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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_samplenorm.wasp
Title produced by softwareMinimum Sample Size - Testing Mean
Date of computationTue, 29 Oct 2013 17:53:10 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/29/t13830836132l8wpah31w3yymr.htm/, Retrieved Thu, 31 Oct 2024 22:49:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=220818, Retrieved Thu, 31 Oct 2024 22:49:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [WS 4: Vraag 3 Sof...] [2013-10-29 17:31:19] [d1ad2890024735eb49a4f5b5ae8e3b4b]
- RMPD  [Testing Variance - p-value (probability)] [Vraag 9: Female] [2013-10-29 21:27:31] [d1ad2890024735eb49a4f5b5ae8e3b4b]
- RM      [Testing Variance - Critical Value (Region)] [WS4: Vraag 9 Male] [2013-10-29 21:32:32] [d1ad2890024735eb49a4f5b5ae8e3b4b]
- RM        [Minimum Sample Size - Testing Mean] [WS4: Vraag 9 Male] [2013-10-29 21:49:31] [d1ad2890024735eb49a4f5b5ae8e3b4b]
- R             [Minimum Sample Size - Testing Mean] [Vraag 9: Male 20] [2013-10-29 21:53:10] [0d4b5c001fcd12491258e86d922016e4] [Current]
-                 [Minimum Sample Size - Testing Mean] [WS4: Vraag 10 ] [2013-10-29 22:01:12] [d1ad2890024735eb49a4f5b5ae8e3b4b]
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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220818&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220818&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Minimum Sample Size
Population Size98
Margin of Error0.05
Confidence0.95
Power0.2
Population Variance0.13
z(alpha/2) + z(beta)2.80158521811297
z(alpha) + z(beta)2.48647486052439
Minimum Sample Size (2 sided test)79.1815196986374
Minimum Sample Size (1 sided test)75.2851623714638

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 98 \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.2 \tabularnewline
Population Variance & 0.13 \tabularnewline
z(alpha/2) + z(beta) & 2.80158521811297 \tabularnewline
z(alpha) + z(beta) & 2.48647486052439 \tabularnewline
Minimum Sample Size (2 sided test) & 79.1815196986374 \tabularnewline
Minimum Sample Size (1 sided test) & 75.2851623714638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220818&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]98[/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]0.2[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]2.80158521811297[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]2.48647486052439[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]79.1815196986374[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]75.2851623714638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220818&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Minimum Sample Size
Population Size98
Margin of Error0.05
Confidence0.95
Power0.2
Population Variance0.13
z(alpha/2) + z(beta)2.80158521811297
z(alpha) + z(beta)2.48647486052439
Minimum Sample Size (2 sided test)79.1815196986374
Minimum Sample Size (1 sided test)75.2851623714638






Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error0.05
Confidence0.95
Power0.2
Population Variance0.13
z(alpha/2) + z(beta)2.80158521811297
z(alpha) + z(beta)2.48647486052439
Minimum Sample Size (2 sided test)408.141746186152
Minimum Sample Size (1 sided test)321.492976065028

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.2 \tabularnewline
Population Variance & 0.13 \tabularnewline
z(alpha/2) + z(beta) & 2.80158521811297 \tabularnewline
z(alpha) + z(beta) & 2.48647486052439 \tabularnewline
Minimum Sample Size (2 sided test) & 408.141746186152 \tabularnewline
Minimum Sample Size (1 sided test) & 321.492976065028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220818&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]0.05[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.2[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]2.80158521811297[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]2.48647486052439[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]408.141746186152[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]321.492976065028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220818&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error0.05
Confidence0.95
Power0.2
Population Variance0.13
z(alpha/2) + z(beta)2.80158521811297
z(alpha) + z(beta)2.48647486052439
Minimum Sample Size (2 sided test)408.141746186152
Minimum Sample Size (1 sided test)321.492976065028






Minimum Sample Size (Unknown Population Variance)
Population Size98
Margin of Error0.05
Confidence0.95
Power0.2
Population Varianceunknown
t(alpha/2) + t(beta)2.83701720762858
t(alpha) + t(beta)2.51211252618015
Minimum Sample Size (2 sided test)79.5607477039074
Minimum Sample Size (1 sided test)75.6411947793741

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 98 \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.2 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.83701720762858 \tabularnewline
t(alpha) + t(beta) & 2.51211252618015 \tabularnewline
Minimum Sample Size (2 sided test) & 79.5607477039074 \tabularnewline
Minimum Sample Size (1 sided test) & 75.6411947793741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220818&T=3

[TABLE]
[ROW][C]Minimum Sample Size (Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]98[/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]0.2[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.83701720762858[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]2.51211252618015[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]79.5607477039074[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]75.6411947793741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220818&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220818&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Minimum Sample Size (Unknown Population Variance)
Population Size98
Margin of Error0.05
Confidence0.95
Power0.2
Population Varianceunknown
t(alpha/2) + t(beta)2.83701720762858
t(alpha) + t(beta)2.51211252618015
Minimum Sample Size (2 sided test)79.5607477039074
Minimum Sample Size (1 sided test)75.6411947793741






Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error0.05
Confidence0.95
Power0.2
Population Varianceunknown
t(alpha/2) + t(beta)2.80831266093703
t(alpha) + t(beta)2.49236613416491
Minimum Sample Size (2 sided test)410.104240082119
Minimum Sample Size (1 sided test)323.018225230072

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.2 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.80831266093703 \tabularnewline
t(alpha) + t(beta) & 2.49236613416491 \tabularnewline
Minimum Sample Size (2 sided test) & 410.104240082119 \tabularnewline
Minimum Sample Size (1 sided test) & 323.018225230072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220818&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]0.05[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.2[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.80831266093703[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]2.49236613416491[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]410.104240082119[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]323.018225230072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220818&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220818&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error0.05
Confidence0.95
Power0.2
Population Varianceunknown
t(alpha/2) + t(beta)2.80831266093703
t(alpha) + t(beta)2.49236613416491
Minimum Sample Size (2 sided test)410.104240082119
Minimum Sample Size (1 sided test)323.018225230072


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.95 ; par2 = 0 ;
Parameters (R input):
par1 = 98 ; par2 = 0.05 ; par3 = 0.95 ; par4 = 0.13 ; par5 = 0.20 ;
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')