Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_samplenorm.wasp

Title produced by software

Minimum Sample Size - Testing Mean

Date of computation

Mon, 08 Oct 2012 10:19:13 -0400

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/2012/Oct/08/t1349705998jsx4zjglhf7d580.htm/, Retrieved Thu, 02 May 2024 13:23:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173629, Retrieved Thu, 02 May 2024 13:23:20 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Minimum Sample Size - Testing Mean] [W4Q1021] [2012-10-08 14:19:13] [23d3ba14def8a953a1634f373cd0859d] [Current]

Feedback Forum

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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173629&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173629&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Minimum Sample Size
Population Size	21
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	13
z(alpha/2) + z(beta)	2.99639737403384
z(alpha) + z(beta)	2.68128701644526
Minimum Sample Size (2 sided test)	20.919347380442
Minimum Sample Size (1 sided test)	20.8993727041744

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 21 \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.15 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 2.99639737403384 \tabularnewline
z(alpha) + z(beta) & 2.68128701644526 \tabularnewline
Minimum Sample Size (2 sided test) & 20.919347380442 \tabularnewline
Minimum Sample Size (1 sided test) & 20.8993727041744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173629&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]21[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.15[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]2.99639737403384[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]2.68128701644526[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]20.919347380442[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]20.8993727041744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173629&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	21
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	13
z(alpha/2) + z(beta)	2.99639737403384
z(alpha) + z(beta)	2.68128701644526
Minimum Sample Size (2 sided test)	20.919347380442
Minimum Sample Size (1 sided test)	20.8993727041744

Minimum Sample Size (for Infinite Populations)
Population Size	infinite
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	13
z(alpha/2) + z(beta)	2.99639737403384
z(alpha) + z(beta)	2.68128701644526
Minimum Sample Size (2 sided test)	5187.51839557866
Minimum Sample Size (1 sided test)	4153.81781507792

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.15 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 2.99639737403384 \tabularnewline
z(alpha) + z(beta) & 2.68128701644526 \tabularnewline
Minimum Sample Size (2 sided test) & 5187.51839557866 \tabularnewline
Minimum Sample Size (1 sided test) & 4153.81781507792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173629&T=2

[TABLE]
[ROW][C]Minimum Sample Size (for Infinite Populations)[/C][/ROW]
[ROW][C]Population Size[/C][C]infinite[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.15[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]2.99639737403384[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]2.68128701644526[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]5187.51839557866[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]4153.81781507792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173629&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 (for Infinite Populations)
Population Size	infinite
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	13
z(alpha/2) + z(beta)	2.99639737403384
z(alpha) + z(beta)	2.68128701644526
Minimum Sample Size (2 sided test)	5187.51839557866
Minimum Sample Size (1 sided test)	4153.81781507792

Minimum Sample Size (Unknown Population Variance)
Population Size	21
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	unknown
t(alpha/2) + t(beta)	3.15063540721813
t(alpha) + t(beta)	2.78930035298091
Minimum Sample Size (2 sided test)	20.927023953073
Minimum Sample Size (1 sided test)	20.9069813718543

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 21 \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.15 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.15063540721813 \tabularnewline
t(alpha) + t(beta) & 2.78930035298091 \tabularnewline
Minimum Sample Size (2 sided test) & 20.927023953073 \tabularnewline
Minimum Sample Size (1 sided test) & 20.9069813718543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173629&T=3

[TABLE]
[ROW][C]Minimum Sample Size (Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]21[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.15[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.15063540721813[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]2.78930035298091[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]20.927023953073[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]20.9069813718543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173629&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173629&T=3

As an alternative you can also use a QR Code:

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

Minimum Sample Size (Unknown Population Variance)
Population Size	21
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	unknown
t(alpha/2) + t(beta)	3.15063540721813
t(alpha) + t(beta)	2.78930035298091
Minimum Sample Size (2 sided test)	20.927023953073
Minimum Sample Size (1 sided test)	20.9069813718543

Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Size	infinite
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	unknown
t(alpha/2) + t(beta)	2.99695850394025
t(alpha) + t(beta)	2.68178345519841
Minimum Sample Size (2 sided test)	5189.46149184076
Minimum Sample Size (1 sided test)	4155.35611144386

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.15 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.99695850394025 \tabularnewline
t(alpha) + t(beta) & 2.68178345519841 \tabularnewline
Minimum Sample Size (2 sided test) & 5189.46149184076 \tabularnewline
Minimum Sample Size (1 sided test) & 4155.35611144386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173629&T=4

[TABLE]
[ROW][C]Minimum Sample Size(Infinite Population, Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]infinite[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.15[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.99695850394025[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]2.68178345519841[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]5189.46149184076[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]4155.35611144386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173629&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173629&T=4

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, Unknown Population Variance)
Population Size	infinite
Margin of Error	0.15
Confidence	0.95
Power	0.15
Population Variance	unknown
t(alpha/2) + t(beta)	2.99695850394025
t(alpha) + t(beta)	2.68178345519841
Minimum Sample Size (2 sided test)	5189.46149184076
Minimum Sample Size (1 sided test)	4155.35611144386

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 20 ; par2 = 0.05 ; par3 = 0.95 ; par4 = 13 ; par5 = 21 ;

Parameters (R input):

par1 = 21 ; par2 = 0.15 ; par3 = 0.95 ; par4 = 13 ; par5 = 0.15 ;

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)))
z2 <- z*z
z2one <- z1*z1
z24 <- z2 * par4
z24one <- z2one * par4
npop <- array(NA, 200)
ppop <- array(NA, 200)
for (i in 1:200)
{
ppop[i] <- i * 100
npop[i] <- ppop[i] * z24 / (z24 + (ppop[i] - 1) * par2*par2)
}
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,' Population Var. = ')
dumtext <- paste(dumtext, par4)
mtext(dumtext)
grid()
dev.off()
par2sq <- par2 * par2
num <- par1 * z24
denom <- z24 + (par1 - 1) * par2sq
(n <- num/denom)
num1 <- par1 * z24one
denom1 <- z24one + (par1 - 1) * par2sq
(n1 <- num1/denom1)
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,'Population Variance',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')
(ni <- z24 / (par2sq))
(ni1 <- z24one / (par2sq))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (for Infinite Populations)',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,'Population Variance',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,ni)
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,ni1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
(z <- abs(qt((1-par3)/2,n-1)) + abs(qt(1-par5,n-1)))
(z1 <- abs(qt(1-par3,n1-1)) + abs(qt(1-par5,n1-1)))
z2 <- z*z
z2one <- z1*z1
z24 <- z2 * par4
z24one <- z2one * par4
par2sq <- par2 * par2
num <- par1 * z24
denom <- z24 + (par1 - 1) * par2sq
(n <- num/denom)
num1 <- par1 * z24one
denom1 <- z24one + (par1 - 1) * par2sq
(n1 <- num1/denom1)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (Unknown Population Variance)',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,'Population Variance',header=TRUE)
a<-table.element(a,'unknown')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha/2) + t(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha) + t(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')
(z <- abs(qt((1-par3)/2,ni-1)) + abs(qt(1-par5,ni-1)))
(z1 <- abs(qt(1-par3,ni1-1)) + abs(qt(1-par5,ni1-1)))
z2 <- z*z
z2one <- z1*z1
z24 <- z2 * par4
z24one <- z2one * par4
(ni <- z24 / (par2sq))
(ni1 <- z24one / (par2sq))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size
(Infinite Population, Unknown Population Variance)',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,'Population Variance',header=TRUE)
a<-table.element(a,'unknown')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha/2) + t(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha) + t(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,ni)
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,ni1)
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