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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Wed, 19 Dec 2012 04:51:32 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/19/t1355910931wdie3cicmo85ed4.htm/, Retrieved Fri, 03 May 2024 20:20:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201789, Retrieved Fri, 03 May 2024 20:20:37 +0000

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Estimated Impact

109

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

-       [Two-Way ANOVA] [] [2012-12-19 09:51:32] [24c042819fd2b1ab385eb96782c689cf] [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	'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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201789&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201789&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201789&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	'Sir Maurice George Kendall' @ kendall.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.872	-0.155	-0.11	-0.032

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.872 & -0.155 & -0.11 & -0.032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201789&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.872[/C][C]-0.155[/C][C]-0.11[/C][C]-0.032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201789&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201789&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	0.872	-0.155	-0.11	-0.032

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	1.329	1.329	7.083	0.009
Treatment_B	1	0.602	0.602	3.208	0.075
Treatment_A:Treatment_B	1	0.009	0.009	0.047	0.829
Residuals	150	28.145	0.188

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 1.329 & 1.329 & 7.083 & 0.009 \tabularnewline
Treatment_B & 1 & 0.602 & 0.602 & 3.208 & 0.075 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.009 & 0.009 & 0.047 & 0.829 \tabularnewline
Residuals & 150 & 28.145 & 0.188 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201789&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]1.329[/C][C]1.329[/C][C]7.083[/C][C]0.009[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.602[/C][C]0.602[/C][C]3.208[/C][C]0.075[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.009[/C][C]0.009[/C][C]0.047[/C][C]0.829[/C][/ROW]
[ROW][C]Residuals[/C][C]150[/C][C]28.145[/C][C]0.188[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201789&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201789&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	1.329	1.329	7.083	0.009
Treatment_B	1	0.602	0.602	3.208	0.075
Treatment_A:Treatment_B	1	0.009	0.009	0.047	0.829
Residuals	150	28.145	0.188

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
4-2	-0.187	-0.326	-0.048	0.009
1-0	-0.126	-0.267	0.015	0.079
4:0-2:0	-0.155	-0.388	0.078	0.315
2:1-2:0	-0.11	-0.406	0.185	0.766
4:1-2:0	-0.297	-0.539	-0.055	0.009
2:1-4:0	0.045	-0.252	0.341	0.98
4:1-4:0	-0.142	-0.386	0.101	0.428
4:1-2:1	-0.187	-0.49	0.116	0.381

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
4-2 & -0.187 & -0.326 & -0.048 & 0.009 \tabularnewline
1-0 & -0.126 & -0.267 & 0.015 & 0.079 \tabularnewline
4:0-2:0 & -0.155 & -0.388 & 0.078 & 0.315 \tabularnewline
2:1-2:0 & -0.11 & -0.406 & 0.185 & 0.766 \tabularnewline
4:1-2:0 & -0.297 & -0.539 & -0.055 & 0.009 \tabularnewline
2:1-4:0 & 0.045 & -0.252 & 0.341 & 0.98 \tabularnewline
4:1-4:0 & -0.142 & -0.386 & 0.101 & 0.428 \tabularnewline
4:1-2:1 & -0.187 & -0.49 & 0.116 & 0.381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201789&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]4-2[/C][C]-0.187[/C][C]-0.326[/C][C]-0.048[/C][C]0.009[/C][/ROW]
[ROW][C]1-0[/C][C]-0.126[/C][C]-0.267[/C][C]0.015[/C][C]0.079[/C][/ROW]
[ROW][C]4:0-2:0[/C][C]-0.155[/C][C]-0.388[/C][C]0.078[/C][C]0.315[/C][/ROW]
[ROW][C]2:1-2:0[/C][C]-0.11[/C][C]-0.406[/C][C]0.185[/C][C]0.766[/C][/ROW]
[ROW][C]4:1-2:0[/C][C]-0.297[/C][C]-0.539[/C][C]-0.055[/C][C]0.009[/C][/ROW]
[ROW][C]2:1-4:0[/C][C]0.045[/C][C]-0.252[/C][C]0.341[/C][C]0.98[/C][/ROW]
[ROW][C]4:1-4:0[/C][C]-0.142[/C][C]-0.386[/C][C]0.101[/C][C]0.428[/C][/ROW]
[ROW][C]4:1-2:1[/C][C]-0.187[/C][C]-0.49[/C][C]0.116[/C][C]0.381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201789&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201789&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
4-2	-0.187	-0.326	-0.048	0.009
1-0	-0.126	-0.267	0.015	0.079
4:0-2:0	-0.155	-0.388	0.078	0.315
2:1-2:0	-0.11	-0.406	0.185	0.766
4:1-2:0	-0.297	-0.539	-0.055	0.009
2:1-4:0	0.045	-0.252	0.341	0.98
4:1-4:0	-0.142	-0.386	0.101	0.428
4:1-2:1	-0.187	-0.49	0.116	0.381

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	3.446	0.018
	150

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.446 & 0.018 \tabularnewline
  & 150 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201789&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]3.446[/C][C]0.018[/C][/ROW]
[ROW][C] [/C][C]150[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201789&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201789&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	3.446	0.018
	150

Figure 1

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Postscript link

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Figure 2

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Figure 3

PNG link

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Figure 4

PNG link

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PDF link

Parameters (Session):

par1 = 3 ; par2 = 2 ; par3 = 1 ; par4 = TRUE ;

Parameters (R input):

par1 = 3 ; par2 = 2 ; par3 = 1 ; par4 = TRUE ;

R code (references can be found in the software module):

par4 <- 'TRUE'
par3 <- '1'
par2 <- '2'
par1 <- '3'
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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Input Parameters & R Code