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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

Fri, 16 May 2008 20:29:11 -0600

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/May/17/t1210991608euk5lpsy613awfa.htm/, Retrieved Tue, 14 May 2024 19:47:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12618, Retrieved Tue, 14 May 2024 19:47:07 +0000

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Original text written by user:

This is based on a worst case estimate of 75% usage, and provides a error range of +/- 3% at 95% confidence

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

221

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

-       [Minimum Sample Size - Testing Proportions] [Foley Sample Calc...] [2008-05-17 02:29:11] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12618&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12618&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Minimum Sample Size
Population Size	10200
Margin of Error	0.03
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.75
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	742.146962446078
Minimum Sample Size (1 sided test)	534.187884003158

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 10200 \tabularnewline
Margin of Error & 0.03 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Response Distribution (Proportion) & 0.75 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 742.146962446078 \tabularnewline
Minimum Sample Size (1 sided test) & 534.187884003158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12618&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]10200[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.03[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Response Distribution (Proportion)[/C][C]0.75[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]1.95996398454005[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]1.64485362695147[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]742.146962446078[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]534.187884003158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12618&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	10200
Margin of Error	0.03
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.75
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	742.146962446078
Minimum Sample Size (1 sided test)	534.187884003158

Minimum Sample Size (infinite population)
Population Size	infinite
Margin of Error	0.03
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.75
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	800.303920977942
Minimum Sample Size (1 sided test)	563.654886269877

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (infinite population) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.03 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Response Distribution (Proportion) & 0.75 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 800.303920977942 \tabularnewline
Minimum Sample Size (1 sided test) & 563.654886269877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12618&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]0.03[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Response Distribution (Proportion)[/C][C]0.75[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]1.95996398454005[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]1.64485362695147[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]800.303920977942[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]563.654886269877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12618&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12618&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	0.03
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.75
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	800.303920977942
Minimum Sample Size (1 sided test)	563.654886269877

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 10200 ; par2 = 0.03 ; par3 = 0.95 ; par4 = 0.75 ; par5 = 0.50 ;

Parameters (R input):

par1 = 10200 ; par2 = 0.03 ; par3 = 0.95 ; par4 = 0.75 ; par5 = 0.50 ;

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code