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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, 02 Apr 2020 21:46:12 +0200

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/2020/Apr/02/t1585856933zhvguwr9w5rvlv8.htm/, Retrieved Sat, 20 Apr 2024 00:35:49 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 20 Apr 2024 00:35:49 +0200

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Estimated Impact

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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	Big Analytics Cloud Computing Center

Minimum Sample Size
Population Size	900
Margin of Error	0.05
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.33
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	246.835572754175
Minimum Sample Size (1 sided test)	189.189624151687

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 900 \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Response Distribution (Proportion) & 0.33 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 246.835572754175 \tabularnewline
Minimum Sample Size (1 sided test) & 189.189624151687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]900[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.05[/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]0.33[/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]246.835572754175[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]189.189624151687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	900
Margin of Error	0.05
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.33
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	246.835572754175
Minimum Sample Size (1 sided test)	189.189624151687

Minimum Sample Size (infinite population)
Population Size	infinite
Margin of Error	0.05
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.33
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	339.738618102188
Minimum Sample Size (1 sided test)	239.278263080198

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (infinite population) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Response Distribution (Proportion) & 0.33 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 339.738618102188 \tabularnewline
Minimum Sample Size (1 sided test) & 239.278263080198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.05[/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]0.33[/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]339.738618102188[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]239.278263080198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.05
Confidence	0.95
Power	0.5
Response Distribution (Proportion)	0.33
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	339.738618102188
Minimum Sample Size (1 sided test)	239.278263080198

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 900 ; par2 = 0.05 ; par3 = 0.95 ; par4 = 0.33 ; 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('Minimum Required Sample Size (Confidence =',round(par3*100,2),'%)'))
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