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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Mon, 17 Dec 2012 03:50:24 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355734301d4av0ttoj0ec1ar.htm/, Retrieved Fri, 19 Apr 2024 07:14:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200711, Retrieved Fri, 19 Apr 2024 07:14:07 +0000

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-       [Two-Way ANOVA] [anova] [2012-12-17 08:50:24] [69fed4bf76000787e6433dea6d892b14] [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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200711&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200711&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	2.985	0.015	0.276	0.191

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 2.985 & 0.015 & 0.276 & 0.191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200711&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]2.985[/C][C]0.015[/C][C]0.276[/C][C]0.191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200711&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	2.985	0.015	0.276	0.191

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.162	0.162	0.165	0.685
Treatment_B	1	3.889	3.889	3.953	0.049
Treatment_A:Treatment_B	1	0.257	0.257	0.261	0.61
Residuals	150	147.588	0.984

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.162 & 0.162 & 0.165 & 0.685 \tabularnewline
Treatment_B & 1 & 3.889 & 3.889 & 3.953 & 0.049 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.257 & 0.257 & 0.261 & 0.61 \tabularnewline
Residuals & 150 & 147.588 & 0.984 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200711&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]0.162[/C][C]0.162[/C][C]0.165[/C][C]0.685[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]3.889[/C][C]3.889[/C][C]3.953[/C][C]0.049[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.257[/C][C]0.257[/C][C]0.261[/C][C]0.61[/C][/ROW]
[ROW][C]Residuals[/C][C]150[/C][C]147.588[/C][C]0.984[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200711&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200711&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	0.162	0.162	0.165	0.685
Treatment_B	1	3.889	3.889	3.953	0.049
Treatment_A:Treatment_B	1	0.257	0.257	0.261	0.61
Residuals	150	147.588	0.984

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	0.073	-0.284	0.431	0.685
1-0	0.325	0.002	0.648	0.049
1:0-0:0	0.015	-0.581	0.61	1
0:1-0:0	0.276	-0.218	0.769	0.469
1:1-0:0	0.482	-0.255	1.218	0.327
0:1-1:0	0.261	-0.371	0.893	0.707
1:1-1:0	0.467	-0.369	1.302	0.47
1:1-0:1	0.206	-0.56	0.972	0.898

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.073 & -0.284 & 0.431 & 0.685 \tabularnewline
1-0 & 0.325 & 0.002 & 0.648 & 0.049 \tabularnewline
1:0-0:0 & 0.015 & -0.581 & 0.61 & 1 \tabularnewline
0:1-0:0 & 0.276 & -0.218 & 0.769 & 0.469 \tabularnewline
1:1-0:0 & 0.482 & -0.255 & 1.218 & 0.327 \tabularnewline
0:1-1:0 & 0.261 & -0.371 & 0.893 & 0.707 \tabularnewline
1:1-1:0 & 0.467 & -0.369 & 1.302 & 0.47 \tabularnewline
1:1-0:1 & 0.206 & -0.56 & 0.972 & 0.898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200711&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]0.073[/C][C]-0.284[/C][C]0.431[/C][C]0.685[/C][/ROW]
[ROW][C]1-0[/C][C]0.325[/C][C]0.002[/C][C]0.648[/C][C]0.049[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.015[/C][C]-0.581[/C][C]0.61[/C][C]1[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.276[/C][C]-0.218[/C][C]0.769[/C][C]0.469[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.482[/C][C]-0.255[/C][C]1.218[/C][C]0.327[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]0.261[/C][C]-0.371[/C][C]0.893[/C][C]0.707[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.467[/C][C]-0.369[/C][C]1.302[/C][C]0.47[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.206[/C][C]-0.56[/C][C]0.972[/C][C]0.898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200711&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200711&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	0.073	-0.284	0.431	0.685
1-0	0.325	0.002	0.648	0.049
1:0-0:0	0.015	-0.581	0.61	1
0:1-0:0	0.276	-0.218	0.769	0.469
1:1-0:0	0.482	-0.255	1.218	0.327
0:1-1:0	0.261	-0.371	0.893	0.707
1:1-1:0	0.467	-0.369	1.302	0.47
1:1-0:1	0.206	-0.56	0.972	0.898

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	1.569	0.199
	150

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.569 & 0.199 \tabularnewline
  & 150 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200711&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]1.569[/C][C]0.199[/C][/ROW]
[ROW][C] [/C][C]150[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200711&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200711&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	1.569	0.199
	150

Figure 1

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Figure 2

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Figure 3

PNG link

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Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

par4 <- 'FALSE'
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')

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