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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationSun, 07 Dec 2014 15:34:35 +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/2014/Dec/07/t1417966912o1ehbhtak6igh9i.htm/, Retrieved Thu, 31 Oct 2024 23:12:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263823, Retrieved Thu, 31 Oct 2024 23:12:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 12:05:48] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D  [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 12:31:37] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D    [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 12:52:27] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D      [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 13:04:05] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D        [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 13:08:43] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D          [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 13:16:58] [8d160a85bfd9526a7d0e42afc5fb569b]
-   PD            [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-07 13:26:34] [8d160a85bfd9526a7d0e42afc5fb569b]
- RM D                [Two-Way ANOVA] [] [2014-12-07 15:34:35] [1d338d9433eb3ecdb4d9d35f41140a45] [Current]
-    D                  [Two-Way ANOVA] [] [2014-12-07 16:22:10] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D                    [Two-Way ANOVA] [] [2014-12-07 17:48:21] [8d160a85bfd9526a7d0e42afc5fb569b]
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Dataseries X:
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Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263823&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]3 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=263823&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263823&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means52.2550.4161.5271.533-0.619-1.901

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 52.255 & 0.416 & 1.527 & 1.533 & -0.619 & -1.901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263823&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]52.255[/C][C]0.416[/C][C]1.527[/C][C]1.533[/C][C]-0.619[/C][C]-1.901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263823&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263823&T=1

As an alternative you can also use a QR Code:  

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

ANOVA Model
Response ~ Treatment_A * Treatment_B
means52.2550.4161.5271.533-0.619-1.901







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A219.7079.8530.0940.91
Treatment_B230.74130.7410.2950.588
Treatment_A:Treatment_B275.0337.5150.3590.698
Residuals48250298.685104.354

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 19.707 & 9.853 & 0.094 & 0.91 \tabularnewline
Treatment_B & 2 & 30.741 & 30.741 & 0.295 & 0.588 \tabularnewline
Treatment_A:Treatment_B & 2 & 75.03 & 37.515 & 0.359 & 0.698 \tabularnewline
Residuals & 482 & 50298.685 & 104.354 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263823&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C][/C][C]2[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]2[/C][C]19.707[/C][C]9.853[/C][C]0.094[/C][C]0.91[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]30.741[/C][C]30.741[/C][C]0.295[/C][C]0.588[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]75.03[/C][C]37.515[/C][C]0.359[/C][C]0.698[/C][/ROW]
[ROW][C]Residuals[/C][C]482[/C][C]50298.685[/C][C]104.354[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263823&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263823&T=2

As an alternative you can also use a QR Code:  

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

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A219.7079.8530.0940.91
Treatment_B230.74130.7410.2950.588
Treatment_A:Treatment_B275.0337.5150.3590.698
Residuals48250298.685104.354







Tukey Honest Significant Difference Comparisons
difflwruprp adj
2012-20110.035-2.892.9611
2014-20110.426-2.383.2330.932
2014-20120.391-2.1042.8870.928
'Male'-'Female'0.506-1.3272.3390.588
2012:'Female'-2011:'Female'0.416-5.055.8821
2014:'Female'-2011:'Female'1.527-3.7136.7680.961
2011:'Male'-2011:'Female'1.533-4.0467.1110.97
2012:'Male'-2011:'Female'1.33-3.8926.5510.978
2014:'Male'-2011:'Female'1.158-3.8956.2120.986
2014:'Female'-2012:'Female'1.111-3.475.6930.983
2011:'Male'-2012:'Female'1.117-3.8486.0810.988
2012:'Male'-2012:'Female'0.914-3.6465.4740.993
2014:'Male'-2012:'Female'0.743-3.6245.1090.997
2011:'Male'-2014:'Female'0.005-4.714.721
2012:'Male'-2014:'Female'-0.198-4.4844.0891
2014:'Male'-2014:'Female'-0.369-4.4493.7121
2012:'Male'-2011:'Male'-0.203-4.8974.4911
2014:'Male'-2011:'Male'-0.374-4.8814.1321
2014:'Male'-2012:'Male'-0.171-4.2283.8851

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2012-2011 & 0.035 & -2.89 & 2.961 & 1 \tabularnewline
2014-2011 & 0.426 & -2.38 & 3.233 & 0.932 \tabularnewline
2014-2012 & 0.391 & -2.104 & 2.887 & 0.928 \tabularnewline
'Male'-'Female' & 0.506 & -1.327 & 2.339 & 0.588 \tabularnewline
2012:'Female'-2011:'Female' & 0.416 & -5.05 & 5.882 & 1 \tabularnewline
2014:'Female'-2011:'Female' & 1.527 & -3.713 & 6.768 & 0.961 \tabularnewline
2011:'Male'-2011:'Female' & 1.533 & -4.046 & 7.111 & 0.97 \tabularnewline
2012:'Male'-2011:'Female' & 1.33 & -3.892 & 6.551 & 0.978 \tabularnewline
2014:'Male'-2011:'Female' & 1.158 & -3.895 & 6.212 & 0.986 \tabularnewline
2014:'Female'-2012:'Female' & 1.111 & -3.47 & 5.693 & 0.983 \tabularnewline
2011:'Male'-2012:'Female' & 1.117 & -3.848 & 6.081 & 0.988 \tabularnewline
2012:'Male'-2012:'Female' & 0.914 & -3.646 & 5.474 & 0.993 \tabularnewline
2014:'Male'-2012:'Female' & 0.743 & -3.624 & 5.109 & 0.997 \tabularnewline
2011:'Male'-2014:'Female' & 0.005 & -4.71 & 4.72 & 1 \tabularnewline
2012:'Male'-2014:'Female' & -0.198 & -4.484 & 4.089 & 1 \tabularnewline
2014:'Male'-2014:'Female' & -0.369 & -4.449 & 3.712 & 1 \tabularnewline
2012:'Male'-2011:'Male' & -0.203 & -4.897 & 4.491 & 1 \tabularnewline
2014:'Male'-2011:'Male' & -0.374 & -4.881 & 4.132 & 1 \tabularnewline
2014:'Male'-2012:'Male' & -0.171 & -4.228 & 3.885 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263823&T=3

[TABLE]
[ROW][C]Tukey Honest Significant Difference Comparisons[/C][/ROW]
[ROW][C] [/C][C]diff[/C][C]lwr[/C][C]upr[/C][C]p adj[/C][/ROW]
[ROW][C]2012-2011[/C][C]0.035[/C][C]-2.89[/C][C]2.961[/C][C]1[/C][/ROW]
[ROW][C]2014-2011[/C][C]0.426[/C][C]-2.38[/C][C]3.233[/C][C]0.932[/C][/ROW]
[ROW][C]2014-2012[/C][C]0.391[/C][C]-2.104[/C][C]2.887[/C][C]0.928[/C][/ROW]
[ROW][C]'Male'-'Female'[/C][C]0.506[/C][C]-1.327[/C][C]2.339[/C][C]0.588[/C][/ROW]
[ROW][C]2012:'Female'-2011:'Female'[/C][C]0.416[/C][C]-5.05[/C][C]5.882[/C][C]1[/C][/ROW]
[ROW][C]2014:'Female'-2011:'Female'[/C][C]1.527[/C][C]-3.713[/C][C]6.768[/C][C]0.961[/C][/ROW]
[ROW][C]2011:'Male'-2011:'Female'[/C][C]1.533[/C][C]-4.046[/C][C]7.111[/C][C]0.97[/C][/ROW]
[ROW][C]2012:'Male'-2011:'Female'[/C][C]1.33[/C][C]-3.892[/C][C]6.551[/C][C]0.978[/C][/ROW]
[ROW][C]2014:'Male'-2011:'Female'[/C][C]1.158[/C][C]-3.895[/C][C]6.212[/C][C]0.986[/C][/ROW]
[ROW][C]2014:'Female'-2012:'Female'[/C][C]1.111[/C][C]-3.47[/C][C]5.693[/C][C]0.983[/C][/ROW]
[ROW][C]2011:'Male'-2012:'Female'[/C][C]1.117[/C][C]-3.848[/C][C]6.081[/C][C]0.988[/C][/ROW]
[ROW][C]2012:'Male'-2012:'Female'[/C][C]0.914[/C][C]-3.646[/C][C]5.474[/C][C]0.993[/C][/ROW]
[ROW][C]2014:'Male'-2012:'Female'[/C][C]0.743[/C][C]-3.624[/C][C]5.109[/C][C]0.997[/C][/ROW]
[ROW][C]2011:'Male'-2014:'Female'[/C][C]0.005[/C][C]-4.71[/C][C]4.72[/C][C]1[/C][/ROW]
[ROW][C]2012:'Male'-2014:'Female'[/C][C]-0.198[/C][C]-4.484[/C][C]4.089[/C][C]1[/C][/ROW]
[ROW][C]2014:'Male'-2014:'Female'[/C][C]-0.369[/C][C]-4.449[/C][C]3.712[/C][C]1[/C][/ROW]
[ROW][C]2012:'Male'-2011:'Male'[/C][C]-0.203[/C][C]-4.897[/C][C]4.491[/C][C]1[/C][/ROW]
[ROW][C]2014:'Male'-2011:'Male'[/C][C]-0.374[/C][C]-4.881[/C][C]4.132[/C][C]1[/C][/ROW]
[ROW][C]2014:'Male'-2012:'Male'[/C][C]-0.171[/C][C]-4.228[/C][C]3.885[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263823&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263823&T=3

As an alternative you can also use a QR Code:  

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

Tukey Honest Significant Difference Comparisons
difflwruprp adj
2012-20110.035-2.892.9611
2014-20110.426-2.383.2330.932
2014-20120.391-2.1042.8870.928
'Male'-'Female'0.506-1.3272.3390.588
2012:'Female'-2011:'Female'0.416-5.055.8821
2014:'Female'-2011:'Female'1.527-3.7136.7680.961
2011:'Male'-2011:'Female'1.533-4.0467.1110.97
2012:'Male'-2011:'Female'1.33-3.8926.5510.978
2014:'Male'-2011:'Female'1.158-3.8956.2120.986
2014:'Female'-2012:'Female'1.111-3.475.6930.983
2011:'Male'-2012:'Female'1.117-3.8486.0810.988
2012:'Male'-2012:'Female'0.914-3.6465.4740.993
2014:'Male'-2012:'Female'0.743-3.6245.1090.997
2011:'Male'-2014:'Female'0.005-4.714.721
2012:'Male'-2014:'Female'-0.198-4.4844.0891
2014:'Male'-2014:'Female'-0.369-4.4493.7121
2012:'Male'-2011:'Male'-0.203-4.8974.4911
2014:'Male'-2011:'Male'-0.374-4.8814.1321
2014:'Male'-2012:'Male'-0.171-4.2283.8851







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.3640.873
482

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.364 & 0.873 \tabularnewline
  & 482 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263823&T=4

[TABLE]
[ROW][C]Levenes Test for Homogeneity of Variance[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Group[/C][C]5[/C][C]0.364[/C][C]0.873[/C][/ROW]
[ROW][C] [/C][C]482[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263823&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263823&T=4

As an alternative you can also use a QR Code:  

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

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.3640.873
482



Parameters (Session):
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = 3 ; par4 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
cat3 <- as.numeric(par3)
intercept<-as.logical(par4)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
f2 <- as.character(x[,cat3])
xdf<-data.frame(x1,f1, f2)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
(V3 <-dimnames(y)[[1]][cat3])
names(xdf)<-c('Response', 'Treatment_A', 'Treatment_B')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment_A * Treatment_B- 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment_A * Treatment_B, data = xdf) )
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmxdf$coefficients)){
a<-table.element(a, round(lmxdf$coefficients[i], digits=3),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
for(i in 1 : length(rownames(anova.xdf))-1){
a<-table.row.start(a)
a<-table.element(a,rownames(anova.xdf)[i] ,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[i], digits=3),,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$'Df'[i+1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='anovaplot.png')
boxplot(Response ~ Treatment_A + Treatment_B, data=xdf, xlab=V2, ylab=V1, main='Boxplots of ANOVA Groups')
dev.off()
bitmap(file='designplot.png')
xdf2 <- xdf # to preserve xdf make copy for function
names(xdf2) <- c(V1, V2, V3)
plot.design(xdf2, main='Design Plot of Group Means')
dev.off()
bitmap(file='interactionplot.png')
interaction.plot(xdf$Treatment_A, xdf$Treatment_B, xdf$Response, xlab=V2, ylab=V1, trace.label=V3, main='Possible Interactions Between Anova Groups')
dev.off()
if(intercept==TRUE){
thsd<-TukeyHSD(aov.xdf)
names(thsd) <- c(V2, V3, paste(V2, ':', V3, sep=''))
bitmap(file='TukeyHSDPlot.png')
layout(matrix(c(1,2,3,3), 2,2))
plot(thsd, las=1)
dev.off()
}
if(intercept==TRUE){
ntables<-length(names(thsd))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Honest Significant Difference Comparisons', 5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1, TRUE)
for(i in 1:4){
a<-table.element(a,colnames(thsd[[1]])[i], 1, TRUE)
}
a<-table.row.end(a)
for(nt in 1:ntables){
for(i in 1:length(rownames(thsd[[nt]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[nt]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[nt]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
} # end nt
a<-table.end(a)
table.save(a,file='hsdtable.tab')
}#end if hsd tables
if(intercept==FALSE){
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'TukeyHSD Message', 1,TRUE)
a<-table.row.end(a)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Must Include Intercept to use Tukey Test ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
library(car)
lt.lmxdf<-levene.test(lmxdf)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Levenes Test for Homogeneity of Variance', 4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
for (i in 1:3){
a<-table.element(a,names(lt.lmxdf)[i], 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Group', 1, TRUE)
for (i in 1:3){
a<-table.element(a,round(lt.lmxdf[[i]][1], digits=3), 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
a<-table.element(a,lt.lmxdf[[1]][2], 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')