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Author's title

Author

*Unverified author*

R Software Module

rwasp_sample.wasp

Title produced by software

Minimum Sample Size - Testing Proportions

Date of computation

Mon, 12 Nov 2007 14:10:39 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/12/t1194901553on988lzyp8gafjb.htm/, Retrieved Sun, 28 Apr 2024 19:23:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5348, Retrieved Sun, 28 Apr 2024 19:23:51 +0000

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No (this computation is public)

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Estimated Impact

233

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Minimum Sample Size - Testing Proportions] [Case II Part III ...] [2007-11-12 21:10:39] [fd802f308f037a9692de8c23f8b60e49] [Current]
-   P     [Minimum Sample Size - Testing Proportions] [Oplossing_part3_Q4] [2007-11-17 12:56:30] [74be16979710d4c4e7c6647856088456] 

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=5348&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=5348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5348&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Minimum Sample Size
Population Size	20000
Margin of Error	0.07
Confidence	0.69
Power	0.05
Response Distribution (Proportion)	0.05
z(alpha/2) + z(beta)	2.6600756601685
z(alpha) + z(beta)	2.14070397429892
Minimum Sample Size (2 sided test)	68.3628563479884
Minimum Sample Size (1 sided test)	44.3270528539119

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 20000 \tabularnewline
Margin of Error & 0.07 \tabularnewline
Confidence & 0.69 \tabularnewline
Power & 0.05 \tabularnewline
Response Distribution (Proportion) & 0.05 \tabularnewline
z(alpha/2) + z(beta) & 2.6600756601685 \tabularnewline
z(alpha) + z(beta) & 2.14070397429892 \tabularnewline
Minimum Sample Size (2 sided test) & 68.3628563479884 \tabularnewline
Minimum Sample Size (1 sided test) & 44.3270528539119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5348&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]20000[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.07[/C][/ROW]
[ROW][C]Confidence[/C][C]0.69[/C][/ROW]
[ROW][C]Power[/C][C]0.05[/C][/ROW]
[ROW][C]Response Distribution (Proportion)[/C][C]0.05[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]2.6600756601685[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]2.14070397429892[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]68.3628563479884[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]44.3270528539119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5348&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Minimum Sample Size
Population Size	20000
Margin of Error	0.07
Confidence	0.69
Power	0.05
Response Distribution (Proportion)	0.05
z(alpha/2) + z(beta)	2.6600756601685
z(alpha) + z(beta)	2.14070397429892
Minimum Sample Size (2 sided test)	68.3628563479884
Minimum Sample Size (1 sided test)	44.3270528539119

Minimum Sample Size (infinite population)
Population Size	infinite
Margin of Error	0.07
Confidence	0.69
Power	0.05
Response Distribution (Proportion)	0.05
z(alpha/2) + z(beta)	2.6600756601685
z(alpha) + z(beta)	2.14070397429892
Minimum Sample Size (2 sided test)	68.5939019584677
Minimum Sample Size (1 sided test)	44.4232941867372

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (infinite population) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.07 \tabularnewline
Confidence & 0.69 \tabularnewline
Power & 0.05 \tabularnewline
Response Distribution (Proportion) & 0.05 \tabularnewline
z(alpha/2) + z(beta) & 2.6600756601685 \tabularnewline
z(alpha) + z(beta) & 2.14070397429892 \tabularnewline
Minimum Sample Size (2 sided test) & 68.5939019584677 \tabularnewline
Minimum Sample Size (1 sided test) & 44.4232941867372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5348&T=2

[TABLE]
[ROW][C]Minimum Sample Size (infinite population)[/C][/ROW]
[ROW][C]Population Size[/C][C]infinite[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.07[/C][/ROW]
[ROW][C]Confidence[/C][C]0.69[/C][/ROW]
[ROW][C]Power[/C][C]0.05[/C][/ROW]
[ROW][C]Response Distribution (Proportion)[/C][C]0.05[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]2.6600756601685[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]2.14070397429892[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]68.5939019584677[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]44.4232941867372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5348&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Minimum Sample Size (infinite population)
Population Size	infinite
Margin of Error	0.07
Confidence	0.69
Power	0.05
Response Distribution (Proportion)	0.05
z(alpha/2) + z(beta)	2.6600756601685
z(alpha) + z(beta)	2.14070397429892
Minimum Sample Size (2 sided test)	68.5939019584677
Minimum Sample Size (1 sided test)	44.4232941867372

Figure 1

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Postscript link

PDF link

Parameters (Session):

par1 = 20000 ; par2 = 0.07 ; par3 = 0.69 ; par4 = 0.05 ; par5 = 0.05 ;

Parameters (R input):

par1 = 20000 ; par2 = 0.07 ; par3 = 0.69 ; par4 = 0.05 ; par5 = 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)
par5 <- as.numeric(par5)
(z <- abs(qnorm((1-par3)/2)) + abs(qnorm(1-par5)))
(z1 <- abs(qnorm(1-par3)) + abs(qnorm(1-par5)))
dum <- z*z * par4*(1-par4)
dum1 <- z1*z1 * par4*(1-par4)
par22 <- par2*par2
npop <- array(NA, 200)
ppop <- array(NA, 200)
for (i in 1:200)
{
ppop[i] <- i * 100
npop[i] <- ppop[i] * dum / (dum + (ppop[i]-1)*par22)
}
bitmap(file='pic1.png')
plot(ppop,npop, xlab='population size', ylab='sample size (2 sided test)', main = paste('Confidence',par3))
dumtext <- paste('Margin of error = ',par2)
dumtext <- paste(dumtext,' Response Rate = ')
dumtext <- paste(dumtext, par4)
mtext(dumtext)
grid()
dev.off()
(n <- par1 * dum / (dum + (par1-1)*par22))
(n1 <- par1 * dum1 / (dum1 + (par1-1)*par22))
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Margin of Error',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Power',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Response Distribution (Proportion)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha/2) + z(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha) + z(beta)',header=TRUE)
a<-table.element(a,z1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (2 sided test)',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (1 sided test)',header=TRUE)
a<-table.element(a,n1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
(n <- dum / par22)
(n1 <- dum1 / par22)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (infinite population)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Size',header=TRUE)
a<-table.element(a,'infinite')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Margin of Error',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Power',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Response Distribution (Proportion)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha/2) + z(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha) + z(beta)',header=TRUE)
a<-table.element(a,z1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (2 sided test)',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (1 sided test)',header=TRUE)
a<-table.element(a,n1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

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Input Parameters & R Code