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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 computationSun, 11 Nov 2012 14:32:56 -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/Nov/11/t135266241369u40cucir4tyqv.htm/, Retrieved Fri, 03 May 2024 13:04:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187576, Retrieved Fri, 03 May 2024 13:04:46 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [vraag 8] [2012-10-15 14:18:52] [93b3e8d0ee7e4ccb504c2c04707a9358]
-   PD    [Two-Way ANOVA] [2-way anova ] [2012-11-11 19:32:56] [18a55f974a2e8651a7d8da0218fcbdb6] [Current]
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Dataseries X:
0	'News'	11
0	'News'	8
0	'News'	6
0	'News'	8
0	'Business'	10
0	'Business'	12
0	'Business'	13
0	'Business'	11
0	'Sports'	4
0	'Sports'	3
0	'Sports'	5
0	'Sports'	6
1	'News'	13
1	'News'	12
1	'News'	11
1	'News'	14
1	'Business'	10
1	'Business'	9
1	'Business'	9
1	'Business'	8
1	'Sports'	12
1	'Sports'	10
1	'Sports'	11
1	'Sports'	12




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=187576&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=187576&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187576&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
means11.5-3.25-7-2.56.759.25

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 11.5 & -3.25 & -7 & -2.5 & 6.75 & 9.25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187576&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]11.5[/C][C]-3.25[/C][C]-7[/C][C]-2.5[/C][C]6.75[/C][C]9.25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187576&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187576&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
means11.5-3.25-7-2.56.759.25







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A231.7515.8758.7920.002
Treatment_B248.16748.16726.6770
Treatment_A:Treatment_B291.58345.79225.3620
Residuals1832.51.806

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 31.75 & 15.875 & 8.792 & 0.002 \tabularnewline
Treatment_B & 2 & 48.167 & 48.167 & 26.677 & 0 \tabularnewline
Treatment_A:Treatment_B & 2 & 91.583 & 45.792 & 25.362 & 0 \tabularnewline
Residuals & 18 & 32.5 & 1.806 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187576&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]31.75[/C][C]15.875[/C][C]8.792[/C][C]0.002[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]48.167[/C][C]48.167[/C][C]26.677[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]91.583[/C][C]45.792[/C][C]25.362[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]18[/C][C]32.5[/C][C]1.806[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187576&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187576&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_A231.7515.8758.7920.002
Treatment_B248.16748.16726.6770
Treatment_A:Treatment_B291.58345.79225.3620
Residuals1832.51.806







Tukey Honest Significant Difference Comparisons
difflwruprp adj
News-Business0.125-1.591.840.981
Sports-Business-2.375-4.09-0.660.006
Sports-News-2.5-4.215-0.7850.004
1-02.8331.6813.9860
News:0-Business:0-3.25-6.27-0.230.031
Sports:0-Business:0-7-10.02-3.980
Business:1-Business:0-2.5-5.520.520.14
News:1-Business:01-2.024.020.893
Sports:1-Business:0-0.25-3.272.771
Sports:0-News:0-3.75-6.77-0.730.01
Business:1-News:00.75-2.273.770.966
News:1-News:04.251.237.270.003
Sports:1-News:03-0.026.020.052
Business:1-Sports:04.51.487.520.002
News:1-Sports:084.9811.020
Sports:1-Sports:06.753.739.770
News:1-Business:13.50.486.520.018
Sports:1-Business:12.25-0.775.270.219
Sports:1-News:1-1.25-4.271.770.773

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
News-Business & 0.125 & -1.59 & 1.84 & 0.981 \tabularnewline
Sports-Business & -2.375 & -4.09 & -0.66 & 0.006 \tabularnewline
Sports-News & -2.5 & -4.215 & -0.785 & 0.004 \tabularnewline
1-0 & 2.833 & 1.681 & 3.986 & 0 \tabularnewline
News:0-Business:0 & -3.25 & -6.27 & -0.23 & 0.031 \tabularnewline
Sports:0-Business:0 & -7 & -10.02 & -3.98 & 0 \tabularnewline
Business:1-Business:0 & -2.5 & -5.52 & 0.52 & 0.14 \tabularnewline
News:1-Business:0 & 1 & -2.02 & 4.02 & 0.893 \tabularnewline
Sports:1-Business:0 & -0.25 & -3.27 & 2.77 & 1 \tabularnewline
Sports:0-News:0 & -3.75 & -6.77 & -0.73 & 0.01 \tabularnewline
Business:1-News:0 & 0.75 & -2.27 & 3.77 & 0.966 \tabularnewline
News:1-News:0 & 4.25 & 1.23 & 7.27 & 0.003 \tabularnewline
Sports:1-News:0 & 3 & -0.02 & 6.02 & 0.052 \tabularnewline
Business:1-Sports:0 & 4.5 & 1.48 & 7.52 & 0.002 \tabularnewline
News:1-Sports:0 & 8 & 4.98 & 11.02 & 0 \tabularnewline
Sports:1-Sports:0 & 6.75 & 3.73 & 9.77 & 0 \tabularnewline
News:1-Business:1 & 3.5 & 0.48 & 6.52 & 0.018 \tabularnewline
Sports:1-Business:1 & 2.25 & -0.77 & 5.27 & 0.219 \tabularnewline
Sports:1-News:1 & -1.25 & -4.27 & 1.77 & 0.773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187576&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]News-Business[/C][C]0.125[/C][C]-1.59[/C][C]1.84[/C][C]0.981[/C][/ROW]
[ROW][C]Sports-Business[/C][C]-2.375[/C][C]-4.09[/C][C]-0.66[/C][C]0.006[/C][/ROW]
[ROW][C]Sports-News[/C][C]-2.5[/C][C]-4.215[/C][C]-0.785[/C][C]0.004[/C][/ROW]
[ROW][C]1-0[/C][C]2.833[/C][C]1.681[/C][C]3.986[/C][C]0[/C][/ROW]
[ROW][C]News:0-Business:0[/C][C]-3.25[/C][C]-6.27[/C][C]-0.23[/C][C]0.031[/C][/ROW]
[ROW][C]Sports:0-Business:0[/C][C]-7[/C][C]-10.02[/C][C]-3.98[/C][C]0[/C][/ROW]
[ROW][C]Business:1-Business:0[/C][C]-2.5[/C][C]-5.52[/C][C]0.52[/C][C]0.14[/C][/ROW]
[ROW][C]News:1-Business:0[/C][C]1[/C][C]-2.02[/C][C]4.02[/C][C]0.893[/C][/ROW]
[ROW][C]Sports:1-Business:0[/C][C]-0.25[/C][C]-3.27[/C][C]2.77[/C][C]1[/C][/ROW]
[ROW][C]Sports:0-News:0[/C][C]-3.75[/C][C]-6.77[/C][C]-0.73[/C][C]0.01[/C][/ROW]
[ROW][C]Business:1-News:0[/C][C]0.75[/C][C]-2.27[/C][C]3.77[/C][C]0.966[/C][/ROW]
[ROW][C]News:1-News:0[/C][C]4.25[/C][C]1.23[/C][C]7.27[/C][C]0.003[/C][/ROW]
[ROW][C]Sports:1-News:0[/C][C]3[/C][C]-0.02[/C][C]6.02[/C][C]0.052[/C][/ROW]
[ROW][C]Business:1-Sports:0[/C][C]4.5[/C][C]1.48[/C][C]7.52[/C][C]0.002[/C][/ROW]
[ROW][C]News:1-Sports:0[/C][C]8[/C][C]4.98[/C][C]11.02[/C][C]0[/C][/ROW]
[ROW][C]Sports:1-Sports:0[/C][C]6.75[/C][C]3.73[/C][C]9.77[/C][C]0[/C][/ROW]
[ROW][C]News:1-Business:1[/C][C]3.5[/C][C]0.48[/C][C]6.52[/C][C]0.018[/C][/ROW]
[ROW][C]Sports:1-Business:1[/C][C]2.25[/C][C]-0.77[/C][C]5.27[/C][C]0.219[/C][/ROW]
[ROW][C]Sports:1-News:1[/C][C]-1.25[/C][C]-4.27[/C][C]1.77[/C][C]0.773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187576&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187576&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
News-Business0.125-1.591.840.981
Sports-Business-2.375-4.09-0.660.006
Sports-News-2.5-4.215-0.7850.004
1-02.8331.6813.9860
News:0-Business:0-3.25-6.27-0.230.031
Sports:0-Business:0-7-10.02-3.980
Business:1-Business:0-2.5-5.520.520.14
News:1-Business:01-2.024.020.893
Sports:1-Business:0-0.25-3.272.771
Sports:0-News:0-3.75-6.77-0.730.01
Business:1-News:00.75-2.273.770.966
News:1-News:04.251.237.270.003
Sports:1-News:03-0.026.020.052
Business:1-Sports:04.51.487.520.002
News:1-Sports:084.9811.020
Sports:1-Sports:06.753.739.770
News:1-Business:13.50.486.520.018
Sports:1-Business:12.25-0.775.270.219
Sports:1-News:1-1.25-4.271.770.773







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.4170.83
18

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.417 & 0.83 \tabularnewline
  & 18 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187576&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]0.417[/C][C]0.83[/C][/ROW]
[ROW][C] [/C][C]18[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187576&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187576&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)
Group50.4170.83
18



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')