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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_hypothesisprop1.wasp
Title produced by softwareTesting Population Proportion - Critical Value
Date of computationMon, 12 Nov 2007 03:27:10 -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/2007/Nov/12/t1194863501cu7jsqzeh8d7zc8.htm/, Retrieved Mon, 29 Apr 2024 00:32:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5189, Retrieved Mon, 29 Apr 2024 00:32:38 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJeroen G, Nick VH, Michiel VdB, Jef J, Liesje V en Evi V
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Testing Population Proportion - Critical Value] [Q3 Various types ...] [2007-11-12 10:27:10] [9ec4fcc2bfe8b6d942eac6074e595603] [Current]
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Dataset

Tables (Output of Computation)





Summary of compuational 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 compuational 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=5189&T=0

[TABLE]
[ROW][C]Summary of compuational 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=5189&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5189&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 compuational 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






Testing Population Proportion (normal approximation)
Sample size200
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
1-sided critical value0.743791994982107
1-sided testReject the Null Hypothesis
2-sided Confidence Interval(sample proportion)[ 0.79304574155217 , 0.92123997244783 ]
2-sided testReject the Null Hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (normal approximation) \tabularnewline
Sample size & 200 \tabularnewline
Sample Proportion & 0.857142857 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
1-sided critical value & 0.743791994982107 \tabularnewline
1-sided test & Reject the Null Hypothesis \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.79304574155217 , 0.92123997244783 ] \tabularnewline
2-sided test & Reject the Null Hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5189&T=1

[TABLE]
[ROW][C]Testing Population Proportion (normal approximation)[/C][/ROW]
[ROW][C]Sample size[/C][C]200[/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]0.743791994982107[/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][ 0.79304574155217 , 0.92123997244783 ][/C][/ROW]
[ROW][C]2-sided test[/C][C]Reject the Null Hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5189&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5189&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 size200
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
1-sided critical value0.743791994982107
1-sided testReject the Null Hypothesis
2-sided Confidence Interval(sample proportion)[ 0.79304574155217 , 0.92123997244783 ]
2-sided testReject the Null Hypothesis






Testing Population Proportion (Agresti-Coull method)
Sample size200
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval[ 0.798884063489961 , 1 ]
Right 1-sided confidence interval[ 0 , 0.90586796433187 ]
2-sided Confidence Interval(sample proportion)[ 0.786821219645626 , 0.914003546947425 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Agresti-Coull method) \tabularnewline
Sample size & 200 \tabularnewline
Sample Proportion & 0.857142857 \tabularnewline
Null hypothesis & 0.69 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval & [ 0.798884063489961 , 1 ] \tabularnewline
Right 1-sided confidence interval & [ 0 , 0.90586796433187  ] \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.786821219645626 , 0.914003546947425 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5189&T=2

[TABLE]
[ROW][C]Testing Population Proportion (Agresti-Coull method)[/C][/ROW]
[ROW][C]Sample size[/C][C]200[/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][ 0.798884063489961 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval[/C][C][ 0 , 0.90586796433187  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(sample proportion)[/C][C][ 0.786821219645626 , 0.914003546947425 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5189&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5189&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 size200
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval[ 0.798884063489961 , 1 ]
Right 1-sided confidence interval[ 0 , 0.90586796433187 ]
2-sided Confidence Interval(sample proportion)[ 0.786821219645626 , 0.914003546947425 ]






Testing Population Proportion (Exact and Wilson method)
Sample size200
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval(Exact method)[ 0.809965705263543 , 1 ]
Right 1-sided confidence interval(Exact method)[ 0 , 0.896153516480279 ]
2-sided Confidence Interval(Exact method)[ 0.800843085091497 , 0.902502896711533 ]
Left 1-sided confidence interval(Wilson method)[ 0.811668901546815 , 1 ]
Right 1-sided confidence interval(Wilson method)[ 0 , 0.893083126275016 ]
2-sided Confidence Interval(Wilson method)[ 0.801905783094413 , 0.898918983498638 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Exact and Wilson method) \tabularnewline
Sample size & 200 \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) & [ 0.809965705263543 , 1 ] \tabularnewline
Right 1-sided confidence interval(Exact method) & [ 0 , 0.896153516480279  ] \tabularnewline
2-sided Confidence Interval(Exact method) & [ 0.800843085091497 , 0.902502896711533 ] \tabularnewline
Left 1-sided confidence interval(Wilson method) & [ 0.811668901546815 , 1 ] \tabularnewline
Right 1-sided confidence interval(Wilson method) & [ 0 , 0.893083126275016  ] \tabularnewline
2-sided Confidence Interval(Wilson method) & [ 0.801905783094413 , 0.898918983498638 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5189&T=3

[TABLE]
[ROW][C]Testing Population Proportion (Exact and Wilson method)[/C][/ROW]
[ROW][C]Sample size[/C][C]200[/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][ 0.809965705263543 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Exact method)[/C][C][ 0 , 0.896153516480279  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Exact method)[/C][C][ 0.800843085091497 , 0.902502896711533 ][/C][/ROW]
[ROW][C]Left 1-sided confidence interval(Wilson method)[/C][C][ 0.811668901546815 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Wilson method)[/C][C][ 0 , 0.893083126275016  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Wilson method)[/C][C][ 0.801905783094413 , 0.898918983498638 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5189&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5189&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 size200
Sample Proportion0.857142857
Null hypothesis0.69
Type I error (alpha)0.05
Left 1-sided confidence interval(Exact method)[ 0.809965705263543 , 1 ]
Right 1-sided confidence interval(Exact method)[ 0 , 0.896153516480279 ]
2-sided Confidence Interval(Exact method)[ 0.800843085091497 , 0.902502896711533 ]
Left 1-sided confidence interval(Wilson method)[ 0.811668901546815 , 1 ]
Right 1-sided confidence interval(Wilson method)[ 0 , 0.893083126275016 ]
2-sided Confidence Interval(Wilson method)[ 0.801905783094413 , 0.898918983498638 ]


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 200 ; par2 = 0.857142857 ; par3 = 0.69 ; par4 = 0.05 ;
Parameters (R input):
par1 = 200 ; 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')