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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 computationMon, 25 Oct 2010 21:43:18 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/25/t1288042941s14oyux5inq1wlp.htm/, Retrieved Mon, 29 Apr 2024 18:26:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=88614, Retrieved Mon, 29 Apr 2024 18:26:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Minimum Sample Size - Testing Mean] [Ws 4 - Q11] [2010-10-25 21:43:18] [0829c729852d8a4b1b0c41cf0848af95] [Current]
Feedback Forum
2010-10-31 08:37:48 [48eb36e2c01435ad7e4ea7854a9d98fe] [reply] 
De student heeft een aantal gegevens verkeerd ingevuld in de software:
Margin of error = 1 en niet = 0,01
Variance = 13 en niet = 0,13

Dit maakt natuurlijk dat ook de bekomen resultaten niet correct zijn. De minimale steekproef bij een tweezijdige test dient namelijk gelijkt te zijn aan 65 en bij een eenzijdige test aan 60. Een correcte oplossing staat hier: http://www.freestatistics.org/blog/date/2010/Oct/26/t1288044528d0rcid0goac0tw9.htm/

Post a new message

Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=88614&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=88614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88614&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Minimum Sample Size
Population Size105
Margin of Error0.01
Confidence0.95
Power0.95
Population Variance0.13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)104.357538332230
Minimum Sample Size (1 sided test)104.229511458772

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 0.01 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & 0.13 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 104.357538332230 \tabularnewline
Minimum Sample Size (1 sided test) & 104.229511458772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=88614&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]105[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.01[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.13[/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]104.357538332230[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]104.229511458772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=88614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88614&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 Size105
Margin of Error0.01
Confidence0.95
Power0.95
Population Variance0.13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)104.357538332230
Minimum Sample Size (1 sided test)104.229511458772






Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error0.01
Confidence0.95
Power0.95
Population Variance0.13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)16893.1230157553
Minimum Sample Size (1 sided test)14068.8259612961

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.01 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & 0.13 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 16893.1230157553 \tabularnewline
Minimum Sample Size (1 sided test) & 14068.8259612961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=88614&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]0.01[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.13[/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]16893.1230157553[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]14068.8259612961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=88614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88614&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 Error0.01
Confidence0.95
Power0.95
Population Variance0.13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)16893.1230157553
Minimum Sample Size (1 sided test)14068.8259612961






Minimum Sample Size (Unknown Population Variance)
Population Size105
Margin of Error0.01
Confidence0.95
Power0.95
Population Varianceunknown
t(alpha/2) + t(beta)3.64291277451715
t(alpha) + t(beta)3.31949756270803
Minimum Sample Size (2 sided test)104.370824855664
Minimum Sample Size (1 sided test)104.243179429553

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 0.01 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.64291277451715 \tabularnewline
t(alpha) + t(beta) & 3.31949756270803 \tabularnewline
Minimum Sample Size (2 sided test) & 104.370824855664 \tabularnewline
Minimum Sample Size (1 sided test) & 104.243179429553 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=88614&T=3

[TABLE]
[ROW][C]Minimum Sample Size (Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]105[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.01[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.64291277451715[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]3.31949756270803[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]104.370824855664[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]104.243179429553[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=88614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88614&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 Size105
Margin of Error0.01
Confidence0.95
Power0.95
Population Varianceunknown
t(alpha/2) + t(beta)3.64291277451715
t(alpha) + t(beta)3.31949756270803
Minimum Sample Size (2 sided test)104.370824855664
Minimum Sample Size (1 sided test)104.243179429553






Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error0.01
Confidence0.95
Power0.95
Population Varianceunknown
t(alpha/2) + t(beta)3.60504826879559
t(alpha) + t(beta)3.28992390004439
Minimum Sample Size (2 sided test)16895.2849264499
Minimum Sample Size (1 sided test)14070.6790485083

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.01 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.60504826879559 \tabularnewline
t(alpha) + t(beta) & 3.28992390004439 \tabularnewline
Minimum Sample Size (2 sided test) & 16895.2849264499 \tabularnewline
Minimum Sample Size (1 sided test) & 14070.6790485083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=88614&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]0.01[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.60504826879559[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]3.28992390004439[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]16895.2849264499[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]14070.6790485083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=88614&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88614&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 Error0.01
Confidence0.95
Power0.95
Population Varianceunknown
t(alpha/2) + t(beta)3.60504826879559
t(alpha) + t(beta)3.28992390004439
Minimum Sample Size (2 sided test)16895.2849264499
Minimum Sample Size (1 sided test)14070.6790485083


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 105 ; par2 = 0.01 ; par3 = 0.95 ; par4 = 0.13 ; par5 = 0.95 ;
Parameters (R input):
par1 = 105 ; par2 = 0.01 ; par3 = 0.95 ; par4 = 0.13 ; 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)))
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')