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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Tue, 21 Oct 2014 20:39:56 +0100

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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/Oct/21/t1413920412wq54shhxgrdan5s.htm/, Retrieved Sun, 12 May 2024 14:51:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=244722, Retrieved Sun, 12 May 2024 14:51:43 +0000

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Estimated Impact

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-       [Two-Way ANOVA] [] [2014-10-21 19:39:56] [feba87b71495ef91d18b6c2716812399] [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	'George Udny Yule' @ yule.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244722&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244722&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	'George Udny Yule' @ yule.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0	0	0.021	0.115

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0 & 0 & 0.021 & 0.115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244722&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]0.021[/C][C]0.115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244722&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	0.021	0.115

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.107	0.107	3.382	0.069
Treatment_B	1	0.103	0.103	3.256	0.074
Treatment_A:Treatment_B	1	0.084	0.084	2.657	0.106
Residuals	113	3.57	0.032

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.107 & 0.107 & 3.382 & 0.069 \tabularnewline
Treatment_B & 1 & 0.103 & 0.103 & 3.256 & 0.074 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.084 & 0.084 & 2.657 & 0.106 \tabularnewline
Residuals & 113 & 3.57 & 0.032 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244722&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]0.107[/C][C]0.107[/C][C]3.382[/C][C]0.069[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.103[/C][C]0.103[/C][C]3.256[/C][C]0.074[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.084[/C][C]0.084[/C][C]2.657[/C][C]0.106[/C][/ROW]
[ROW][C]Residuals[/C][C]113[/C][C]3.57[/C][C]0.032[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244722&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244722&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	0.107	0.107	3.382	0.069
Treatment_B	1	0.103	0.103	3.256	0.074
Treatment_A:Treatment_B	1	0.084	0.084	2.657	0.106
Residuals	113	3.57	0.032

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	0.064	-0.005	0.133	0.069
1-0	0.06	-0.006	0.126	0.074
1:0-0:0	0	-0.14	0.14	1
0:1-0:0	0.021	-0.086	0.129	0.955
1:1-0:0	0.136	0.007	0.266	0.034
0:1-1:0	0.021	-0.11	0.152	0.974
1:1-1:0	0.136	-0.013	0.286	0.088
1:1-0:1	0.115	-0.005	0.235	0.064

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.064 & -0.005 & 0.133 & 0.069 \tabularnewline
1-0 & 0.06 & -0.006 & 0.126 & 0.074 \tabularnewline
1:0-0:0 & 0 & -0.14 & 0.14 & 1 \tabularnewline
0:1-0:0 & 0.021 & -0.086 & 0.129 & 0.955 \tabularnewline
1:1-0:0 & 0.136 & 0.007 & 0.266 & 0.034 \tabularnewline
0:1-1:0 & 0.021 & -0.11 & 0.152 & 0.974 \tabularnewline
1:1-1:0 & 0.136 & -0.013 & 0.286 & 0.088 \tabularnewline
1:1-0:1 & 0.115 & -0.005 & 0.235 & 0.064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244722&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]0.064[/C][C]-0.005[/C][C]0.133[/C][C]0.069[/C][/ROW]
[ROW][C]1-0[/C][C]0.06[/C][C]-0.006[/C][C]0.126[/C][C]0.074[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0[/C][C]-0.14[/C][C]0.14[/C][C]1[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.021[/C][C]-0.086[/C][C]0.129[/C][C]0.955[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.136[/C][C]0.007[/C][C]0.266[/C][C]0.034[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]0.021[/C][C]-0.11[/C][C]0.152[/C][C]0.974[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.136[/C][C]-0.013[/C][C]0.286[/C][C]0.088[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.115[/C][C]-0.005[/C][C]0.235[/C][C]0.064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244722&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244722&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	0.064	-0.005	0.133	0.069
1-0	0.06	-0.006	0.126	0.074
1:0-0:0	0	-0.14	0.14	1
0:1-0:0	0.021	-0.086	0.129	0.955
1:1-0:0	0.136	0.007	0.266	0.034
0:1-1:0	0.021	-0.11	0.152	0.974
1:1-1:0	0.136	-0.013	0.286	0.088
1:1-0:1	0.115	-0.005	0.235	0.064

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	3.098	0.03
	113

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.098 & 0.03 \tabularnewline
  & 113 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244722&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]3.098[/C][C]0.03[/C][/ROW]
[ROW][C] [/C][C]113[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244722&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244722&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	3.098	0.03
	113

Figure 1

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Postscript link

PDF link

Figure 2

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Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 3 ; 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code