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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Wed, 17 Dec 2014 19:27:27 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418844458iiyazrrc15q1wwm.htm/, Retrieved Sun, 19 May 2024 18:45:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270598, Retrieved Sun, 19 May 2024 18:45:33 +0000

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-       [Two-Way ANOVA] [] [2014-12-17 19:27:27] [e63466588bf3c49b37383cc70d2c7b07] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270598&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]2 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=270598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270598&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	13.592	-0.279	-0.778	-0.335

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 13.592 & -0.279 & -0.778 & -0.335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270598&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]13.592[/C][C]-0.279[/C][C]-0.778[/C][C]-0.335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270598&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
means	13.592	-0.279	-0.778	-0.335

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	11.04	11.04	0.955	0.329
Treatment_B	1	61.891	61.891	5.352	0.021
Treatment_A:Treatment_B	1	1.952	1.952	0.169	0.682
Residuals	282	3261.058	11.564

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 11.04 & 11.04 & 0.955 & 0.329 \tabularnewline
Treatment_B & 1 & 61.891 & 61.891 & 5.352 & 0.021 \tabularnewline
Treatment_A:Treatment_B & 1 & 1.952 & 1.952 & 0.169 & 0.682 \tabularnewline
Residuals & 282 & 3261.058 & 11.564 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270598&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]11.04[/C][C]11.04[/C][C]0.955[/C][C]0.329[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]61.891[/C][C]61.891[/C][C]5.352[/C][C]0.021[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]1.952[/C][C]1.952[/C][C]0.169[/C][C]0.682[/C][/ROW]
[ROW][C]Residuals[/C][C]282[/C][C]3261.058[/C][C]11.564[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270598&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270598&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
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	11.04	11.04	0.955	0.329
Treatment_B	1	61.891	61.891	5.352	0.021
Treatment_A:Treatment_B	1	1.952	1.952	0.169	0.682
Residuals	282	3261.058	11.564

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	-0.393	-1.186	0.399	0.329
1-0	-0.936	-1.734	-0.137	0.022
1:0-0:0	-0.279	-1.859	1.302	0.969
0:1-0:0	-0.778	-2.25	0.694	0.522
1:1-0:0	-1.391	-2.934	0.152	0.094
0:1-1:0	-0.499	-1.93	0.931	0.804
1:1-1:0	-1.112	-2.616	0.391	0.225
1:1-0:1	-0.613	-2.003	0.777	0.665

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.393 & -1.186 & 0.399 & 0.329 \tabularnewline
1-0 & -0.936 & -1.734 & -0.137 & 0.022 \tabularnewline
1:0-0:0 & -0.279 & -1.859 & 1.302 & 0.969 \tabularnewline
0:1-0:0 & -0.778 & -2.25 & 0.694 & 0.522 \tabularnewline
1:1-0:0 & -1.391 & -2.934 & 0.152 & 0.094 \tabularnewline
0:1-1:0 & -0.499 & -1.93 & 0.931 & 0.804 \tabularnewline
1:1-1:0 & -1.112 & -2.616 & 0.391 & 0.225 \tabularnewline
1:1-0:1 & -0.613 & -2.003 & 0.777 & 0.665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270598&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]-0.393[/C][C]-1.186[/C][C]0.399[/C][C]0.329[/C][/ROW]
[ROW][C]1-0[/C][C]-0.936[/C][C]-1.734[/C][C]-0.137[/C][C]0.022[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.279[/C][C]-1.859[/C][C]1.302[/C][C]0.969[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-0.778[/C][C]-2.25[/C][C]0.694[/C][C]0.522[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-1.391[/C][C]-2.934[/C][C]0.152[/C][C]0.094[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.499[/C][C]-1.93[/C][C]0.931[/C][C]0.804[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-1.112[/C][C]-2.616[/C][C]0.391[/C][C]0.225[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.613[/C][C]-2.003[/C][C]0.777[/C][C]0.665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270598&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270598&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
	diff	lwr	upr	p adj
1-0	-0.393	-1.186	0.399	0.329
1-0	-0.936	-1.734	-0.137	0.022
1:0-0:0	-0.279	-1.859	1.302	0.969
0:1-0:0	-0.778	-2.25	0.694	0.522
1:1-0:0	-1.391	-2.934	0.152	0.094
0:1-1:0	-0.499	-1.93	0.931	0.804
1:1-1:0	-1.112	-2.616	0.391	0.225
1:1-0:1	-0.613	-2.003	0.777	0.665

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	1.008	0.39
	282

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.008 & 0.39 \tabularnewline
  & 282 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270598&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]1.008[/C][C]0.39[/C][/ROW]
[ROW][C] [/C][C]282[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270598&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270598&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
	Df	F value	Pr(>F)
Group	3	1.008	0.39
	282

Figure 1

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Figure 2

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Figure 3

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Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 3 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;

Parameters (R input):

par1 = 3 ; par2 = 1 ; par3 = 2 ; 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')

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