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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 computationSun, 09 Nov 2008 03:20:32 -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/09/t1226226086dv3kfd67daoomgl.htm/, Retrieved Sun, 19 May 2024 09:18:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22686, Retrieved Sun, 19 May 2024 09:18:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

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] [TPP] [2008-11-09 10:20:32] [54ae75b68e6a45c6d55fa4235827d5b3] [Current]
Feedback Forum
2008-11-16 16:21:32 [Astrid Sniekers] [reply] 
Part 2

Mijn antwoorden zijn fout. De juiste antwoorden vind ik terug op de website freestatistics.org (moodle).

Part 3

Q1+Q3+Q5

Mijn antwoord is fout. De juiste antwoorden vind ik terug op de website freestatistics.org (moodle).

Q2+Q4

Mijn antwoord is juist.
2008-11-21 18:42:18 [Dorien Peeters] [reply] 
de oplossing van Q1 PART 3 zijn correct. We kijken naar de 1zijdige toets (wat de student ook zei)=>we krijgen proporties, en dit wil zeggen dat er slaagkans is.
Indien we kijken naar de tabel zien we dat de sample proportion>1 sided critical value. =>de peer assessment heeft duidelijk positieve invloed op de slaagkansen.
We verwerpen dus de nulhypothese.
Er zijn nog andere methoden:
• Normal approximation
• Agresti-Coull method
• Exact & Wilson method
Deze zullen bij éénzijdige kritieke waarde telkens een andere waarde weergeven, maar deze zijn afhankelijk van de assumpties.

Welke methode de beste is, is afhankelijk van de steekproefgrootte en de proportie. We hebben de luxe te kiezen, daar er een zeer groot verschil is tussen de nulhypothese en de steekproef.

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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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22686&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22686&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Testing Population Proportion (normal approximation)
Sample size98
Sample Proportion0.857142857
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)[ 0.765575549217387 , 0.948710164782613 ]
2-sided testReject the Null Hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (normal approximation) \tabularnewline
Sample size & 98 \tabularnewline
Sample Proportion & 0.857142857 \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) & [ 0.765575549217387 , 0.948710164782613 ] \tabularnewline
2-sided test & Reject the Null Hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22686&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]0.857142857[/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][ 0.765575549217387 , 0.948710164782613 ][/C][/ROW]
[ROW][C]2-sided test[/C][C]Reject the Null Hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22686&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 Proportion0.857142857
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)[ 0.765575549217387 , 0.948710164782613 ]
2-sided testReject the Null Hypothesis






Testing Population Proportion (Agresti-Coull method)
Sample size98
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval[ 0.771569818001552 , 1 ]
Right 1-sided confidence interval[ 0 , 0.923525978824251 ]
2-sided Confidence Interval(sample proportion)[ 0.753562226647685 , 0.933780637276178 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Agresti-Coull method) \tabularnewline
Sample size & 98 \tabularnewline
Sample Proportion & 0.857142857 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval & [ 0.771569818001552 , 1 ] \tabularnewline
Right 1-sided confidence interval & [ 0 , 0.923525978824251  ] \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.753562226647685 , 0.933780637276178 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22686&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]0.857142857[/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][ 0.771569818001552 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval[/C][C][ 0 , 0.923525978824251  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(sample proportion)[/C][C][ 0.753562226647685 , 0.933780637276178 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22686&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22686&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 Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval[ 0.771569818001552 , 1 ]
Right 1-sided confidence interval[ 0 , 0.923525978824251 ]
2-sided Confidence Interval(sample proportion)[ 0.753562226647685 , 0.933780637276178 ]






Testing Population Proportion (Exact and Wilson method)
Sample size98
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval(Exact method)[ 0.785719343294818 , 1 ]
Right 1-sided confidence interval(Exact method)[ 0 , 0.911518963115213 ]
2-sided Confidence Interval(Exact method)[ 0.771939502911796 , 0.919640487298203 ]
Left 1-sided confidence interval(Wilson method)[ 0.789394967950623 , 1 ]
Right 1-sided confidence interval(Wilson method)[ 0 , 0.90570082887518 ]
2-sided Confidence Interval(Wilson method)[ 0.774387569504507 , 0.912955294419355 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Exact and Wilson method) \tabularnewline
Sample size & 98 \tabularnewline
Sample Proportion & 0.857142857 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval(Exact method) & [ 0.785719343294818 , 1 ] \tabularnewline
Right 1-sided confidence interval(Exact method) & [ 0 , 0.911518963115213  ] \tabularnewline
2-sided Confidence Interval(Exact method) & [ 0.771939502911796 , 0.919640487298203 ] \tabularnewline
Left 1-sided confidence interval(Wilson method) & [ 0.789394967950623 , 1 ] \tabularnewline
Right 1-sided confidence interval(Wilson method) & [ 0 , 0.90570082887518  ] \tabularnewline
2-sided Confidence Interval(Wilson method) & [ 0.774387569504507 , 0.912955294419355 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22686&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]0.857142857[/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][ 0.785719343294818 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Exact method)[/C][C][ 0 , 0.911518963115213  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Exact method)[/C][C][ 0.771939502911796 , 0.919640487298203 ][/C][/ROW]
[ROW][C]Left 1-sided confidence interval(Wilson method)[/C][C][ 0.789394967950623 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Wilson method)[/C][C][ 0 , 0.90570082887518  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Wilson method)[/C][C][ 0.774387569504507 , 0.912955294419355 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22686&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22686&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 Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval(Exact method)[ 0.785719343294818 , 1 ]
Right 1-sided confidence interval(Exact method)[ 0 , 0.911518963115213 ]
2-sided Confidence Interval(Exact method)[ 0.771939502911796 , 0.919640487298203 ]
Left 1-sided confidence interval(Wilson method)[ 0.789394967950623 , 1 ]
Right 1-sided confidence interval(Wilson method)[ 0 , 0.90570082887518 ]
2-sided Confidence Interval(Wilson method)[ 0.774387569504507 , 0.912955294419355 ]


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 98 ; par2 = 0.857142857 ; par3 = 0.69 ; par4 = 0.05 ;
Parameters (R input):
par1 = 98 ; par2 = 0.857142857 ; 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')