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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Thu, 27 Oct 2011 05:15:57 -0400

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/2011/Oct/27/t1319707560oaecdpqzehff0ak.htm/, Retrieved Thu, 16 May 2024 19:52:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=136810, Retrieved Thu, 16 May 2024 19:52:05 +0000

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Estimated Impact

104

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

-       [Two-Way ANOVA] [Vraag 7] [2011-10-27 09:15:57] [c8f7c4812ba63eaa5bf379ee3b4bd6a3] [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	13 seconds
R Server	'AstonUniversity' @ aston.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 & 13 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136810&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]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136810&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	13 seconds
R Server	'AstonUniversity' @ aston.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.038	0.314	-0.038	0.062	-0.314	-0.214

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.038 & 0.314 & -0.038 & 0.062 & -0.314 & -0.214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136810&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.038[/C][C]0.314[/C][C]-0.038[/C][C]0.062[/C][C]-0.314[/C][C]-0.214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136810&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	0.038	0.314	-0.038	0.062	-0.314	-0.214

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	1.742	1.742	17.441	0
Treatment_B	1	0.321	0.161	1.607	0.205
Treatment_A:Treatment_B	1	0.416	0.208	2.08	0.13
Residuals	114	11.388	0.1

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 1.742 & 1.742 & 17.441 & 0 \tabularnewline
Treatment_B & 1 & 0.321 & 0.161 & 1.607 & 0.205 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.416 & 0.208 & 2.08 & 0.13 \tabularnewline
Residuals & 114 & 11.388 & 0.1 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136810&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]1.742[/C][C]1.742[/C][C]17.441[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.321[/C][C]0.161[/C][C]1.607[/C][C]0.205[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.416[/C][C]0.208[/C][C]2.08[/C][C]0.13[/C][/ROW]
[ROW][C]Residuals[/C][C]114[/C][C]11.388[/C][C]0.1[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136810&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136810&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	1.742	1.742	17.441	0
Treatment_B	1	0.321	0.161	1.607	0.205
Treatment_A:Treatment_B	1	0.416	0.208	2.08	0.13
Residuals	114	11.388	0.1

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	0.249	0.131	0.367	0
1-0	-0.143	-0.333	0.047	0.179
NA-0	-0.014	-0.224	0.196	0.986
NA-1	0.129	-0.13	0.388	0.467
1:0-0:0	0.314	0.112	0.517	0
0:1-0:0	-0.038	-0.323	0.246	0.999
1:1-0:0	-0.038	-0.433	0.357	1
0:NA-0:0	0.062	-0.255	0.378	0.993
1:NA-0:0	0.162	-0.267	0.591	0.884
0:1-1:0	-0.353	-0.652	-0.054	0.011
1:1-1:0	-0.353	-0.759	0.053	0.126
0:NA-1:0	-0.253	-0.583	0.077	0.235
1:NA-1:0	-0.153	-0.592	0.286	0.914
1:1-0:1	0	-0.452	0.452	1
0:NA-0:1	0.1	-0.285	0.485	0.975
1:NA-0:1	0.2	-0.282	0.682	0.835
0:NA-1:1	0.1	-0.373	0.573	0.99
1:NA-1:1	0.2	-0.355	0.755	0.902
1:NA-0:NA	0.1	-0.402	0.602	0.992

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.249 & 0.131 & 0.367 & 0 \tabularnewline
1-0 & -0.143 & -0.333 & 0.047 & 0.179 \tabularnewline
NA-0 & -0.014 & -0.224 & 0.196 & 0.986 \tabularnewline
NA-1 & 0.129 & -0.13 & 0.388 & 0.467 \tabularnewline
1:0-0:0 & 0.314 & 0.112 & 0.517 & 0 \tabularnewline
0:1-0:0 & -0.038 & -0.323 & 0.246 & 0.999 \tabularnewline
1:1-0:0 & -0.038 & -0.433 & 0.357 & 1 \tabularnewline
0:NA-0:0 & 0.062 & -0.255 & 0.378 & 0.993 \tabularnewline
1:NA-0:0 & 0.162 & -0.267 & 0.591 & 0.884 \tabularnewline
0:1-1:0 & -0.353 & -0.652 & -0.054 & 0.011 \tabularnewline
1:1-1:0 & -0.353 & -0.759 & 0.053 & 0.126 \tabularnewline
0:NA-1:0 & -0.253 & -0.583 & 0.077 & 0.235 \tabularnewline
1:NA-1:0 & -0.153 & -0.592 & 0.286 & 0.914 \tabularnewline
1:1-0:1 & 0 & -0.452 & 0.452 & 1 \tabularnewline
0:NA-0:1 & 0.1 & -0.285 & 0.485 & 0.975 \tabularnewline
1:NA-0:1 & 0.2 & -0.282 & 0.682 & 0.835 \tabularnewline
0:NA-1:1 & 0.1 & -0.373 & 0.573 & 0.99 \tabularnewline
1:NA-1:1 & 0.2 & -0.355 & 0.755 & 0.902 \tabularnewline
1:NA-0:NA & 0.1 & -0.402 & 0.602 & 0.992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136810&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]0.249[/C][C]0.131[/C][C]0.367[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]-0.143[/C][C]-0.333[/C][C]0.047[/C][C]0.179[/C][/ROW]
[ROW][C]NA-0[/C][C]-0.014[/C][C]-0.224[/C][C]0.196[/C][C]0.986[/C][/ROW]
[ROW][C]NA-1[/C][C]0.129[/C][C]-0.13[/C][C]0.388[/C][C]0.467[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.314[/C][C]0.112[/C][C]0.517[/C][C]0[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-0.038[/C][C]-0.323[/C][C]0.246[/C][C]0.999[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-0.038[/C][C]-0.433[/C][C]0.357[/C][C]1[/C][/ROW]
[ROW][C]0:NA-0:0[/C][C]0.062[/C][C]-0.255[/C][C]0.378[/C][C]0.993[/C][/ROW]
[ROW][C]1:NA-0:0[/C][C]0.162[/C][C]-0.267[/C][C]0.591[/C][C]0.884[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.353[/C][C]-0.652[/C][C]-0.054[/C][C]0.011[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-0.353[/C][C]-0.759[/C][C]0.053[/C][C]0.126[/C][/ROW]
[ROW][C]0:NA-1:0[/C][C]-0.253[/C][C]-0.583[/C][C]0.077[/C][C]0.235[/C][/ROW]
[ROW][C]1:NA-1:0[/C][C]-0.153[/C][C]-0.592[/C][C]0.286[/C][C]0.914[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0[/C][C]-0.452[/C][C]0.452[/C][C]1[/C][/ROW]
[ROW][C]0:NA-0:1[/C][C]0.1[/C][C]-0.285[/C][C]0.485[/C][C]0.975[/C][/ROW]
[ROW][C]1:NA-0:1[/C][C]0.2[/C][C]-0.282[/C][C]0.682[/C][C]0.835[/C][/ROW]
[ROW][C]0:NA-1:1[/C][C]0.1[/C][C]-0.373[/C][C]0.573[/C][C]0.99[/C][/ROW]
[ROW][C]1:NA-1:1[/C][C]0.2[/C][C]-0.355[/C][C]0.755[/C][C]0.902[/C][/ROW]
[ROW][C]1:NA-0:NA[/C][C]0.1[/C][C]-0.402[/C][C]0.602[/C][C]0.992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136810&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136810&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	0.249	0.131	0.367	0
1-0	-0.143	-0.333	0.047	0.179
NA-0	-0.014	-0.224	0.196	0.986
NA-1	0.129	-0.13	0.388	0.467
1:0-0:0	0.314	0.112	0.517	0
0:1-0:0	-0.038	-0.323	0.246	0.999
1:1-0:0	-0.038	-0.433	0.357	1
0:NA-0:0	0.062	-0.255	0.378	0.993
1:NA-0:0	0.162	-0.267	0.591	0.884
0:1-1:0	-0.353	-0.652	-0.054	0.011
1:1-1:0	-0.353	-0.759	0.053	0.126
0:NA-1:0	-0.253	-0.583	0.077	0.235
1:NA-1:0	-0.153	-0.592	0.286	0.914
1:1-0:1	0	-0.452	0.452	1
0:NA-0:1	0.1	-0.285	0.485	0.975
1:NA-0:1	0.2	-0.282	0.682	0.835
0:NA-1:1	0.1	-0.373	0.573	0.99
1:NA-1:1	0.2	-0.355	0.755	0.902
1:NA-0:NA	0.1	-0.402	0.602	0.992

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	4.963	0
	114

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 4.963 & 0 \tabularnewline
  & 114 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136810&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]4.963[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]114[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136810&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136810&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	4.963	0
	114

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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):

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