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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_sample.wasp

Title produced by software

Minimum Sample Size - Testing Proportions

Date of computation

Thu, 13 Nov 2008 09:29:57 -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/2008/Nov/13/t12265938862htx1t9r1cuuwi5.htm/, Retrieved Tue, 28 May 2024 10:15:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24686, Retrieved Tue, 28 May 2024 10:15:38 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

165

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

F       [Minimum Sample Size - Testing Proportions] [tinneke_debock.pa...] [2008-11-13 16:29:57] [20137734a2343a7bbbd59daaec7ad301] [Current]

Feedback Forum

2008-11-24 19:08:19 [Marlies Polfliet] [reply] 
De student heeft bij deze vraag een foute en een correcte berekening gemaakt, maar kon toch concluderen dat wanneer we ervan uitgaan dat de populatie steeds in beweging is (oneindig), moet de steekproef voor een 1-sided test minstens 552.151725325594 observaties bedragen
2008-11-24 21:50:21 [Jonas Scheltjens] [reply] 
Mijn conclusie: 
Q4: De student is hier wel juist: wanneer we van een ‘infinite population’ uitgaan is de minimum verseiste sample grootte 552,151725325594. 

Post a new message

Summary of computational 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 computational 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=24686&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]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=24686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24686&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 computational 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	NA
Margin of Error	0.07
Confidence	0.95
Power	0.95
Response Distribution (Proportion)	0.5
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	NA
Minimum Sample Size (1 sided test)	NA

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & NA \tabularnewline
Margin of Error & 0.07 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Response Distribution (Proportion) & 0.5 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & NA \tabularnewline
Minimum Sample Size (1 sided test) & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24686&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]NA[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.07[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Response Distribution (Proportion)[/C][C]0.5[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]3.60481761149153[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]3.28970725390294[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]NA[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24686&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	NA
Margin of Error	0.07
Confidence	0.95
Power	0.95
Response Distribution (Proportion)	0.5
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	NA
Minimum Sample Size (1 sided test)	NA

Minimum Sample Size (infinite population)
Population Size	infinite
Margin of Error	0.07
Confidence	0.95
Power	0.95
Response Distribution (Proportion)	0.5
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	662.995408781605
Minimum Sample Size (1 sided test)	552.151725325594

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (infinite population) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.07 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Response Distribution (Proportion) & 0.5 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 662.995408781605 \tabularnewline
Minimum Sample Size (1 sided test) & 552.151725325594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24686&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]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Response Distribution (Proportion)[/C][C]0.5[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]3.60481761149153[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]3.28970725390294[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]662.995408781605[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]552.151725325594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24686&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24686&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	0.95
Power	0.95
Response Distribution (Proportion)	0.5
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	662.995408781605
Minimum Sample Size (1 sided test)	552.151725325594

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = infinite ; par2 = 0.07 ; par3 = 0.95 ; par4 = 0.5 ; par5 = 0.95 ;

Parameters (R input):

par1 = infinite ; par2 = 0.07 ; par3 = 0.95 ; par4 = 0.5 ; par5 = 0.95 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code