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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 17:48:21 +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/t1417974571uw509on10pg6hfe.htm/, Retrieved Thu, 16 May 2024 08:36:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263864, Retrieved Thu, 16 May 2024 08:36:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
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] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D                [Two-Way ANOVA] [] [2014-12-07 16:22:10] [8d160a85bfd9526a7d0e42afc5fb569b]
-    D                    [Two-Way ANOVA] [] [2014-12-07 17:48:21] [1d338d9433eb3ecdb4d9d35f41140a45] [Current]
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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'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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263864&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263864&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263864&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'George Udny Yule' @ yule.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means6.128-0.073-0.682-0.5061.3561.13

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 6.128 & -0.073 & -0.682 & -0.506 & 1.356 & 1.13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263864&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]6.128[/C][C]-0.073[/C][C]-0.682[/C][C]-0.506[/C][C]1.356[/C][C]1.13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263864&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263864&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
means6.128-0.073-0.682-0.5061.3561.13







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A258.02129.0112.8380.06
Treatment_B223.42223.4222.2910.131
Treatment_A:Treatment_B233.20316.6011.6240.198
Residuals4824926.8610.222

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 58.021 & 29.011 & 2.838 & 0.06 \tabularnewline
Treatment_B & 2 & 23.422 & 23.422 & 2.291 & 0.131 \tabularnewline
Treatment_A:Treatment_B & 2 & 33.203 & 16.601 & 1.624 & 0.198 \tabularnewline
Residuals & 482 & 4926.86 & 10.222 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263864&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]58.021[/C][C]29.011[/C][C]2.838[/C][C]0.06[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]23.422[/C][C]23.422[/C][C]2.291[/C][C]0.131[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]33.203[/C][C]16.601[/C][C]1.624[/C][C]0.198[/C][/ROW]
[ROW][C]Residuals[/C][C]482[/C][C]4926.86[/C][C]10.222[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263864&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263864&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_A258.02129.0112.8380.06
Treatment_B223.42223.4222.2910.131
Treatment_A:Treatment_B233.20316.6011.6240.198
Residuals4824926.8610.222







Tukey Honest Significant Difference Comparisons
difflwruprp adj
2012-20110.701-0.2141.6170.171
2014-2011-0.039-0.9170.840.994
2014-2012-0.74-1.5210.0410.068
'Male'-'Female'0.442-0.1321.0160.131
2012:'Female'-2011:'Female'-0.073-1.7841.6381
2014:'Female'-2011:'Female'-0.682-2.3220.9580.842
2011:'Male'-2011:'Female'-0.506-2.2521.240.962
2012:'Male'-2011:'Female'0.777-0.8582.4110.751
2014:'Male'-2011:'Female'-0.059-1.641.5231
2014:'Female'-2012:'Female'-0.609-2.0430.8250.829
2011:'Male'-2012:'Female'-0.434-1.9871.120.968
2012:'Male'-2012:'Female'0.849-0.5782.2770.53
2014:'Male'-2012:'Female'0.014-1.3521.3811
2011:'Male'-2014:'Female'0.176-1.31.6510.999
2012:'Male'-2014:'Female'1.4590.1172.80.024
2014:'Male'-2014:'Female'0.623-0.6541.90.729
2012:'Male'-2011:'Male'1.283-0.1862.7520.126
2014:'Male'-2011:'Male'0.448-0.9631.8580.944
2014:'Male'-2012:'Male'-0.835-2.1050.4340.414

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2012-2011 & 0.701 & -0.214 & 1.617 & 0.171 \tabularnewline
2014-2011 & -0.039 & -0.917 & 0.84 & 0.994 \tabularnewline
2014-2012 & -0.74 & -1.521 & 0.041 & 0.068 \tabularnewline
'Male'-'Female' & 0.442 & -0.132 & 1.016 & 0.131 \tabularnewline
2012:'Female'-2011:'Female' & -0.073 & -1.784 & 1.638 & 1 \tabularnewline
2014:'Female'-2011:'Female' & -0.682 & -2.322 & 0.958 & 0.842 \tabularnewline
2011:'Male'-2011:'Female' & -0.506 & -2.252 & 1.24 & 0.962 \tabularnewline
2012:'Male'-2011:'Female' & 0.777 & -0.858 & 2.411 & 0.751 \tabularnewline
2014:'Male'-2011:'Female' & -0.059 & -1.64 & 1.523 & 1 \tabularnewline
2014:'Female'-2012:'Female' & -0.609 & -2.043 & 0.825 & 0.829 \tabularnewline
2011:'Male'-2012:'Female' & -0.434 & -1.987 & 1.12 & 0.968 \tabularnewline
2012:'Male'-2012:'Female' & 0.849 & -0.578 & 2.277 & 0.53 \tabularnewline
2014:'Male'-2012:'Female' & 0.014 & -1.352 & 1.381 & 1 \tabularnewline
2011:'Male'-2014:'Female' & 0.176 & -1.3 & 1.651 & 0.999 \tabularnewline
2012:'Male'-2014:'Female' & 1.459 & 0.117 & 2.8 & 0.024 \tabularnewline
2014:'Male'-2014:'Female' & 0.623 & -0.654 & 1.9 & 0.729 \tabularnewline
2012:'Male'-2011:'Male' & 1.283 & -0.186 & 2.752 & 0.126 \tabularnewline
2014:'Male'-2011:'Male' & 0.448 & -0.963 & 1.858 & 0.944 \tabularnewline
2014:'Male'-2012:'Male' & -0.835 & -2.105 & 0.434 & 0.414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263864&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]0.701[/C][C]-0.214[/C][C]1.617[/C][C]0.171[/C][/ROW]
[ROW][C]2014-2011[/C][C]-0.039[/C][C]-0.917[/C][C]0.84[/C][C]0.994[/C][/ROW]
[ROW][C]2014-2012[/C][C]-0.74[/C][C]-1.521[/C][C]0.041[/C][C]0.068[/C][/ROW]
[ROW][C]'Male'-'Female'[/C][C]0.442[/C][C]-0.132[/C][C]1.016[/C][C]0.131[/C][/ROW]
[ROW][C]2012:'Female'-2011:'Female'[/C][C]-0.073[/C][C]-1.784[/C][C]1.638[/C][C]1[/C][/ROW]
[ROW][C]2014:'Female'-2011:'Female'[/C][C]-0.682[/C][C]-2.322[/C][C]0.958[/C][C]0.842[/C][/ROW]
[ROW][C]2011:'Male'-2011:'Female'[/C][C]-0.506[/C][C]-2.252[/C][C]1.24[/C][C]0.962[/C][/ROW]
[ROW][C]2012:'Male'-2011:'Female'[/C][C]0.777[/C][C]-0.858[/C][C]2.411[/C][C]0.751[/C][/ROW]
[ROW][C]2014:'Male'-2011:'Female'[/C][C]-0.059[/C][C]-1.64[/C][C]1.523[/C][C]1[/C][/ROW]
[ROW][C]2014:'Female'-2012:'Female'[/C][C]-0.609[/C][C]-2.043[/C][C]0.825[/C][C]0.829[/C][/ROW]
[ROW][C]2011:'Male'-2012:'Female'[/C][C]-0.434[/C][C]-1.987[/C][C]1.12[/C][C]0.968[/C][/ROW]
[ROW][C]2012:'Male'-2012:'Female'[/C][C]0.849[/C][C]-0.578[/C][C]2.277[/C][C]0.53[/C][/ROW]
[ROW][C]2014:'Male'-2012:'Female'[/C][C]0.014[/C][C]-1.352[/C][C]1.381[/C][C]1[/C][/ROW]
[ROW][C]2011:'Male'-2014:'Female'[/C][C]0.176[/C][C]-1.3[/C][C]1.651[/C][C]0.999[/C][/ROW]
[ROW][C]2012:'Male'-2014:'Female'[/C][C]1.459[/C][C]0.117[/C][C]2.8[/C][C]0.024[/C][/ROW]
[ROW][C]2014:'Male'-2014:'Female'[/C][C]0.623[/C][C]-0.654[/C][C]1.9[/C][C]0.729[/C][/ROW]
[ROW][C]2012:'Male'-2011:'Male'[/C][C]1.283[/C][C]-0.186[/C][C]2.752[/C][C]0.126[/C][/ROW]
[ROW][C]2014:'Male'-2011:'Male'[/C][C]0.448[/C][C]-0.963[/C][C]1.858[/C][C]0.944[/C][/ROW]
[ROW][C]2014:'Male'-2012:'Male'[/C][C]-0.835[/C][C]-2.105[/C][C]0.434[/C][C]0.414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263864&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263864&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
2012-20110.701-0.2141.6170.171
2014-2011-0.039-0.9170.840.994
2014-2012-0.74-1.5210.0410.068
'Male'-'Female'0.442-0.1321.0160.131
2012:'Female'-2011:'Female'-0.073-1.7841.6381
2014:'Female'-2011:'Female'-0.682-2.3220.9580.842
2011:'Male'-2011:'Female'-0.506-2.2521.240.962
2012:'Male'-2011:'Female'0.777-0.8582.4110.751
2014:'Male'-2011:'Female'-0.059-1.641.5231
2014:'Female'-2012:'Female'-0.609-2.0430.8250.829
2011:'Male'-2012:'Female'-0.434-1.9871.120.968
2012:'Male'-2012:'Female'0.849-0.5782.2770.53
2014:'Male'-2012:'Female'0.014-1.3521.3811
2011:'Male'-2014:'Female'0.176-1.31.6510.999
2012:'Male'-2014:'Female'1.4590.1172.80.024
2014:'Male'-2014:'Female'0.623-0.6541.90.729
2012:'Male'-2011:'Male'1.283-0.1862.7520.126
2014:'Male'-2011:'Male'0.448-0.9631.8580.944
2014:'Male'-2012:'Male'-0.835-2.1050.4340.414







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group52.0390.072
482

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 2.039 & 0.072 \tabularnewline
  & 482 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263864&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]2.039[/C][C]0.072[/C][/ROW]
[ROW][C] [/C][C]482[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263864&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263864&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)
Group52.0390.072
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')