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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, 26 Oct 2010 16:47:49 +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/26/t12881116160wxsn4rwnshcvu6.htm/, Retrieved Sun, 28 Apr 2024 12:35:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=89381, Retrieved Sun, 28 Apr 2024 12:35:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Factor Analysis] [Sleep in Mammals ...] [2010-03-21 11:39:53] [b98453cac15ba1066b407e146608df68]
- RMPD  [Testing Mean with unknown Variance - Critical Value] [Hypothesis Test a...] [2010-10-19 11:45:26] [b98453cac15ba1066b407e146608df68]
F   PD    [Testing Mean with unknown Variance - Critical Value] [] [2010-10-26 15:36:52] [7f2363d2c77d3bf71367965cc53be730]
-    D      [Testing Mean with unknown Variance - Critical Value] [] [2010-10-26 15:46:24] [7f2363d2c77d3bf71367965cc53be730]
-             [Testing Mean with unknown Variance - Critical Value] [] [2010-10-26 16:01:05] [7f2363d2c77d3bf71367965cc53be730]
- RM D          [Testing Mean with known Variance - Sample Size] [] [2010-10-26 16:24:34] [7f2363d2c77d3bf71367965cc53be730]
-                 [Testing Mean with known Variance - Sample Size] [] [2010-10-26 16:33:07] [7f2363d2c77d3bf71367965cc53be730]
-                   [Testing Mean with known Variance - Sample Size] [] [2010-10-26 16:34:09] [7f2363d2c77d3bf71367965cc53be730]
F                     [Testing Mean with known Variance - Sample Size] [] [2010-10-26 16:38:31] [7f2363d2c77d3bf71367965cc53be730]
F RM                      [Minimum Sample Size - Testing Mean] [] [2010-10-26 16:47:49] [4dba6678eac10ee5c3460d144a14bd5c] [Current]
Feedback Forum
2010-10-30 09:54:08 [7d66e2e510b144c68ca0882fd178e17c] [reply
je hebt de juiste calculator gebruikt, maar de power heb je verkeerd ingegeven. Power is 1- de bèta fout= 0,95
Je bekomt onderstaande ouput:

http://www.freestatistics.org/blog/index.php?v=date/2010/Oct/28/t1288266688ql048qomqz1jo78.htm/

Je hebt ook in de verkeerde tabel gekeken. In de eerste en tweede tabel is de variantie gekend. In de derde en vierde kolom is de variantie niet gekend. We moeten kijken in de eerste en tweede tabel omdat in deze vraag de variantie gekend is. Vervolgens kijken we enkel in de eerste tabel omdat bij ons de populatie gekend is nl. 105 mannelijke studenten. Bijgevolg kunnen we besluiten dat de minimum steekproefgrootte voor een éénzijdige test 60 bedraagt. Voor de tweezijdige test is dit 65.

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Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89381&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89381&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Minimum Sample Size
Population Size105
Margin of Error1
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)34.0627943128074
Minimum Sample Size (1 sided test)26.5359777294951

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 34.0627943128074 \tabularnewline
Minimum Sample Size (1 sided test) & 26.5359777294951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89381&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]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/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]34.0627943128074[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]26.5359777294951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89381&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 Size105
Margin of Error1
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)34.0627943128074
Minimum Sample Size (1 sided test)26.5359777294951







Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)49.9389646690236
Minimum Sample Size (1 sided test)35.1720649032403

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 49.9389646690236 \tabularnewline
Minimum Sample Size (1 sided test) & 35.1720649032403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89381&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]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/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]49.9389646690236[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]35.1720649032403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89381&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 Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)49.9389646690236
Minimum Sample Size (1 sided test)35.1720649032403







Minimum Sample Size (Unknown Population Variance)
Population Size105
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.0343685160221
t(alpha) + t(beta)1.70676309978817
Minimum Sample Size (2 sided test)35.799583472935
Minimum Sample Size (1 sided test)28.0278658796924

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.0343685160221 \tabularnewline
t(alpha) + t(beta) & 1.70676309978817 \tabularnewline
Minimum Sample Size (2 sided test) & 35.799583472935 \tabularnewline
Minimum Sample Size (1 sided test) & 28.0278658796924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89381&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]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.0343685160221[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.70676309978817[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]35.799583472935[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]28.0278658796924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89381&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 Size105
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.0343685160221
t(alpha) + t(beta)1.70676309978817
Minimum Sample Size (2 sided test)35.799583472935
Minimum Sample Size (1 sided test)28.0278658796924







Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.00963863419992
t(alpha) + t(beta)1.69068586822280
Minimum Sample Size (2 sided test)52.5024167208958
Minimum Sample Size (1 sided test)37.1594431651079

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.00963863419992 \tabularnewline
t(alpha) + t(beta) & 1.69068586822280 \tabularnewline
Minimum Sample Size (2 sided test) & 52.5024167208958 \tabularnewline
Minimum Sample Size (1 sided test) & 37.1594431651079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89381&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]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.00963863419992[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.69068586822280[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]52.5024167208958[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]37.1594431651079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89381&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89381&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 Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.00963863419992
t(alpha) + t(beta)1.69068586822280
Minimum Sample Size (2 sided test)52.5024167208958
Minimum Sample Size (1 sided test)37.1594431651079



Parameters (Session):
par1 = 0.95 ; par2 = 20 ;
Parameters (R input):
par1 = 105 ; par2 = 1 ; par3 = 0.95 ; par4 = 13 ; par5 = 0.5 ;
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')