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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, 02 Nov 2010 14:20:41 +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/Nov/02/t1288707554p6o74hdeqb1b7d7.htm/, Retrieved Sun, 28 Apr 2024 07:16:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=91533, Retrieved Sun, 28 Apr 2024 07:16:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Paired and Unpaired Two Samples Tests about the Mean] [] [2010-11-02 14:20:41] [a8abc7260f3c847aeac0a796e7895a2e] [Current]
Feedback Forum
2010-11-06 17:52:27 [Stefanie Van Esbroeck] [reply] 
De student(e) heeft ook hier bij de berekening aangeduid dat het om unpaired gegevens gaat, terwijl er wel een duidelijk verband bestaat.

In zijn interpretatie kijkt de student(e) naar de p-waarde om te concluderen dat beide varianties gelijk zijn. De p-waarde toont dit echter niet aan. Deze waarde toont ons of er een verschil is tussen beide gegevens en of er in dit voorbeeld een beter of slechter resultaat te zien is. Als we dus willen bekijken of de varianties gelijk zijn, moeten we kijken naar de F-statisticswaarde (0,99). Deze waarde ligt dit tegen 1 waardoor we inderdaad kunnen afleiden dat de varianties gelijk zijn.

Bij deze vraag kijkt de student(e) ook naar de grafieken. Om een goede conclusie te vormen, is dit niet nodig. Bovendien is zijn gevormde conclusie over de boxplots verkeerd. De algemene conclusie van de vraag is wel correct.
2010-11-09 22:21:32 [f0479c8ad85b1406c7a3120008048c58] [reply] 
We nemen een paired T-test omdat deze 2 gebeurtenissen betrekking hebben op eenzelfde groep van studenten. We spreken hier dus van afhankelijke gebeurtenissen. http://www.freestatistics.org/blog/index.php?v=date/2010/Oct/29/t1288353157w9s85hhko9p1rsj.htm/
We zien dat de p-value (0.53488101573388) relatief groot is. Dit wijst erop dat de 0-Hypothese (De variantie van de 2 gebeurtenissen zijn gelijk) niet kunnen verwerpen.
Ook zien we dat de 0-Hypothese waarde (0) wel in het C-interval: [-0.242370800813192,0.128085086527478] ligt. Dit betekent dat we de nulhypothese dienen te behouden en dat de 2 gebeurtenissen significant van elkaar verschillen. Het verschil bedraagt slechts: -0.0571428571428571. Dit betekent dus dat de S treatment niet zorgt voor een verbetering in de score.

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Dataset

Dataseries X:
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Histogram
Boxplots 
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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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91533&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91533&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Two Sample t-test (unpaired)
Mean of Sample 10.457142857142857
Mean of Sample 20.514285714285714
t-stat-0.885331280035804
df68
p-value0.37909800005437
H0 value0.05
Alternativetwo.sided
CI Level0.95
CI[-0.298634655156083,0.184348940870369]
F-test to compare two variances
F-stat0.993464052287582
df34
p-value0.984858744073723
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.501466047576137,1.96817078236551]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 0.457142857142857 \tabularnewline
Mean of Sample 2 & 0.514285714285714 \tabularnewline
t-stat & -0.885331280035804 \tabularnewline
df & 68 \tabularnewline
p-value & 0.37909800005437 \tabularnewline
H0 value & 0.05 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.298634655156083,0.184348940870369] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.993464052287582 \tabularnewline
df & 34 \tabularnewline
p-value & 0.984858744073723 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.501466047576137,1.96817078236551] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91533&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]0.457142857142857[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]0.514285714285714[/C][/ROW]
[ROW][C]t-stat[/C][C]-0.885331280035804[/C][/ROW]
[ROW][C]df[/C][C]68[/C][/ROW]
[ROW][C]p-value[/C][C]0.37909800005437[/C][/ROW]
[ROW][C]H0 value[/C][C]0.05[/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][-0.298634655156083,0.184348940870369][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.993464052287582[/C][/ROW]
[ROW][C]df[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]0.984858744073723[/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][0.501466047576137,1.96817078236551][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91533&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 10.457142857142857
Mean of Sample 20.514285714285714
t-stat-0.885331280035804
df68
p-value0.37909800005437
H0 value0.05
Alternativetwo.sided
CI Level0.95
CI[-0.298634655156083,0.184348940870369]
F-test to compare two variances
F-stat0.993464052287582
df34
p-value0.984858744073723
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.501466047576137,1.96817078236551]






Welch Two Sample t-test (unpaired)
Mean of Sample 10.457142857142857
Mean of Sample 20.514285714285714
t-stat-0.885331280035804
df67.9992690215639
p-value0.379098033480006
H0 value0.05
Alternativetwo.sided
CI Level0.95
CI[-0.298634702161487,0.184348987875773]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 0.457142857142857 \tabularnewline
Mean of Sample 2 & 0.514285714285714 \tabularnewline
t-stat & -0.885331280035804 \tabularnewline
df & 67.9992690215639 \tabularnewline
p-value & 0.379098033480006 \tabularnewline
H0 value & 0.05 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.298634702161487,0.184348987875773] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91533&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]0.457142857142857[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]0.514285714285714[/C][/ROW]
[ROW][C]t-stat[/C][C]-0.885331280035804[/C][/ROW]
[ROW][C]df[/C][C]67.9992690215639[/C][/ROW]
[ROW][C]p-value[/C][C]0.379098033480006[/C][/ROW]
[ROW][C]H0 value[/C][C]0.05[/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][-0.298634702161487,0.184348987875773][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91533&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 10.457142857142857
Mean of Sample 20.514285714285714
t-stat-0.885331280035804
df67.9992690215639
p-value0.379098033480006
H0 value0.05
Alternativetwo.sided
CI Level0.95
CI[-0.298634702161487,0.184348987875773]






Wicoxon rank sum test with continuity correction (unpaired)
W272
p-value3.69272461472916e-05
H0 value0.05
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0571428571428571
p-value0.999999995591453
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.485714285714286
p-value0.000518798147327804

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 272 \tabularnewline
p-value & 3.69272461472916e-05 \tabularnewline
H0 value & 0.05 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.0571428571428571 \tabularnewline
p-value & 0.999999995591453 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.485714285714286 \tabularnewline
p-value & 0.000518798147327804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91533&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]272[/C][/ROW]
[ROW][C]p-value[/C][C]3.69272461472916e-05[/C][/ROW]
[ROW][C]H0 value[/C][C]0.05[/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]0.0571428571428571[/C][/ROW]
[ROW][C]p-value[/C][C]0.999999995591453[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.485714285714286[/C][/ROW]
[ROW][C]p-value[/C][C]0.000518798147327804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91533&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91533&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)
W272
p-value3.69272461472916e-05
H0 value0.05
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0571428571428571
p-value0.999999995591453
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.485714285714286
p-value0.000518798147327804


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.05 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.05 ;
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')