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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 computationMon, 17 Dec 2012 15:38:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355776753yae51ui77j7r94n.htm/, Retrieved Fri, 29 Mar 2024 13:30:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201196, Retrieved Fri, 29 Mar 2024 13:30:33 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [Paper DEEL 5 Anova] [2012-12-17 20:38:23] [da88ff92d0f3f911fcfcae5db1e1c5cd] [Current]
- R PD    [Two-Way ANOVA] [Paper Deel 5 Anova] [2012-12-17 20:46:52] [d8d1612a641ba4e70b7599810359239a]
- RMPD    [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [Paper DEEL 5 One-...] [2012-12-17 20:51:08] [d8d1612a641ba4e70b7599810359239a]
- R P       [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [Paper DEEL 5 ANOV...] [2012-12-21 12:31:05] [74be16979710d4c4e7c6647856088456]
- R P       [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [Paper DEEL 5 ANOV...] [2012-12-21 12:32:46] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
4	1	2	NA	4	0	0	6
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	7
4	1	3	NA	4	0	1	6
4	0	3	NA	4	0	0	7
4	0	2	NA	4	0	0	7
4	0	3	NA	4	0	0	6
4	1	3	NA	4	0	0	7
4	1	2	NA	4	0	0	7
4	0	3	NA	4	0	0	7
4	0	3	NA	5	0	1	7
4	1	2	NA	4	0	0	7
4	0	3	NA	5	0	1	6
4	0	2	NA	5	0	1	6
4	1	2	NA	5	1	1	7
4	1	2	NA	4	0	0	7
4	0	3	NA	4	0	0	6
4	0	2	NA	5	1	1	6
4	1	3	NA	4	0	1	7
4	1	3	NA	5	0	1	6
4	0	3	NA	4	0	1	6
4	1	3	NA	4	0	1	6
4	0	2	NA	5	0	0	6
4	0	3	NA	5	0	1	7
4	1	3	NA	4	0	0	6
4	0	3	NA	5	0	0	7
4	0	3	NA	4	0	0	6
4	0	3	NA	4	0	1	7
4	0	3	NA	4	0	0	7
4	1	3	NA	4	0	0	7
4	1	3	NA	4	0	1	7
4	0	2	NA	4	0	0	6
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	7
4	1	2	NA	5	0	1	7
4	0	3	NA	5	0	0	6
4	0	3	NA	4	0	1	6
4	0	2	NA	4	0	1	7
4	0	3	NA	5	1	1	6
4	0	3	NA	5	0	0	6
4	1	3	NA	4	0	1	6
4	1	2	NA	4	0	0	7
4	0	3	NA	4	0	1	7
4	0	3	NA	4	0	1	6
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	6
4	0	3	NA	4	0	1	6
4	0	3	NA	4	0	0	7
4	0	2	NA	5	0	0	7
4	1	2	NA	5	1	1	7
4	0	3	NA	4	0	0	6
4	0	3	NA	5	1	0	7
4	0	3	NA	4	0	0	7
4	0	2	NA	5	0	0	6
4	0	3	NA	5	0	1	6
4	0	3	NA	4	0	0	6
4	0	3	NA	4	0	0	6
4	1	2	NA	5	1	1	6
4	1	2	NA	4	0	0	6
4	0	3	NA	5	0	1	7
4	0	3	NA	4	0	0	7
4	1	2	NA	4	0	0	6
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	7
4	0	2	NA	5	1	1	7
4	1	3	NA	4	0	0	7
4	0	3	NA	4	0	0	6
4	0	3	NA	5	0	0	7
4	0	3	NA	4	0	0	7
4	0	3	NA	4	0	0	6
4	0	3	NA	5	0	0	6
4	1	3	NA	5	0	0	7
4	0	3	NA	4	0	0	6
4	0	2	NA	4	0	1	6
4	0	3	NA	4	0	0	6
4	0	3	NA	5	0	1	6
4	0	2	NA	5	1	0	6
4	0	2	NA	4	0	1	7
4	0	3	NA	4	0	0	7
4	1	3	NA	5	0	0	6
4	0	3	NA	4	0	0	7
4	0	3	NA	5	1	0	7
4	0	3	NA	4	0	1	6
4	1	3	NA	4	0	0	7
2	1	3	3	4	0	0	6
2	1	3	2	5	0	0	6
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	6
2	0	3	3	4	0	1	7
2	1	3	2	4	0	0	7
2	1	3	3	4	0	1	7
2	0	3	3	4	0	0	7
2	0	3	2	4	0	0	7
2	0	3	3	4	0	0	6
2	1	3	2	4	0	0	7
2	0	3	3	4	0	0	7
2	1	3	3	4	0	0	7
2	0	3	3	4	0	0	6
2	1	3	3	4	0	0	6
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	0	3	2	5	0	0	7
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	1	3	2	5	0	0	7
2	0	3	3	4	0	0	7
2	1	3	3	4	0	0	7
2	1	3	2	5	0	1	7
2	0	3	2	4	0	0	7
2	0	3	3	5	0	0	7
2	1	3	2	5	0	0	7
2	1	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	1	3	3	4	0	0	6
2	1	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	6
2	1	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	1	3	2	5	0	0	7
2	0	3	3	5	0	1	6
2	0	3	3	4	0	0	6
2	0	3	2	4	0	0	7
2	0	3	3	4	0	1	7
2	0	3	3	4	0	0	6
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	6
2	1	3	3	4	0	0	7
2	1	3	3	4	0	0	6
2	1	3	3	5	0	0	7
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	0	3	3	4	0	0	7
2	1	3	3	5	0	1	6
2	1	3	2	5	0	1	6
2	0	3	2	4	0	0	7
2	0	3	3	4	0	0	7
2	0	3	3	5	1	0	6
2	0	3	2	5	0	0	6
2	1	3	3	4	0	0	7
2	0	3	3	4	0	1	6
2	0	3	3	4	0	1	7
2	0	3	2	4	0	0	6
2	0	3	2	5	0	0	7
2	0	3	2	4	0	0	7
2	1	3	3	4	0	0	7
2	0	3	3	4	0	1	6
2	0	3	3	4	0	0	6
2	1	3	3	5	1	0	7
2	1	3	3	5	1	1	7
2	1	3	3	5	0	0	7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=201196&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=201196&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201196&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.







ANOVA Model
Response ~ Treatment_A * Treatment_B - 1
means44-0.913-0.42

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B - 1 \tabularnewline
means & 4 & 4 & -0.913 & -0.42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201196&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B - 1[/C][/ROW]
[ROW][C]means[/C][C]4[/C][C]4[/C][C]-0.913[/C][C]-0.42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201196&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201196&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 - 1
means44-0.913-0.42







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A21497.926748.963891.8280
Treatment_B223.26523.26527.7020
Treatment_A:Treatment_B20.8380.8380.9980.319
Residuals150125.9710.84

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 1497.926 & 748.963 & 891.828 & 0 \tabularnewline
Treatment_B & 2 & 23.265 & 23.265 & 27.702 & 0 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.838 & 0.838 & 0.998 & 0.319 \tabularnewline
Residuals & 150 & 125.971 & 0.84 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201196&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]1497.926[/C][C]748.963[/C][C]891.828[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]23.265[/C][C]23.265[/C][C]27.702[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.838[/C][C]0.838[/C][C]0.998[/C][C]0.319[/C][/ROW]
[ROW][C]Residuals[/C][C]150[/C][C]125.971[/C][C]0.84[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201196&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201196&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_A21497.926748.963891.8280
Treatment_B223.26523.26527.7020
Treatment_A:Treatment_B20.8380.8380.9980.319
Residuals150125.9710.84







Must Include Intercept to use Tukey Test

\begin{tabular}{lllllllll}
\hline
Must Include Intercept to use Tukey Test  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201196&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201196&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201196&T=3

As an alternative you can also use a QR Code:  

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

Must Include Intercept to use Tukey Test







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group36.1350.001
150

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 6.135 & 0.001 \tabularnewline
  & 150 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201196&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]6.135[/C][C]0.001[/C][/ROW]
[ROW][C] [/C][C]150[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201196&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201196&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)
Group36.1350.001
150



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