FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 29 Nov 2017 17:42:08 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/29/t1511973757sqvsejkor208m9n.htm/, Retrieved Fri, 24 May 2024 23:14:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308342, Retrieved Fri, 24 May 2024 23:14:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51

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 test P...] [2017-11-29 16:42:08] [fda4350e119ddbaf0177fa3308cc9af4] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14	18
21	16
20	17
20	19
20	21
18	18
17	18
15	19
18	14
21	21
15	19
16	14
17	18
18	11
16	17
15	18
15	12
19	13
19	18
15	17
17	17
13	21
12	12
15	13
19	20
13	19
17	19
20	18
16	17
22	15
16	12
23	17
20	10
23	10
18	16
18	10
13	13
19	15
16	17
17	15
18	13
18	15
19	20
16	12
20	16
21	15
18	17
17	15
21	12
19	17
15	11
14	16
15	16
16	15
19	20
17	13
17	15
15	16
21	16
18	19
18	17
15	19
19	14
19	11
18	20
20	13
12	20
15	20
17	14
20	20
11	19
14	18
14	17
12	17
19	19
22	21
16	19
15	21
15	15
18	15
18	13
22	19
12	19
10	18
20	21
20	15
19	19
19	16
12	19
14	16
17	18
7	18
14	15
21	15
15	11
20	18
19	13
14	9
16	21
16	19
17	13
20	18
17	16
17	10
16	12
19	18
17	17
10	15
12	16
19	15
21	24
17	15
14	14
14	16
14	16
17	20
12	20
15	20
19	20
9	14
23	22
10	16
10	14
8	11
17	21
10	18
20	15
19	20
20	5
18	14
16	19
21	15
18	12
18	11
8	15
13	15
13	20
18	20
12	16
16	21
18	22
18	17
18	21
19	19
19	23
19	21
23	22
18	11
14	20
17	18
19	16
16	18
14	13
16	17
18	20
16	20
21	15
16	18
14	15
19	19
19	19
19	19
18	20
14	20
19	16
11	18
20	17
18	18
18	13
19	21
15	17
21	19
13	20
21	15
18	15
20	19
20	18

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308342&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308342&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Two Sample t-test (unpaired)
Mean of Sample 116.8531073446328
Mean of Sample 216.6779661016949
t-stat0.512731087205384
df352
p-value0.608461038894444
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.496662915252525,0.846945401128227]
F-test to compare two variances
F-stat1.0030511345239
df176
p-value0.983900232626037
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.745732402063825,1.34915899548585]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 16.8531073446328 \tabularnewline
Mean of Sample 2 & 16.6779661016949 \tabularnewline
t-stat & 0.512731087205384 \tabularnewline
df & 352 \tabularnewline
p-value & 0.608461038894444 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.496662915252525,0.846945401128227] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 1.0030511345239 \tabularnewline
df & 176 \tabularnewline
p-value & 0.983900232626037 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.745732402063825,1.34915899548585] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308342&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]16.8531073446328[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]16.6779661016949[/C][/ROW]
[ROW][C]t-stat[/C][C]0.512731087205384[/C][/ROW]
[ROW][C]df[/C][C]352[/C][/ROW]
[ROW][C]p-value[/C][C]0.608461038894444[/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][-0.496662915252525,0.846945401128227][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]1.0030511345239[/C][/ROW]
[ROW][C]df[/C][C]176[/C][/ROW]
[ROW][C]p-value[/C][C]0.983900232626037[/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][0.745732402063825,1.34915899548585][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308342&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 116.8531073446328
Mean of Sample 216.6779661016949
t-stat0.512731087205384
df352
p-value0.608461038894444
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.496662915252525,0.846945401128227]
F-test to compare two variances
F-stat1.0030511345239
df176
p-value0.983900232626037
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.745732402063825,1.34915899548585]






Welch Two Sample t-test (unpaired)
Mean of Sample 116.8531073446328
Mean of Sample 216.6779661016949
t-stat0.512731087205384
df351.999183266639
p-value0.608461039640305
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.496662920630223,0.846945406505925]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 16.8531073446328 \tabularnewline
Mean of Sample 2 & 16.6779661016949 \tabularnewline
t-stat & 0.512731087205384 \tabularnewline
df & 351.999183266639 \tabularnewline
p-value & 0.608461039640305 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.496662920630223,0.846945406505925] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308342&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]16.8531073446328[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]16.6779661016949[/C][/ROW]
[ROW][C]t-stat[/C][C]0.512731087205384[/C][/ROW]
[ROW][C]df[/C][C]351.999183266639[/C][/ROW]
[ROW][C]p-value[/C][C]0.608461039640305[/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][-0.496662920630223,0.846945406505925][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308342&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 116.8531073446328
Mean of Sample 216.6779661016949
t-stat0.512731087205384
df351.999183266639
p-value0.608461039640305
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.496662920630223,0.846945406505925]






Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)
W16190.5
p-value0.583276965478419
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0451977401129944
p-value0.993589132743971
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.135593220338983
p-value0.0772160711925923

\begin{tabular}{lllllllll}
\hline
Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired) \tabularnewline
W & 16190.5 \tabularnewline
p-value & 0.583276965478419 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.0451977401129944 \tabularnewline
p-value & 0.993589132743971 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.135593220338983 \tabularnewline
p-value & 0.0772160711925923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308342&T=3

[TABLE]
[ROW][C]Wilcoxon Rank-Sum Test (Mann–Whitney U test) with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]16190.5[/C][/ROW]
[ROW][C]p-value[/C][C]0.583276965478419[/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]0.0451977401129944[/C][/ROW]
[ROW][C]p-value[/C][C]0.993589132743971[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.135593220338983[/C][/ROW]
[ROW][C]p-value[/C][C]0.0772160711925923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308342&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)
W16190.5
p-value0.583276965478419
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0451977401129944
p-value0.993589132743971
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.135593220338983
p-value0.0772160711925923


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)
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')