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Author

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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 16:45:35 -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/t13837743658nnus4vzchzs50e.htm/, Retrieved Fri, 03 May 2024 01:56:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=223175, Retrieved Fri, 03 May 2024 01:56:02 +0000

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Estimated Impact

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

-       [Two-Way ANOVA] [Workshop 5 Vraag 8] [2013-11-06 21:45:35] [1cde2327ff3821ae0b83ebec6b0558f7] [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=223175&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=223175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223175&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	0	0	1	0	0.061	NA

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0 & 0 & 1 & 0 & 0.061 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223175&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]1[/C][C]0[/C][C]0.061[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223175&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	1	0	0.061	NA

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	23.112	11.556	459.57	0
Treatment_B	2	0.048	0.048	1.922	0.168
Treatment_A:Treatment_B	2	0.023	0.023	0.908	0.343
Residuals	112	2.816	0.025

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 23.112 & 11.556 & 459.57 & 0 \tabularnewline
Treatment_B & 2 & 0.048 & 0.048 & 1.922 & 0.168 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.023 & 0.023 & 0.908 & 0.343 \tabularnewline
Residuals & 112 & 2.816 & 0.025 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223175&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]23.112[/C][C]11.556[/C][C]459.57[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0.048[/C][C]0.048[/C][C]1.922[/C][C]0.168[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.023[/C][C]0.023[/C][C]0.908[/C][C]0.343[/C][/ROW]
[ROW][C]Residuals[/C][C]112[/C][C]2.816[/C][C]0.025[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223175&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223175&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	23.112	11.556	459.57	0
Treatment_B	2	0.048	0.048	1.922	0.168
Treatment_A:Treatment_B	2	0.023	0.023	0.908	0.343
Residuals	112	2.816	0.025

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
0--1	0.038	-0.342	0.417	0.97
1--1	1	0.618	1.382	0
1-0	0.962	0.887	1.038	0
1-0	0.041	-0.018	0.1	0.171
0:0--1:0	NA	NA	NA	NA
1:0--1:0	NA	NA	NA	NA
-1:1--1:0	NA	NA	NA	NA
0:1--1:0	NA	NA	NA	NA
1:1--1:0	NA	NA	NA	NA
1:0-0:0	1	0.861	1.139	0
-1:1-0:0	0	-0.467	0.467	1
0:1-0:0	0.061	-0.044	0.167	0.546
1:1-0:0	1	0.866	1.134	0
-1:1-1:0	-1	-1.473	-0.527	0
0:1-1:0	-0.939	-1.068	-0.809	0
1:1-1:0	0	-0.154	0.154	1
0:1--1:1	0.061	-0.403	0.526	0.999
1:1--1:1	1	0.528	1.472	0
1:1-0:1	0.939	0.815	1.063	0

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
0--1 & 0.038 & -0.342 & 0.417 & 0.97 \tabularnewline
1--1 & 1 & 0.618 & 1.382 & 0 \tabularnewline
1-0 & 0.962 & 0.887 & 1.038 & 0 \tabularnewline
1-0 & 0.041 & -0.018 & 0.1 & 0.171 \tabularnewline
0:0--1:0 & NA & NA & NA & NA \tabularnewline
1:0--1:0 & NA & NA & NA & NA \tabularnewline
-1:1--1:0 & NA & NA & NA & NA \tabularnewline
0:1--1:0 & NA & NA & NA & NA \tabularnewline
1:1--1:0 & NA & NA & NA & NA \tabularnewline
1:0-0:0 & 1 & 0.861 & 1.139 & 0 \tabularnewline
-1:1-0:0 & 0 & -0.467 & 0.467 & 1 \tabularnewline
0:1-0:0 & 0.061 & -0.044 & 0.167 & 0.546 \tabularnewline
1:1-0:0 & 1 & 0.866 & 1.134 & 0 \tabularnewline
-1:1-1:0 & -1 & -1.473 & -0.527 & 0 \tabularnewline
0:1-1:0 & -0.939 & -1.068 & -0.809 & 0 \tabularnewline
1:1-1:0 & 0 & -0.154 & 0.154 & 1 \tabularnewline
0:1--1:1 & 0.061 & -0.403 & 0.526 & 0.999 \tabularnewline
1:1--1:1 & 1 & 0.528 & 1.472 & 0 \tabularnewline
1:1-0:1 & 0.939 & 0.815 & 1.063 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223175&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]0--1[/C][C]0.038[/C][C]-0.342[/C][C]0.417[/C][C]0.97[/C][/ROW]
[ROW][C]1--1[/C][C]1[/C][C]0.618[/C][C]1.382[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]0.962[/C][C]0.887[/C][C]1.038[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]0.041[/C][C]-0.018[/C][C]0.1[/C][C]0.171[/C][/ROW]
[ROW][C]0:0--1:0[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:0--1:0[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]-1:1--1:0[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]0:1--1:0[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:1--1:0[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]1[/C][C]0.861[/C][C]1.139[/C][C]0[/C][/ROW]
[ROW][C]-1:1-0:0[/C][C]0[/C][C]-0.467[/C][C]0.467[/C][C]1[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.061[/C][C]-0.044[/C][C]0.167[/C][C]0.546[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]1[/C][C]0.866[/C][C]1.134[/C][C]0[/C][/ROW]
[ROW][C]-1:1-1:0[/C][C]-1[/C][C]-1.473[/C][C]-0.527[/C][C]0[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.939[/C][C]-1.068[/C][C]-0.809[/C][C]0[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0[/C][C]-0.154[/C][C]0.154[/C][C]1[/C][/ROW]
[ROW][C]0:1--1:1[/C][C]0.061[/C][C]-0.403[/C][C]0.526[/C][C]0.999[/C][/ROW]
[ROW][C]1:1--1:1[/C][C]1[/C][C]0.528[/C][C]1.472[/C][C]0[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.939[/C][C]0.815[/C][C]1.063[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223175&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223175&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
0--1	0.038	-0.342	0.417	0.97
1--1	1	0.618	1.382	0
1-0	0.962	0.887	1.038	0
1-0	0.041	-0.018	0.1	0.171
0:0--1:0	NA	NA	NA	NA
1:0--1:0	NA	NA	NA	NA
-1:1--1:0	NA	NA	NA	NA
0:1--1:0	NA	NA	NA	NA
1:1--1:0	NA	NA	NA	NA
1:0-0:0	1	0.861	1.139	0
-1:1-0:0	0	-0.467	0.467	1
0:1-0:0	0.061	-0.044	0.167	0.546
1:1-0:0	1	0.866	1.134	0
-1:1-1:0	-1	-1.473	-0.527	0
0:1-1:0	-0.939	-1.068	-0.809	0
1:1-1:0	0	-0.154	0.154	1
0:1--1:1	0.061	-0.403	0.526	0.999
1:1--1:1	1	0.528	1.472	0
1:1-0:1	0.939	0.815	1.063	0

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	4	1.061	0.379
	112

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 4 & 1.061 & 0.379 \tabularnewline
  & 112 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=223175&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]4[/C][C]1.061[/C][C]0.379[/C][/ROW]
[ROW][C] [/C][C]112[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=223175&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=223175&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	4	1.061	0.379
	112

Figure 1

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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):

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