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Author's title

Author*The author of this computation has been verified*
R Software ModuleIan.Hollidayrwasp_Two Factor ANOVA.wasp
Title produced by softwareAnalysis of Variance Free Statistics Software (Calculator)
Date of computationSat, 06 Mar 2010 04:29:26 -0700
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/Mar/06/t12678750547l35uia4msxpz2p.htm/, Retrieved Sat, 22 Jan 2022 17:05:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74029, Retrieved Sat, 22 Jan 2022 17:05:30 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Analysis of Variance Free Statistics Software (Calculator)] [PY2224_2009 Exam ...] [2010-03-06 11:29:26] [a9208f4f8d3b118336aae915785f2bd9] [Current]
-    D    [Analysis of Variance Free Statistics Software (Calculator)] [PY2224_2009 Exam ...] [2010-03-06 12:02:59] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R  D      [Two-Way ANOVA] [Adler data] [2010-05-22 19:26:30] [8431b2cca73e677c29fb8bfdfc230859]
-           [Two-Way ANOVA] [] [2010-05-27 10:03:00] [e8bb49267f0b4e611f4778412d0811f2]
- R         [Two-Way ANOVA] [ANOVA with better...] [2010-05-29 09:36:12] [98fd0e87c3eb04e0cc2efde01dbafab6]
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Dataseries X:
'GOOD'	'HIGH'	25
'GOOD'	'HIGH'	0
'GOOD'	'HIGH'	-16
'GOOD'	'HIGH'	5
'GOOD'	'HIGH'	11
'GOOD'	'HIGH'	-6
'GOOD'	'HIGH'	42
'GOOD'	'HIGH'	-2
'GOOD'	'HIGH'	-13
'GOOD'	'HIGH'	14
'GOOD'	'HIGH'	4
'GOOD'	'HIGH'	-22
'GOOD'	'HIGH'	19
'GOOD'	'HIGH'	6
'GOOD'	'HIGH'	-6
'GOOD'	'LOW'	-25
'GOOD'	'LOW'	-23
'GOOD'	'LOW'	-28
'GOOD'	'LOW'	-22
'GOOD'	'LOW'	-22
'GOOD'	'LOW'	-10
'GOOD'	'LOW'	-20
'GOOD'	'LOW'	-24
'GOOD'	'LOW'	-24
'GOOD'	'LOW'	-22
'GOOD'	'LOW'	-23
'GOOD'	'LOW'	-19
'GOOD'	'LOW'	-2
'GOOD'	'LOW'	12
'GOOD'	'LOW'	-8
'GOOD'	'LOW'	-17
'GOOD'	'LOW'	-30
'SCIENTIFIC'	'HIGH'	-19
'SCIENTIFIC'	'HIGH'	-24
'SCIENTIFIC'	'HIGH'	-4
'SCIENTIFIC'	'HIGH'	-24
'SCIENTIFIC'	'HIGH'	0
'SCIENTIFIC'	'HIGH'	-4
'SCIENTIFIC'	'HIGH'	5
'SCIENTIFIC'	'HIGH'	-1
'SCIENTIFIC'	'HIGH'	-9
'SCIENTIFIC'	'HIGH'	-5
'SCIENTIFIC'	'HIGH'	-6
'SCIENTIFIC'	'HIGH'	4
'SCIENTIFIC'	'HIGH'	-13
'SCIENTIFIC'	'HIGH'	-1
'SCIENTIFIC'	'HIGH'	-3
'SCIENTIFIC'	'HIGH'	-11
'SCIENTIFIC'	'HIGH'	-6
'SCIENTIFIC'	'HIGH'	-4
'SCIENTIFIC'	'LOW'	6
'SCIENTIFIC'	'LOW'	-5
'SCIENTIFIC'	'LOW'	14
'SCIENTIFIC'	'LOW'	-11
'SCIENTIFIC'	'LOW'	14
'SCIENTIFIC'	'LOW'	-5
'SCIENTIFIC'	'LOW'	-22
'SCIENTIFIC'	'LOW'	7
'SCIENTIFIC'	'LOW'	14
'SCIENTIFIC'	'LOW'	15
'SCIENTIFIC'	'LOW'	-6
'SCIENTIFIC'	'LOW'	9
'SCIENTIFIC'	'LOW'	-5
'SCIENTIFIC'	'HIGH'	-26
'SCIENTIFIC'	'HIGH'	-1
'SCIENTIFIC'	'HIGH'	22
'SCIENTIFIC'	'HIGH'	3
'SCIENTIFIC'	'HIGH'	-26
'SCIENTIFIC'	'HIGH'	4
'SCIENTIFIC'	'HIGH'	-21
'SCIENTIFIC'	'HIGH'	-19
'SCIENTIFIC'	'HIGH'	-12
'SCIENTIFIC'	'HIGH'	9
'SCIENTIFIC'	'HIGH'	-9
'SCIENTIFIC'	'HIGH'	-27
'SCIENTIFIC'	'HIGH'	-10
'SCIENTIFIC'	'HIGH'	-37
'SCIENTIFIC'	'HIGH'	0
'SCIENTIFIC'	'HIGH'	-10
'SCIENTIFIC'	'LOW'	-12
'SCIENTIFIC'	'LOW'	-4
'SCIENTIFIC'	'LOW'	13
'SCIENTIFIC'	'LOW'	-27
'SCIENTIFIC'	'LOW'	-7
'SCIENTIFIC'	'LOW'	-20
'SCIENTIFIC'	'LOW'	-4
'SCIENTIFIC'	'LOW'	-10
'SCIENTIFIC'	'LOW'	-3
'SCIENTIFIC'	'LOW'	-11
'SCIENTIFIC'	'LOW'	2
'SCIENTIFIC'	'LOW'	-9
'SCIENTIFIC'	'LOW'	20
'SCIENTIFIC'	'LOW'	9
'SCIENTIFIC'	'LOW'	-8
'SCIENTIFIC'	'LOW'	8
'SCIENTIFIC'	'LOW'	-6
'SCIENTIFIC'	'LOW'	6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74029&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74029&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'Gwilym Jenkins' @ 72.249.127.135







ANOVA Model
Response ~ Treatment_A * Treatment_B
means4.067-22.125-12.44929.282

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 4.067 & -22.125 & -12.449 & 29.282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74029&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]4.067[/C][C]-22.125[/C][C]-12.449[/C][C]29.282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74029&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
means4.067-22.125-12.44929.282







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1165.945165.9451.0430.31
Treatment_B1142.681142.6810.8970.346
Treatment_A:Treatment_B14581.3084581.30828.7930
Residuals9314797.323159.111

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 165.945 & 165.945 & 1.043 & 0.31 \tabularnewline
Treatment_B & 1 & 142.681 & 142.681 & 0.897 & 0.346 \tabularnewline
Treatment_A:Treatment_B & 1 & 4581.308 & 4581.308 & 28.793 & 0 \tabularnewline
Residuals & 93 & 14797.323 & 159.111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74029&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]1[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]1[/C][C]165.945[/C][C]165.945[/C][C]1.043[/C][C]0.31[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]142.681[/C][C]142.681[/C][C]0.897[/C][C]0.346[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]4581.308[/C][C]4581.308[/C][C]28.793[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]93[/C][C]14797.323[/C][C]159.111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74029&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)
1
Treatment_A1165.945165.9451.0430.31
Treatment_B1142.681142.6810.8970.346
Treatment_A:Treatment_B14581.3084581.30828.7930
Residuals9314797.323159.111







Tukey Honest Significant Difference Comparisons
difflwruprp adj
LOW-HIGH-2.616-7.7032.4710.31
SCIENTIFIC-GOOD2.576-2.8337.9850.347
LOW:GOOD-HIGH:GOOD-22.125-33.815-10.4360
HIGH:SCIENTIFIC-HIGH:GOOD-12.449-22.678-2.220.01
LOW:SCIENTIFIC-HIGH:GOOD-5.292-15.6715.0870.544
HIGH:SCIENTIFIC-LOW:GOOD9.676-0.12619.4790.054
LOW:SCIENTIFIC-LOW:GOOD16.8336.87426.7920
LOW:SCIENTIFIC-HIGH:SCIENTIFIC7.157-1.03815.3510.109

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
LOW-HIGH & -2.616 & -7.703 & 2.471 & 0.31 \tabularnewline
SCIENTIFIC-GOOD & 2.576 & -2.833 & 7.985 & 0.347 \tabularnewline
LOW:GOOD-HIGH:GOOD & -22.125 & -33.815 & -10.436 & 0 \tabularnewline
HIGH:SCIENTIFIC-HIGH:GOOD & -12.449 & -22.678 & -2.22 & 0.01 \tabularnewline
LOW:SCIENTIFIC-HIGH:GOOD & -5.292 & -15.671 & 5.087 & 0.544 \tabularnewline
HIGH:SCIENTIFIC-LOW:GOOD & 9.676 & -0.126 & 19.479 & 0.054 \tabularnewline
LOW:SCIENTIFIC-LOW:GOOD & 16.833 & 6.874 & 26.792 & 0 \tabularnewline
LOW:SCIENTIFIC-HIGH:SCIENTIFIC & 7.157 & -1.038 & 15.351 & 0.109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74029&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]LOW-HIGH[/C][C]-2.616[/C][C]-7.703[/C][C]2.471[/C][C]0.31[/C][/ROW]
[ROW][C]SCIENTIFIC-GOOD[/C][C]2.576[/C][C]-2.833[/C][C]7.985[/C][C]0.347[/C][/ROW]
[ROW][C]LOW:GOOD-HIGH:GOOD[/C][C]-22.125[/C][C]-33.815[/C][C]-10.436[/C][C]0[/C][/ROW]
[ROW][C]HIGH:SCIENTIFIC-HIGH:GOOD[/C][C]-12.449[/C][C]-22.678[/C][C]-2.22[/C][C]0.01[/C][/ROW]
[ROW][C]LOW:SCIENTIFIC-HIGH:GOOD[/C][C]-5.292[/C][C]-15.671[/C][C]5.087[/C][C]0.544[/C][/ROW]
[ROW][C]HIGH:SCIENTIFIC-LOW:GOOD[/C][C]9.676[/C][C]-0.126[/C][C]19.479[/C][C]0.054[/C][/ROW]
[ROW][C]LOW:SCIENTIFIC-LOW:GOOD[/C][C]16.833[/C][C]6.874[/C][C]26.792[/C][C]0[/C][/ROW]
[ROW][C]LOW:SCIENTIFIC-HIGH:SCIENTIFIC[/C][C]7.157[/C][C]-1.038[/C][C]15.351[/C][C]0.109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74029&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
LOW-HIGH-2.616-7.7032.4710.31
SCIENTIFIC-GOOD2.576-2.8337.9850.347
LOW:GOOD-HIGH:GOOD-22.125-33.815-10.4360
HIGH:SCIENTIFIC-HIGH:GOOD-12.449-22.678-2.220.01
LOW:SCIENTIFIC-HIGH:GOOD-5.292-15.6715.0870.544
HIGH:SCIENTIFIC-LOW:GOOD9.676-0.12619.4790.054
LOW:SCIENTIFIC-LOW:GOOD16.8336.87426.7920
LOW:SCIENTIFIC-HIGH:SCIENTIFIC7.157-1.03815.3510.109







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.270.289
93

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.27 & 0.289 \tabularnewline
  & 93 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74029&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]3[/C][C]1.27[/C][C]0.289[/C][/ROW]
[ROW][C] [/C][C]93[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74029&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74029&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)
Group31.270.289
93



Parameters (Session):
par1 = 3 ; par2 = 2 ; par3 = 1 ; par4 = TRUE ;
Parameters (R input):
par1 = 3 ; par2 = 2 ; par3 = 1 ; 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')