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*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

Tue, 08 Nov 2011 15:10:41 -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/2011/Nov/08/t132078308200msilsx5jtc97e.htm/, Retrieved Thu, 19 Jun 2025 21:43:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=140927, Retrieved Thu, 19 Jun 2025 21:43:53 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

249

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

-     [Two-Way ANOVA] [] [2010-11-02 14:42:14] [b98453cac15ba1066b407e146608df68]
- R P     [Two-Way ANOVA] [] [2011-11-08 20:10:41] [0f9b7c3b8d01420b2751adc6f98a35df] [Current]

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Dataseries X:

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Histogram

Boxplots

0	0	'E'	0	1
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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	3 seconds
R Server	'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140927&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140927&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.471	0.059	-0.471	-0.171	0.119	0.209

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.471 & 0.059 & -0.471 & -0.171 & 0.119 & 0.209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140927&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.471[/C][C]0.059[/C][C]-0.471[/C][C]-0.171[/C][C]0.119[/C][C]0.209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140927&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	0.471	0.059	-0.471	-0.171	0.119	0.209

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	4.852	2.426	12.601	0
Treatment_B	2	0.105	0.105	0.546	0.462
Treatment_A:Treatment_B	2	0.201	0.101	0.523	0.594
Residuals	111	21.371	0.193

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 4.852 & 2.426 & 12.601 & 0 \tabularnewline
Treatment_B & 2 & 0.105 & 0.105 & 0.546 & 0.462 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.201 & 0.101 & 0.523 & 0.594 \tabularnewline
Residuals & 111 & 21.371 & 0.193 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140927&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]4.852[/C][C]2.426[/C][C]12.601[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0.105[/C][C]0.105[/C][C]0.546[/C][C]0.462[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.201[/C][C]0.101[/C][C]0.523[/C][C]0.594[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]21.371[/C][C]0.193[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140927&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	4.852	2.426	12.601	0
Treatment_B	2	0.105	0.105	0.546	0.462
Treatment_A:Treatment_B	2	0.201	0.101	0.523	0.594
Residuals	111	21.371	0.193

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
F-E	0.122	-0.116	0.359	0.447
H-E	-0.353	-0.591	-0.116	0.002
H-F	-0.475	-0.708	-0.242	0
1-0	-0.061	-0.224	0.103	0.463
F:0-E:0	0.059	-0.378	0.495	0.999
H:0-E:0	-0.471	-0.93	-0.011	0.041
E:1-E:0	-0.171	-0.59	0.249	0.846
F:1-E:0	0.008	-0.399	0.415	1
H:1-E:0	-0.432	-0.829	-0.035	0.024
H:0-F:0	-0.529	-0.989	-0.07	0.014
E:1-F:0	-0.229	-0.649	0.19	0.61
F:1-F:0	-0.051	-0.458	0.356	0.999
H:1-F:0	-0.491	-0.888	-0.094	0.006
E:1-H:0	0.3	-0.143	0.743	0.371
F:1-H:0	0.478	0.047	0.91	0.021
H:1-H:0	0.038	-0.383	0.46	1
F:1-E:1	0.178	-0.211	0.567	0.768
H:1-E:1	-0.262	-0.64	0.117	0.347
H:1-F:1	-0.44	-0.804	-0.076	0.009

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
F-E & 0.122 & -0.116 & 0.359 & 0.447 \tabularnewline
H-E & -0.353 & -0.591 & -0.116 & 0.002 \tabularnewline
H-F & -0.475 & -0.708 & -0.242 & 0 \tabularnewline
1-0 & -0.061 & -0.224 & 0.103 & 0.463 \tabularnewline
F:0-E:0 & 0.059 & -0.378 & 0.495 & 0.999 \tabularnewline
H:0-E:0 & -0.471 & -0.93 & -0.011 & 0.041 \tabularnewline
E:1-E:0 & -0.171 & -0.59 & 0.249 & 0.846 \tabularnewline
F:1-E:0 & 0.008 & -0.399 & 0.415 & 1 \tabularnewline
H:1-E:0 & -0.432 & -0.829 & -0.035 & 0.024 \tabularnewline
H:0-F:0 & -0.529 & -0.989 & -0.07 & 0.014 \tabularnewline
E:1-F:0 & -0.229 & -0.649 & 0.19 & 0.61 \tabularnewline
F:1-F:0 & -0.051 & -0.458 & 0.356 & 0.999 \tabularnewline
H:1-F:0 & -0.491 & -0.888 & -0.094 & 0.006 \tabularnewline
E:1-H:0 & 0.3 & -0.143 & 0.743 & 0.371 \tabularnewline
F:1-H:0 & 0.478 & 0.047 & 0.91 & 0.021 \tabularnewline
H:1-H:0 & 0.038 & -0.383 & 0.46 & 1 \tabularnewline
F:1-E:1 & 0.178 & -0.211 & 0.567 & 0.768 \tabularnewline
H:1-E:1 & -0.262 & -0.64 & 0.117 & 0.347 \tabularnewline
H:1-F:1 & -0.44 & -0.804 & -0.076 & 0.009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140927&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]0.122[/C][C]-0.116[/C][C]0.359[/C][C]0.447[/C][/ROW]
[ROW][C]H-E[/C][C]-0.353[/C][C]-0.591[/C][C]-0.116[/C][C]0.002[/C][/ROW]
[ROW][C]H-F[/C][C]-0.475[/C][C]-0.708[/C][C]-0.242[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]-0.061[/C][C]-0.224[/C][C]0.103[/C][C]0.463[/C][/ROW]
[ROW][C]F:0-E:0[/C][C]0.059[/C][C]-0.378[/C][C]0.495[/C][C]0.999[/C][/ROW]
[ROW][C]H:0-E:0[/C][C]-0.471[/C][C]-0.93[/C][C]-0.011[/C][C]0.041[/C][/ROW]
[ROW][C]E:1-E:0[/C][C]-0.171[/C][C]-0.59[/C][C]0.249[/C][C]0.846[/C][/ROW]
[ROW][C]F:1-E:0[/C][C]0.008[/C][C]-0.399[/C][C]0.415[/C][C]1[/C][/ROW]
[ROW][C]H:1-E:0[/C][C]-0.432[/C][C]-0.829[/C][C]-0.035[/C][C]0.024[/C][/ROW]
[ROW][C]H:0-F:0[/C][C]-0.529[/C][C]-0.989[/C][C]-0.07[/C][C]0.014[/C][/ROW]
[ROW][C]E:1-F:0[/C][C]-0.229[/C][C]-0.649[/C][C]0.19[/C][C]0.61[/C][/ROW]
[ROW][C]F:1-F:0[/C][C]-0.051[/C][C]-0.458[/C][C]0.356[/C][C]0.999[/C][/ROW]
[ROW][C]H:1-F:0[/C][C]-0.491[/C][C]-0.888[/C][C]-0.094[/C][C]0.006[/C][/ROW]
[ROW][C]E:1-H:0[/C][C]0.3[/C][C]-0.143[/C][C]0.743[/C][C]0.371[/C][/ROW]
[ROW][C]F:1-H:0[/C][C]0.478[/C][C]0.047[/C][C]0.91[/C][C]0.021[/C][/ROW]
[ROW][C]H:1-H:0[/C][C]0.038[/C][C]-0.383[/C][C]0.46[/C][C]1[/C][/ROW]
[ROW][C]F:1-E:1[/C][C]0.178[/C][C]-0.211[/C][C]0.567[/C][C]0.768[/C][/ROW]
[ROW][C]H:1-E:1[/C][C]-0.262[/C][C]-0.64[/C][C]0.117[/C][C]0.347[/C][/ROW]
[ROW][C]H:1-F:1[/C][C]-0.44[/C][C]-0.804[/C][C]-0.076[/C][C]0.009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140927&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	0.122	-0.116	0.359	0.447
H-E	-0.353	-0.591	-0.116	0.002
H-F	-0.475	-0.708	-0.242	0
1-0	-0.061	-0.224	0.103	0.463
F:0-E:0	0.059	-0.378	0.495	0.999
H:0-E:0	-0.471	-0.93	-0.011	0.041
E:1-E:0	-0.171	-0.59	0.249	0.846
F:1-E:0	0.008	-0.399	0.415	1
H:1-E:0	-0.432	-0.829	-0.035	0.024
H:0-F:0	-0.529	-0.989	-0.07	0.014
E:1-F:0	-0.229	-0.649	0.19	0.61
F:1-F:0	-0.051	-0.458	0.356	0.999
H:1-F:0	-0.491	-0.888	-0.094	0.006
E:1-H:0	0.3	-0.143	0.743	0.371
F:1-H:0	0.478	0.047	0.91	0.021
H:1-H:0	0.038	-0.383	0.46	1
F:1-E:1	0.178	-0.211	0.567	0.768
H:1-E:1	-0.262	-0.64	0.117	0.347
H:1-F:1	-0.44	-0.804	-0.076	0.009

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	5.504	0
	111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 5.504 & 0 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140927&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]5.504[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140927&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140927&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	5.504	0
	111

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 = 5 ; par2 = 1 ; par3 = TRUE ;

Parameters (R input):

par1 = 4 ; par2 = 3 ; par3 = 5 ; 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