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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesisprop1.wasp
Title produced by softwareTesting Population Proportion - Critical Value
Date of computationThu, 13 Nov 2008 09:04:52 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/13/t1226592401wdmvtfj3nijjniq.htm/, Retrieved Sat, 18 May 2024 23:43:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24663, Retrieved Sat, 18 May 2024 23:43:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Testing Population Proportion - Critical Value] [tinneke_debock.pa...] [2008-11-13 16:04:52] [20137734a2343a7bbbd59daaec7ad301] [Current]
Feedback Forum
2008-11-15 18:21:52 [Philip Van Herck] [reply] 
Het juiste antwoord is: We gebruiken een 1-sided test omdat we wel kunnen stellen dat Peer Assessment volgens ons geen slecht effect zal hebben op het succes ratio. De sample proportion (0.857) is dan ook significant hoger dan de nulhypothese (0.69). Dit kunnen we staven door te zeggen dat:
1/ De sample proportion hoger is dan de 1-sided critical value (normal approx.) (0.766).
2/ Het 1-sided 95% confidence interval van 0.771-1 volgens de Agresti-Coull methode bevat de nulhypothese niet.
3/ Het 1-sided 95% confidence interval van 0.785-1 volgens de exact methode bevat de nulhypothese niet.
4/ Het 1-sided 95% confidence interval van 0.789-1 volgens de Wilson methode bevat de nulhypothese niet.
5/ De 1-sided p-value (normal approx.) is groter dan de Type I Error waarde.
2008-11-24 19:06:33 [Marlies Polfliet] [reply] 
Q1) We gebruiken een 1-sided test omdat deze enkel meet of de Peer assessment een positieve invloed heeft op de examenresultaten. Het is immers onlogisch dat de Peer assessment een negatieve invloed zou hebben. Bovendien is de sample proportion (0.857) SIGNIFICANT hoger dan de nulhypothese (0.69).
2008-11-24 19:06:53 [Marlies Polfliet] [reply] 
We gebruiken een 1-sided test omdat deze enkel meet of de Peer assessment een positieve invloed heeft op de examenresultaten. Het is immers onlogisch dat de Peer assessment een negatieve invloed zou hebben. Bovendien is de sample proportion (0.857) SIGNIFICANT hoger dan de nulhypothese (0.69).
2008-11-24 21:47:22 [Jonas Scheltjens] [reply] 
Q1: De éénzijdige test is hier het best om te gebruiken, wat de student ook heeft gekozen. Deze methode is gebaseerd op de Peer assessments omdat deze die geen negatieve invloed zal hebben op de resultaten. Er werd wel geen uitspraak gedaan i.v.m. de significantie. Indien we hier dan verder op ingaan zien we dat de waarde van de nulhypothese (0,69) significant kleiner is dan deze van de sample proportion (0,857142857) en de sample proportion is dan ook groter dan de 1-zijdige kritieke waarde. de Testing Proportion (normal-approximation-)tabel verschaft ons deze informatie. Dankzij 3 soorten voor de 1-zijdige 95% betrouwbaarheidsintervallen (de Exacte methode, de Wilson methode en de Agresti-Coull methode)komen we tot hetzelfde besluit. In alle 3 de gevallen bevindt de nulhypothese zich niet in het betrouwbaarheidsinterval. Tot slot komen we tot deze conclusie via de 1-zijdige p-waarde omdat deze waarde veel kleiner is dan het Type 1 Error.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24663&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]3 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=24663&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24663&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Testing Population Proportion (normal approximation)
Sample size98
Sample Proportion0.8571
Null hypothesis0.69
Type I error (alpha)0.05
1-sided critical value0.766845707117296
1-sided testReject the Null Hypothesis
2-sided Confidence Interval(sample proportion)[ 0.765532692217387 , 0.948667307782613 ]
2-sided testReject the Null Hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (normal approximation) \tabularnewline
Sample size & 98 \tabularnewline
Sample Proportion & 0.8571 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
1-sided critical value & 0.766845707117296 \tabularnewline
1-sided test & Reject the Null Hypothesis \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.765532692217387 , 0.948667307782613 ] \tabularnewline
2-sided test & Reject the Null Hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24663&T=1

[TABLE]
[ROW][C]Testing Population Proportion (normal approximation)[/C][/ROW]
[ROW][C]Sample size[/C][C]98[/C][/ROW]
[ROW][C]Sample Proportion[/C][C]0.8571[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]0.69[/C][/ROW]
[ROW][C]Type I error (alpha)[/C][C]0.05[/C][/ROW]
[ROW][C]1-sided critical value[/C][C]0.766845707117296[/C][/ROW]
[ROW][C]1-sided test[/C][C]Reject the Null Hypothesis[/C][/ROW]
[ROW][C]2-sided Confidence Interval(sample proportion)[/C][C][ 0.765532692217387 , 0.948667307782613 ][/C][/ROW]
[ROW][C]2-sided test[/C][C]Reject the Null Hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24663&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24663&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:

Testing Population Proportion (normal approximation)
Sample size98
Sample Proportion0.8571
Null hypothesis0.69
Type I error (alpha)0.05
1-sided critical value0.766845707117296
1-sided testReject the Null Hypothesis
2-sided Confidence Interval(sample proportion)[ 0.765532692217387 , 0.948667307782613 ]
2-sided testReject the Null Hypothesis






Testing Population Proportion (Agresti-Coull method)
Sample size98
Sample Proportion0.8571
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval[ 0.771528112392745 , 1 ]
Right 1-sided confidence interval[ 0 , 0.923484273215444 ]
2-sided Confidence Interval(sample proportion)[ 0.753520986213301 , 0.933739396841794 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Agresti-Coull method) \tabularnewline
Sample size & 98 \tabularnewline
Sample Proportion & 0.8571 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval & [ 0.771528112392745 , 1 ] \tabularnewline
Right 1-sided confidence interval & [ 0 , 0.923484273215444  ] \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.753520986213301 , 0.933739396841794 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24663&T=2

[TABLE]
[ROW][C]Testing Population Proportion (Agresti-Coull method)[/C][/ROW]
[ROW][C]Sample size[/C][C]98[/C][/ROW]
[ROW][C]Sample Proportion[/C][C]0.8571[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]0.69[/C][/ROW]
[ROW][C]Type I error (alpha)[/C][C]0.05[/C][/ROW]
[ROW][C]Left 1-sided confidence interval[/C][C][ 0.771528112392745 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval[/C][C][ 0 , 0.923484273215444  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(sample proportion)[/C][C][ 0.753520986213301 , 0.933739396841794 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24663&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24663&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:

Testing Population Proportion (Agresti-Coull method)
Sample size98
Sample Proportion0.8571
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval[ 0.771528112392745 , 1 ]
Right 1-sided confidence interval[ 0 , 0.923484273215444 ]
2-sided Confidence Interval(sample proportion)[ 0.753520986213301 , 0.933739396841794 ]






Testing Population Proportion (Exact and Wilson method)
Sample size98
Sample Proportion0.8571
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval(Exact method)[ 0.785670522351887 , 1 ]
Right 1-sided confidence interval(Exact method)[ 0 , 0.911484312655266 ]
2-sided Confidence Interval(Exact method)[ 0.77188973535872 , 0.91960748793079 ]
Left 1-sided confidence interval(Wilson method)[ 0.789346381933444 , 1 ]
Right 1-sided confidence interval(Wilson method)[ 0 , 0.905666003674745 ]
2-sided Confidence Interval(Wilson method)[ 0.774338311301997 , 0.912922071753098 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Exact and Wilson method) \tabularnewline
Sample size & 98 \tabularnewline
Sample Proportion & 0.8571 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval(Exact method) & [ 0.785670522351887 , 1 ] \tabularnewline
Right 1-sided confidence interval(Exact method) & [ 0 , 0.911484312655266  ] \tabularnewline
2-sided Confidence Interval(Exact method) & [ 0.77188973535872 , 0.91960748793079 ] \tabularnewline
Left 1-sided confidence interval(Wilson method) & [ 0.789346381933444 , 1 ] \tabularnewline
Right 1-sided confidence interval(Wilson method) & [ 0 , 0.905666003674745  ] \tabularnewline
2-sided Confidence Interval(Wilson method) & [ 0.774338311301997 , 0.912922071753098 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24663&T=3

[TABLE]
[ROW][C]Testing Population Proportion (Exact and Wilson method)[/C][/ROW]
[ROW][C]Sample size[/C][C]98[/C][/ROW]
[ROW][C]Sample Proportion[/C][C]0.8571[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]0.69[/C][/ROW]
[ROW][C]Type I error (alpha)[/C][C]0.05[/C][/ROW]
[ROW][C]Left 1-sided confidence interval(Exact method)[/C][C][ 0.785670522351887 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Exact method)[/C][C][ 0 , 0.911484312655266  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Exact method)[/C][C][ 0.77188973535872 , 0.91960748793079 ][/C][/ROW]
[ROW][C]Left 1-sided confidence interval(Wilson method)[/C][C][ 0.789346381933444 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Wilson method)[/C][C][ 0 , 0.905666003674745  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Wilson method)[/C][C][ 0.774338311301997 , 0.912922071753098 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24663&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24663&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:

Testing Population Proportion (Exact and Wilson method)
Sample size98
Sample Proportion0.8571
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval(Exact method)[ 0.785670522351887 , 1 ]
Right 1-sided confidence interval(Exact method)[ 0 , 0.911484312655266 ]
2-sided Confidence Interval(Exact method)[ 0.77188973535872 , 0.91960748793079 ]
Left 1-sided confidence interval(Wilson method)[ 0.789346381933444 , 1 ]
Right 1-sided confidence interval(Wilson method)[ 0 , 0.905666003674745 ]
2-sided Confidence Interval(Wilson method)[ 0.774338311301997 , 0.912922071753098 ]


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 98 ; par2 = 0.8571 ; par3 = 0.69 ; par4 = 0.05 ;
Parameters (R input):
par1 = 98 ; par2 = 0.8571 ; par3 = 0.69 ; par4 = 0.05 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
if (par2 < par3)
{
ucv <- qnorm(par4)
} else {
ucv <- -qnorm(par4)
}
cv1 <- par3 + ucv * sqrt(par3 * (1-par3) / par1)
cv2low <- par2 - abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1)
cv2upp <- par2 + abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1)
z21 <- qnorm(par4/2)^2 / par1
z2 <- qnorm(par4/2)^2 / (2*par1)
z24 <- qnorm(par4/2)^2 / (4*par1^2)
cv2lowexact <- (par2 + z2 - abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1 + z24)) / (1 + z21)
cv2uppexact <- (par2 + z2 + abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1 + z24)) / (1 + z21)
z11 <- qnorm(par4)^2 / par1
z1 <- qnorm(par4)^2 / (2*par1)
z14 <- qnorm(par4)^2 / (4*par1^2)
cv1lowexact <- (par2 + z1 - abs(qnorm(par4)) * sqrt(par3 * (1-par3) / par1 + z14)) / (1 + z11)
cv1uppexact <- (par2 + z1 + abs(qnorm(par4)) * sqrt(par3 * (1-par3) / par1 + z14)) / (1 + z11)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Testing Population Proportion (normal approximation)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample Proportion',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Null hypothesis',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type I error (alpha)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1-sided critical value',header=TRUE)
a<-table.element(a,cv1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1-sided test',header=TRUE)
if (par2 < par3)
{
if (par2 < cv1)
{
a<-table.element(a,'Reject the Null Hypothesis')
} else {
a<-table.element(a,'Do not reject the Null Hypothesis')
}
} else {
if (par2 > cv1)
{
a<-table.element(a,'Reject the Null Hypothesis')
} else {
a<-table.element(a,'Do not reject the Null Hypothesis')
}
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided Confidence Interval
(sample proportion)',header=TRUE)
dum <- paste('[',cv2low)
dum <- paste(dum,',')
dum <- paste(dum,cv2upp)
dum <- paste(dum,']')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided test',header=TRUE)
if ((par3 < cv2low) | (par3 > cv2upp))
{
a<-table.element(a,'Reject the Null Hypothesis')
} else {
a<-table.element(a,'Do not reject the Null Hypothesis')
}
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,'Testing Population Proportion (Agresti-Coull method)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample Proportion',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Null hypothesis',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type I error (alpha)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Left 1-sided confidence interval',header=TRUE)
dum <- paste('[',cv1lowexact)
dum <- paste(dum,', 1 ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Right 1-sided confidence interval',header=TRUE)
dum <- paste('[ 0 ,',cv1uppexact)
dum <- paste(dum,' ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided Confidence Interval
(sample proportion)',header=TRUE)
dum <- paste('[',cv2lowexact)
dum <- paste(dum,',')
dum <- paste(dum,cv2uppexact)
dum <- paste(dum,']')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
library(Hmisc)
re <- binconf(par2*par1,par1,par4,method='exact')
re1 <- binconf(par2*par1,par1,par4*2,method='exact')
rw <- binconf(par2*par1,par1,par4,method='wilson')
rw1 <- binconf(par2*par1,par1,par4*2,method='wilson')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Testing Population Proportion (Exact and Wilson method)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample Proportion',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Null hypothesis',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type I error (alpha)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Left 1-sided confidence interval
(Exact method)',header=TRUE)
dum <- paste('[',re1[2])
dum <- paste(dum,', 1 ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Right 1-sided confidence interval
(Exact method)',header=TRUE)
dum <- paste('[ 0 ,',re1[3])
dum <- paste(dum,' ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided Confidence Interval
(Exact method)',header=TRUE)
dum <- paste('[',re[2])
dum <- paste(dum,',')
dum <- paste(dum,re[3])
dum <- paste(dum,']')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Left 1-sided confidence interval
(Wilson method)',header=TRUE)
dum <- paste('[',rw1[2])
dum <- paste(dum,', 1 ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Right 1-sided confidence interval
(Wilson method)',header=TRUE)
dum <- paste('[ 0 ,',rw1[3])
dum <- paste(dum,' ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided Confidence Interval
(Wilson method)',header=TRUE)
dum <- paste('[',rw[2])
dum <- paste(dum,',')
dum <- paste(dum,rw[3])
dum <- paste(dum,']')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')