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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Wed, 06 Nov 2013 10:11:56 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/06/t1383750726p2d1bb8abaouojd.htm/, Retrieved Fri, 01 Nov 2024 00:35:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=223029, Retrieved Fri, 01 Nov 2024 00:35:41 +0000

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Estimated Impact

121

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Two-Way ANOVA] [] [2013-11-06 15:11:56] [4a4acd0e332e84f1be693c3136326ce2] [Current]

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Dataseries X:

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Histogram

Boxplots

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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	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223029&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223029&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	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0	0	0	0.05	0.037	-0.012

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0 & 0 & 0 & 0.05 & 0.037 & -0.012 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223029&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0[/C][C]0[/C][C]0[/C][C]0.05[/C][C]0.037[/C][C]-0.012[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223029&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	0	0	0	0.05	0.037	-0.012

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	0.015	0.008	0.227	0.797
Treatment_B	2	0.098	0.098	2.914	0.091
Treatment_A:Treatment_B	2	0.012	0.006	0.181	0.834
Residuals	111	3.738	0.034

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 0.015 & 0.008 & 0.227 & 0.797 \tabularnewline
Treatment_B & 2 & 0.098 & 0.098 & 2.914 & 0.091 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.012 & 0.006 & 0.181 & 0.834 \tabularnewline
Residuals & 111 & 3.738 & 0.034 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223029&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]0.015[/C][C]0.008[/C][C]0.227[/C][C]0.797[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0.098[/C][C]0.098[/C][C]2.914[/C][C]0.091[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.012[/C][C]0.006[/C][C]0.181[/C][C]0.834[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]3.738[/C][C]0.034[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223029&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)
	2
Treatment_A	2	0.015	0.008	0.227	0.797
Treatment_B	2	0.098	0.098	2.914	0.091
Treatment_A:Treatment_B	2	0.012	0.006	0.181	0.834
Residuals	111	3.738	0.034

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
F-E	0.023	-0.076	0.122	0.847
H-E	-0.002	-0.101	0.097	0.999
H-F	-0.025	-0.122	0.072	0.815
1-0	0.059	-0.01	0.127	0.092
F:0-E:0	0	-0.183	0.183	1
H:0-E:0	0	-0.192	0.192	1
E:1-E:0	0.05	-0.126	0.226	0.962
F:1-E:0	0.087	-0.083	0.257	0.677
H:1-E:0	0.038	-0.128	0.204	0.985
H:0-F:0	0	-0.192	0.192	1
E:1-F:0	0.05	-0.126	0.226	0.962
F:1-F:0	0.087	-0.083	0.257	0.677
H:1-F:0	0.038	-0.128	0.204	0.985
E:1-H:0	0.05	-0.135	0.235	0.97
F:1-H:0	0.087	-0.093	0.267	0.728
H:1-H:0	0.038	-0.138	0.215	0.988
F:1-E:1	0.037	-0.126	0.2	0.986
H:1-E:1	-0.012	-0.17	0.147	1
H:1-F:1	-0.048	-0.201	0.104	0.94

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
F-E & 0.023 & -0.076 & 0.122 & 0.847 \tabularnewline
H-E & -0.002 & -0.101 & 0.097 & 0.999 \tabularnewline
H-F & -0.025 & -0.122 & 0.072 & 0.815 \tabularnewline
1-0 & 0.059 & -0.01 & 0.127 & 0.092 \tabularnewline
F:0-E:0 & 0 & -0.183 & 0.183 & 1 \tabularnewline
H:0-E:0 & 0 & -0.192 & 0.192 & 1 \tabularnewline
E:1-E:0 & 0.05 & -0.126 & 0.226 & 0.962 \tabularnewline
F:1-E:0 & 0.087 & -0.083 & 0.257 & 0.677 \tabularnewline
H:1-E:0 & 0.038 & -0.128 & 0.204 & 0.985 \tabularnewline
H:0-F:0 & 0 & -0.192 & 0.192 & 1 \tabularnewline
E:1-F:0 & 0.05 & -0.126 & 0.226 & 0.962 \tabularnewline
F:1-F:0 & 0.087 & -0.083 & 0.257 & 0.677 \tabularnewline
H:1-F:0 & 0.038 & -0.128 & 0.204 & 0.985 \tabularnewline
E:1-H:0 & 0.05 & -0.135 & 0.235 & 0.97 \tabularnewline
F:1-H:0 & 0.087 & -0.093 & 0.267 & 0.728 \tabularnewline
H:1-H:0 & 0.038 & -0.138 & 0.215 & 0.988 \tabularnewline
F:1-E:1 & 0.037 & -0.126 & 0.2 & 0.986 \tabularnewline
H:1-E:1 & -0.012 & -0.17 & 0.147 & 1 \tabularnewline
H:1-F:1 & -0.048 & -0.201 & 0.104 & 0.94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223029&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]F-E[/C][C]0.023[/C][C]-0.076[/C][C]0.122[/C][C]0.847[/C][/ROW]
[ROW][C]H-E[/C][C]-0.002[/C][C]-0.101[/C][C]0.097[/C][C]0.999[/C][/ROW]
[ROW][C]H-F[/C][C]-0.025[/C][C]-0.122[/C][C]0.072[/C][C]0.815[/C][/ROW]
[ROW][C]1-0[/C][C]0.059[/C][C]-0.01[/C][C]0.127[/C][C]0.092[/C][/ROW]
[ROW][C]F:0-E:0[/C][C]0[/C][C]-0.183[/C][C]0.183[/C][C]1[/C][/ROW]
[ROW][C]H:0-E:0[/C][C]0[/C][C]-0.192[/C][C]0.192[/C][C]1[/C][/ROW]
[ROW][C]E:1-E:0[/C][C]0.05[/C][C]-0.126[/C][C]0.226[/C][C]0.962[/C][/ROW]
[ROW][C]F:1-E:0[/C][C]0.087[/C][C]-0.083[/C][C]0.257[/C][C]0.677[/C][/ROW]
[ROW][C]H:1-E:0[/C][C]0.038[/C][C]-0.128[/C][C]0.204[/C][C]0.985[/C][/ROW]
[ROW][C]H:0-F:0[/C][C]0[/C][C]-0.192[/C][C]0.192[/C][C]1[/C][/ROW]
[ROW][C]E:1-F:0[/C][C]0.05[/C][C]-0.126[/C][C]0.226[/C][C]0.962[/C][/ROW]
[ROW][C]F:1-F:0[/C][C]0.087[/C][C]-0.083[/C][C]0.257[/C][C]0.677[/C][/ROW]
[ROW][C]H:1-F:0[/C][C]0.038[/C][C]-0.128[/C][C]0.204[/C][C]0.985[/C][/ROW]
[ROW][C]E:1-H:0[/C][C]0.05[/C][C]-0.135[/C][C]0.235[/C][C]0.97[/C][/ROW]
[ROW][C]F:1-H:0[/C][C]0.087[/C][C]-0.093[/C][C]0.267[/C][C]0.728[/C][/ROW]
[ROW][C]H:1-H:0[/C][C]0.038[/C][C]-0.138[/C][C]0.215[/C][C]0.988[/C][/ROW]
[ROW][C]F:1-E:1[/C][C]0.037[/C][C]-0.126[/C][C]0.2[/C][C]0.986[/C][/ROW]
[ROW][C]H:1-E:1[/C][C]-0.012[/C][C]-0.17[/C][C]0.147[/C][C]1[/C][/ROW]
[ROW][C]H:1-F:1[/C][C]-0.048[/C][C]-0.201[/C][C]0.104[/C][C]0.94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223029&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
F-E	0.023	-0.076	0.122	0.847
H-E	-0.002	-0.101	0.097	0.999
H-F	-0.025	-0.122	0.072	0.815
1-0	0.059	-0.01	0.127	0.092
F:0-E:0	0	-0.183	0.183	1
H:0-E:0	0	-0.192	0.192	1
E:1-E:0	0.05	-0.126	0.226	0.962
F:1-E:0	0.087	-0.083	0.257	0.677
H:1-E:0	0.038	-0.128	0.204	0.985
H:0-F:0	0	-0.192	0.192	1
E:1-F:0	0.05	-0.126	0.226	0.962
F:1-F:0	0.087	-0.083	0.257	0.677
H:1-F:0	0.038	-0.128	0.204	0.985
E:1-H:0	0.05	-0.135	0.235	0.97
F:1-H:0	0.087	-0.093	0.267	0.728
H:1-H:0	0.038	-0.138	0.215	0.988
F:1-E:1	0.037	-0.126	0.2	0.986
H:1-E:1	-0.012	-0.17	0.147	1
H:1-F:1	-0.048	-0.201	0.104	0.94

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	0.746	0.591
	111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.746 & 0.591 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223029&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]0.746[/C][C]0.591[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223029&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223029&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	5	0.746	0.591
	111

Figure 1

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Figure 2

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Figure 3

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Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code