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Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationFri, 22 Jan 2016 10:27:31 +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/2016/Jan/22/t1453458469q8ybu3utxkilrm4.htm/, Retrieved Tue, 07 May 2024 22:11:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=291371, Retrieved Tue, 07 May 2024 22:11:26 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2016-01-22 10:27:31] [99e6c1fc4b516bf23f1fe004560f1c88] [Current]
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Dataseries X:
1 "'bach'" 1 0 0 0
0 "'bach'" 0 1 0 1
1 "'bach'" 0 1 1 1
0 "'bach'" 0 1 0 1
1 "'bach'" 0 1 0 0
0 "'bach'" 1 0 0 0
1 "'bach'" 0 1 1 1
0 "'bach'" 0 1 0 1
1 "'bach'" 1 0 0 0
0 "'bach'" 0 1 0 0
1 "'scha'" 0 0 0 1
0 "'scha'" 0 1 0 0
1 "'scha'" 0 0 1 0
0 "'scha'" 1 0 1 0
1 "'scha'" 0 1 0 0
0 "'scha'" 0 0 0 1
1 "'scha'" 0 0 0 0
0 "'scha'" 1 0 1 0
1 "'scha'" 1 1 0 0
0 "'scha'" 0 0 0 0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291371&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291371&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'Gertrude Mary Cox' @ cox.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.4290.1430.238-0.476

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.429 & 0.143 & 0.238 & -0.476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291371&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.429[/C][C]0.143[/C][C]0.238[/C][C]-0.476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291371&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
means0.4290.1430.238-0.476







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10001
Treatment_B10001
Treatment_A:Treatment_B10.2380.2380.80.384
Residuals164.7620.298

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0 & 0 & 0 & 1 \tabularnewline
Treatment_B & 1 & 0 & 0 & 0 & 1 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.238 & 0.238 & 0.8 & 0.384 \tabularnewline
Residuals & 16 & 4.762 & 0.298 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291371&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]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.238[/C][C]0.238[/C][C]0.8[/C][C]0.384[/C][/ROW]
[ROW][C]Residuals[/C][C]16[/C][C]4.762[/C][C]0.298[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291371&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291371&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_A10001
Treatment_B10001
Treatment_A:Treatment_B10.2380.2380.80.384
Residuals164.7620.298







Tukey Honest Significant Difference Comparisons
difflwruprp adj
'scha'-'bach'0-0.5170.5171
1-00-0.5640.5641
'scha':0-'bach':00.143-0.6910.9770.96
'bach':1-'bach':00.238-0.8391.3150.92
'scha':1-'bach':0-0.095-1.1720.9820.994
'bach':1-'scha':00.095-0.9821.1720.994
'scha':1-'scha':0-0.238-1.3150.8390.92
'scha':1-'bach':1-0.333-1.6080.9410.876

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
'scha'-'bach' & 0 & -0.517 & 0.517 & 1 \tabularnewline
1-0 & 0 & -0.564 & 0.564 & 1 \tabularnewline
'scha':0-'bach':0 & 0.143 & -0.691 & 0.977 & 0.96 \tabularnewline
'bach':1-'bach':0 & 0.238 & -0.839 & 1.315 & 0.92 \tabularnewline
'scha':1-'bach':0 & -0.095 & -1.172 & 0.982 & 0.994 \tabularnewline
'bach':1-'scha':0 & 0.095 & -0.982 & 1.172 & 0.994 \tabularnewline
'scha':1-'scha':0 & -0.238 & -1.315 & 0.839 & 0.92 \tabularnewline
'scha':1-'bach':1 & -0.333 & -1.608 & 0.941 & 0.876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291371&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]'scha'-'bach'[/C][C]0[/C][C]-0.517[/C][C]0.517[/C][C]1[/C][/ROW]
[ROW][C]1-0[/C][C]0[/C][C]-0.564[/C][C]0.564[/C][C]1[/C][/ROW]
[ROW][C]'scha':0-'bach':0[/C][C]0.143[/C][C]-0.691[/C][C]0.977[/C][C]0.96[/C][/ROW]
[ROW][C]'bach':1-'bach':0[/C][C]0.238[/C][C]-0.839[/C][C]1.315[/C][C]0.92[/C][/ROW]
[ROW][C]'scha':1-'bach':0[/C][C]-0.095[/C][C]-1.172[/C][C]0.982[/C][C]0.994[/C][/ROW]
[ROW][C]'bach':1-'scha':0[/C][C]0.095[/C][C]-0.982[/C][C]1.172[/C][C]0.994[/C][/ROW]
[ROW][C]'scha':1-'scha':0[/C][C]-0.238[/C][C]-1.315[/C][C]0.839[/C][C]0.92[/C][/ROW]
[ROW][C]'scha':1-'bach':1[/C][C]-0.333[/C][C]-1.608[/C][C]0.941[/C][C]0.876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291371&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291371&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
'scha'-'bach'0-0.5170.5171
1-00-0.5640.5641
'scha':0-'bach':00.143-0.6910.9770.96
'bach':1-'bach':00.238-0.8391.3150.92
'scha':1-'bach':0-0.095-1.1720.9820.994
'bach':1-'scha':00.095-0.9821.1720.994
'scha':1-'scha':0-0.238-1.3150.8390.92
'scha':1-'bach':1-0.333-1.6080.9410.876







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.0430.988
16

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.043 & 0.988 \tabularnewline
  & 16 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291371&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]0.043[/C][C]0.988[/C][/ROW]
[ROW][C] [/C][C]16[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291371&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291371&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)
Group30.0430.988
16



Parameters (Session):
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- 'FALSE'
par3 <- ''
par2 <- ''
par1 <- ''
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')