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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, 29 Oct 2010 16:58:58 +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/2010/Oct/29/t1288371577c4xoy7t4j0kkd6i.htm/, Retrieved Thu, 02 May 2024 19:52:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=90193, Retrieved Thu, 02 May 2024 19:52:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

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] [Dagelijkse omzet ...] [2010-10-25 11:22:12] [b98453cac15ba1066b407e146608df68]
F   PD    [Paired and Unpaired Two Samples Tests about the Mean] [E - treatment] [2010-10-29 16:58:58] [dcc54e7e6e8c80b7c45e040080afe6ab] [Current]
-           [Paired and Unpaired Two Samples Tests about the Mean] [] [2010-11-02 08:14:40] [049b50ae610f671f7417ed8e2d1295c1]
Feedback Forum
2010-11-06 08:07:11 [48eb36e2c01435ad7e4ea7854a9d98fe] [reply] 
De student heeft hier te weinig gegevens ingevoerd wat kan zorgen voor een vertekend beeld. Een berekening met de correcte gegevens is bijvoolbeeld hier te vinden: http://www.freestatistics.org/blog/index.php?v=date/2010/Oct/29/t1288351233f5m1hzoxvzxoy7u.htm/

Zoals de student correct aangaf dienen we eerst na te gaan of alle voorwaarden om de T- test te mogen gebruiken voldaan zijn. Eerst en vooral dienen we inderdaad na te gaan of de varianties gelijk zijn, dit kunnen we zien adhv de F- stat. Deze is 1,3 en moet zo dicht mogelijk bij 1 liggen. We zien een P-waarde die zeer groot is wat betekent dat we de nulhypothese - de varianties zijn gelijk aan elkaar - zullen aanvaarden. Een tweede belangrijke voorwaarde is dat de centrale limietstelling van toepassing moet zijn. Om dit te bepalen moet er voldaan zijn aan een aantal voorwaarden, de belangrijkste is het feit dat het moet gaan om random trekkingen, en dat is hier het geval dus kunnen we concluderen dat de CLT van toepassing is. De belangrijkste voorwaarden zijn vervuld en we mogen de T- test dus gebruiken.

We zien een zeer kleine P- waarde (die kleiner is dan de α – fout 0,05), dus mogen we aannemen dat we de nulhypothese kunnen verwerpen. Er is dus wel degelijk een significant verschil tussen beiden, de T- treatment heeft dus wel degelijk een positieve invloed. Als extra controle kunnen we stellen dat de nulhypothese – 0 – niet gelegen is in het betrouwbaarheidsinterval.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0	1
0	1
1	1
1	1
1	1
1	1
1	1
0	0
0	1
0	1
1	1
1	1
0	0
0	1
1	1
0	1
0	0
0	1
0	1
0	1
0	1
0	0

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=90193&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=90193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=90193&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' @ 72.249.127.135






Two Sample t-test (paired)
Difference: Mean1 - Mean2-0.454545454545455
t-stat-4.18330013267038
df21
p-value0.000419180694913759
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.680510360326038,-0.228580548764871]
F-test to compare two variances
F-stat1.55555555555556
df21
p-value0.319048828623703
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.645836730360957,3.74669474910068]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -0.454545454545455 \tabularnewline
t-stat & -4.18330013267038 \tabularnewline
df & 21 \tabularnewline
p-value & 0.000419180694913759 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.680510360326038,-0.228580548764871] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 1.55555555555556 \tabularnewline
df & 21 \tabularnewline
p-value & 0.319048828623703 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.645836730360957,3.74669474910068] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=90193&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-0.454545454545455[/C][/ROW]
[ROW][C]t-stat[/C][C]-4.18330013267038[/C][/ROW]
[ROW][C]df[/C][C]21[/C][/ROW]
[ROW][C]p-value[/C][C]0.000419180694913759[/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][-0.680510360326038,-0.228580548764871][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]1.55555555555556[/C][/ROW]
[ROW][C]df[/C][C]21[/C][/ROW]
[ROW][C]p-value[/C][C]0.319048828623703[/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][0.645836730360957,3.74669474910068][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=90193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=90193&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 - Mean2-0.454545454545455
t-stat-4.18330013267038
df21
p-value0.000419180694913759
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.680510360326038,-0.228580548764871]
F-test to compare two variances
F-stat1.55555555555556
df21
p-value0.319048828623703
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.645836730360957,3.74669474910068]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean2-0.454545454545455
t-stat-4.18330013267038
df21
p-value0.000419180694913759
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.680510360326038,-0.228580548764871]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & -0.454545454545455 \tabularnewline
t-stat & -4.18330013267038 \tabularnewline
df & 21 \tabularnewline
p-value & 0.000419180694913759 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.680510360326038,-0.228580548764871] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=90193&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]-0.454545454545455[/C][/ROW]
[ROW][C]t-stat[/C][C]-4.18330013267038[/C][/ROW]
[ROW][C]df[/C][C]21[/C][/ROW]
[ROW][C]p-value[/C][C]0.000419180694913759[/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][-0.680510360326038,-0.228580548764871][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=90193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=90193&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 - Mean2-0.454545454545455
t-stat-4.18330013267038
df21
p-value0.000419180694913759
H0 value0
Alternativetwo.sided
CI Level0.95
CI[-0.680510360326038,-0.228580548764871]






Wicoxon rank sum test with continuity correction (paired)
W0
p-value0.00190419504300439
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.454545454545455
p-value0.0212306675278732
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.454545454545455
p-value0.0212306675278732

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (paired) \tabularnewline
W & 0 \tabularnewline
p-value & 0.00190419504300439 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.454545454545455 \tabularnewline
p-value & 0.0212306675278732 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.454545454545455 \tabularnewline
p-value & 0.0212306675278732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=90193&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]0[/C][/ROW]
[ROW][C]p-value[/C][C]0.00190419504300439[/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]0.454545454545455[/C][/ROW]
[ROW][C]p-value[/C][C]0.0212306675278732[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.454545454545455[/C][/ROW]
[ROW][C]p-value[/C][C]0.0212306675278732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=90193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=90193&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 (paired)
W0
p-value0.00190419504300439
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.454545454545455
p-value0.0212306675278732
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.454545454545455
p-value0.0212306675278732


Figures (Output of Computation)

Input Parameters & R Code

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