37
80 49
74 45
76 47
79 49
54 33
67 42
54 33
87 53
58 36
75 45
88 54
64 41
57 36
66 41
68 44
54 33
56 37
86 52
80 47
76 43
69 44
78 45
67 44
80 49
54 33
71 43
84 54
74 42
71 44
63 37
71 43
76 46
69 42
74 45
75 44
54 33
52 31
69 42
68 40
65 43
75 46
74 42
75 45
72 44
67 40
63 37
62 46
63 36
76 47
74 45
67 42
73 43
70 43
53 32
77 45
80 48
52 31
54 33
80 49
66 42
73 41
63 38
69 42
67 44
54 33
81 48
69 40
84 50
80 49
70 43
69 44
77 47
54 33
79 46
71 45
73 43
72 44
77 47
75 45
69 42
54 33
70 43
73 46
54 33
77 46
82 48
80 47
80 47
69 43
78 46
81 48
76 46
76 45
73 45
85 52
66 42
79 47
68 41
76 47
71 43
54 33
46 30
85 52
74 44
88 55
38 11
76 47
86 53
54 33
67 44
69 42
90 55
54 33
76 46
89 54
76 47
73 45
79 47
90 55
74 44
81 53
72 44
71 42
66 40
77 46
65 40
74 46
85 53
54 33
63 42
54 35
64 40
69 41
54 33
84 51
86 53
77 46
89 55
76 47
60 38
75 46
73 46
85 53
79 47
71 41
72 44
69 43
78 51
54 33
69 43
81 53
84 51
84 50
69 46
66 43
81 47
82 50
72 43
54 33
78 48
74 44
82 50
73 41
55 34
72 44
78 47
59 35
72 44
78 44
68 43
69 41
67 41
74 42
54 33
67 41
70 44
80 48
89 55
76 44
74 43
87 52
54 30
61 39
38 11
75 44
69 42
62 41
72 44
70 44
79 48
87 53
62 37
77 44
69 44
69 40
75 42
54 35
72 43
74 45
85 55
52 31
70 44
84 50
64 40
84 53
87 54
79 49
67 40
65 41
85 52
83 52
61 36
82 52
76 46
58 31
72 44
72 44
38 11
78 46
54 33
63 34
66 42
70 43
71 43
67 44
58 36
72 46
72 44
70 43
76 50
50 33
72 43
72 44
88 53
53 34
58 35
66 40
82 53
69 42
68 43
44 29
56 36
53 30
70 42
78 47
71 44
72 45
68 44
67 43
75 43
62 40
67 41
83 52
64 38
68 41
62 39
72 43

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226644&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]5 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=226644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226644&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 time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Two Sample t-test (unpaired)
Mean of Sample 170.4128787878788
Mean of Sample 242.9128787878788
t-stat35.8491889345107
df526
p-value2.46455075772797e-143
H0 value0
Alternativetwo.sided
CI Level0.95
CI[25.993039374355,29.006960625645]
F-test to compare two variances
F-stat2.2856457474765
df263
p-value3.97850641320474e-11
H0 value1
Alternativetwo.sided
CI Level0.95
CI[1.79393354967241,2.9121348914576]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 70.4128787878788 \tabularnewline
Mean of Sample 2 & 42.9128787878788 \tabularnewline
t-stat & 35.8491889345107 \tabularnewline
df & 526 \tabularnewline
p-value & 2.46455075772797e-143 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [25.993039374355,29.006960625645] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 2.2856457474765 \tabularnewline
df & 263 \tabularnewline
p-value & 3.97850641320474e-11 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [1.79393354967241,2.9121348914576] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226644&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]70.4128787878788[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]42.9128787878788[/C][/ROW]
[ROW][C]t-stat[/C][C]35.8491889345107[/C][/ROW]
[ROW][C]df[/C][C]526[/C][/ROW]
[ROW][C]p-value[/C][C]2.46455075772797e-143[/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][25.993039374355,29.006960625645][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]2.2856457474765[/C][/ROW]
[ROW][C]df[/C][C]263[/C][/ROW]
[ROW][C]p-value[/C][C]3.97850641320474e-11[/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][1.79393354967241,2.9121348914576][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226644&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 170.4128787878788
Mean of Sample 242.9128787878788
t-stat35.8491889345107
df526
p-value2.46455075772797e-143
H0 value0
Alternativetwo.sided
CI Level0.95
CI[25.993039374355,29.006960625645]
F-test to compare two variances
F-stat2.2856457474765
df263
p-value3.97850641320474e-11
H0 value1
Alternativetwo.sided
CI Level0.95
CI[1.79393354967241,2.9121348914576]






Welch Two Sample t-test (unpaired)
Mean of Sample 170.4128787878788
Mean of Sample 242.9128787878788
t-stat35.8491889345107
df456.158029253276
p-value8.90515609794355e-135
H0 value0
Alternativetwo.sided
CI Level0.95
CI[25.9925070835409,29.0074929164591]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 70.4128787878788 \tabularnewline
Mean of Sample 2 & 42.9128787878788 \tabularnewline
t-stat & 35.8491889345107 \tabularnewline
df & 456.158029253276 \tabularnewline
p-value & 8.90515609794355e-135 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [25.9925070835409,29.0074929164591] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226644&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]70.4128787878788[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]42.9128787878788[/C][/ROW]
[ROW][C]t-stat[/C][C]35.8491889345107[/C][/ROW]
[ROW][C]df[/C][C]456.158029253276[/C][/ROW]
[ROW][C]p-value[/C][C]8.90515609794355e-135[/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][25.9925070835409,29.0074929164591][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226644&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 170.4128787878788
Mean of Sample 242.9128787878788
t-stat35.8491889345107
df456.158029253276
p-value8.90515609794355e-135
H0 value0
Alternativetwo.sided
CI Level0.95
CI[25.9925070835409,29.0074929164591]






Wicoxon rank sum test with continuity correction (unpaired)
W68495
p-value3.37000444913154e-82
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.909090909090909
p-value0
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.170454545454545
p-value0.000932811545684142

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 68495 \tabularnewline
p-value & 3.37000444913154e-82 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.909090909090909 \tabularnewline
p-value & 0 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.170454545454545 \tabularnewline
p-value & 0.000932811545684142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226644&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]68495[/C][/ROW]
[ROW][C]p-value[/C][C]3.37000444913154e-82[/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]0.909090909090909[/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]0.170454545454545[/C][/ROW]
[ROW][C]p-value[/C][C]0.000932811545684142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226644&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)
W68495
p-value3.37000444913154e-82
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.909090909090909
p-value0
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.170454545454545
p-value0.000932811545684142


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.0 ;
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')