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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 computationWed, 25 Jan 2017 11:11:33 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/25/t1485339102d4vu15a9zu37xpj.htm/, Retrieved Tue, 14 May 2024 12:59:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306602, Retrieved Tue, 14 May 2024 12:59:28 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [vraag 2] [2017-01-25 10:11:33] [74a1aee5dc3270c40ddc0c460955e440] [Current]
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Dataseries X:
6 1 0
7 0 1
2 0 1
11 0 1
13 0 1
3 1 0
17 0 1
10 0 1
4 1 0
12 0 1
7 0 0
11 0 1
3 0 0
5 1 0
1 0 1
12 0 0
18 0 0
8 1 0
6 1 1
1 0 0




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306602&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306602&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306602&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center







ANOVA Model
Response ~ Treatment_A * Treatment_B
means8.2-31.133-0.333

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 8.2 & -3 & 1.133 & -0.333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306602&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]8.2[/C][C]-3[/C][C]1.133[/C][C]-0.333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306602&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306602&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
means8.2-31.133-0.333







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A154.28854.2882.070.169
Treatment_B14.5884.5880.1750.681
Treatment_A:Treatment_B10.0740.0740.0030.958
Residuals16419.626.225

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 54.288 & 54.288 & 2.07 & 0.169 \tabularnewline
Treatment_B & 1 & 4.588 & 4.588 & 0.175 & 0.681 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.074 & 0.074 & 0.003 & 0.958 \tabularnewline
Residuals & 16 & 419.6 & 26.225 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306602&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]54.288[/C][C]54.288[/C][C]2.07[/C][C]0.169[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]4.588[/C][C]4.588[/C][C]0.175[/C][C]0.681[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.074[/C][C]0.074[/C][C]0.003[/C][C]0.958[/C][/ROW]
[ROW][C]Residuals[/C][C]16[/C][C]419.6[/C][C]26.225[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306602&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306602&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_A154.28854.2882.070.169
Treatment_B14.5884.5880.1750.681
Treatment_A:Treatment_B10.0740.0740.0030.958
Residuals16419.626.225







Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-3.595-8.8921.7020.169
1-00.862-3.9935.7170.712
1:0-0:0-3-12.2666.2660.791
0:1-0:01.133-7.0399.3050.978
1:1-0:0-2.2-18.2513.850.979
0:1-1:04.133-4.03912.3050.49
1:1-1:00.8-15.2516.850.999
1:1-0:1-3.333-18.77712.1110.925

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -3.595 & -8.892 & 1.702 & 0.169 \tabularnewline
1-0 & 0.862 & -3.993 & 5.717 & 0.712 \tabularnewline
1:0-0:0 & -3 & -12.266 & 6.266 & 0.791 \tabularnewline
0:1-0:0 & 1.133 & -7.039 & 9.305 & 0.978 \tabularnewline
1:1-0:0 & -2.2 & -18.25 & 13.85 & 0.979 \tabularnewline
0:1-1:0 & 4.133 & -4.039 & 12.305 & 0.49 \tabularnewline
1:1-1:0 & 0.8 & -15.25 & 16.85 & 0.999 \tabularnewline
1:1-0:1 & -3.333 & -18.777 & 12.111 & 0.925 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306602&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]1-0[/C][C]-3.595[/C][C]-8.892[/C][C]1.702[/C][C]0.169[/C][/ROW]
[ROW][C]1-0[/C][C]0.862[/C][C]-3.993[/C][C]5.717[/C][C]0.712[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-3[/C][C]-12.266[/C][C]6.266[/C][C]0.791[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]1.133[/C][C]-7.039[/C][C]9.305[/C][C]0.978[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-2.2[/C][C]-18.25[/C][C]13.85[/C][C]0.979[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]4.133[/C][C]-4.039[/C][C]12.305[/C][C]0.49[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.8[/C][C]-15.25[/C][C]16.85[/C][C]0.999[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-3.333[/C][C]-18.777[/C][C]12.111[/C][C]0.925[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306602&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306602&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
1-0-3.595-8.8921.7020.169
1-00.862-3.9935.7170.712
1:0-0:0-3-12.2666.2660.791
0:1-0:01.133-7.0399.3050.978
1:1-0:0-2.2-18.2513.850.979
0:1-1:04.133-4.03912.3050.49
1:1-1:00.8-15.2516.850.999
1:1-0:1-3.333-18.77712.1110.925







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.3820.284
16

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.382 & 0.284 \tabularnewline
  & 16 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306602&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]1.382[/C][C]0.284[/C][/ROW]
[ROW][C] [/C][C]16[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306602&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306602&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)
Group31.3820.284
16



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- '3'
par2 <- '2'
par1 <- '1'
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')