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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Sun, 27 Apr 2014 18:19:22 -0400

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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/Apr/27/t1398637268hljyy2xq10yc7dq.htm/, Retrieved Fri, 17 May 2024 04:47:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234638, Retrieved Fri, 17 May 2024 04:47:42 +0000

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User-defined keywords

ANOVA test

Estimated Impact

133

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

-       [Two-Way ANOVA] [Rachael Hepburn] [2014-04-27 22:19:22] [d41d8cd98f00b204e9800998ecf8427e] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234638&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234638&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234638&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	'Gertrude Mary Cox' @ cox.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.333	0.436	0.167	-0.474

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.333 & 0.436 & 0.167 & -0.474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234638&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.333[/C][C]0.436[/C][C]0.167[/C][C]-0.474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234638&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234638&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	0.333	0.436	0.167	-0.474

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.47	0.47	1.927	0.171
Treatment_B	1	0.055	0.055	0.225	0.637
Treatment_A:Treatment_B	1	0.751	0.751	3.076	0.086
Residuals	50	12.205	0.244

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.47 & 0.47 & 1.927 & 0.171 \tabularnewline
Treatment_B & 1 & 0.055 & 0.055 & 0.225 & 0.637 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.751 & 0.751 & 3.076 & 0.086 \tabularnewline
Residuals & 50 & 12.205 & 0.244 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234638&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]0.47[/C][C]0.47[/C][C]1.927[/C][C]0.171[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.055[/C][C]0.055[/C][C]0.225[/C][C]0.637[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.751[/C][C]0.751[/C][C]3.076[/C][C]0.086[/C][/ROW]
[ROW][C]Residuals[/C][C]50[/C][C]12.205[/C][C]0.244[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234638&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234638&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	0.47	0.47	1.927	0.171
Treatment_B	1	0.055	0.055	0.225	0.637
Treatment_A:Treatment_B	1	0.751	0.751	3.076	0.086
Residuals	50	12.205	0.244

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
2-1	0.187	-0.083	0.457	0.171
0.6-0.4	-0.064	-0.335	0.207	0.638
2:0.4-1:0.4	0.436	-0.09	0.962	0.136
1:0.6-1:0.4	0.167	-0.335	0.668	0.813
2:0.6-1:0.4	0.128	-0.397	0.654	0.916
1:0.6-2:0.4	-0.269	-0.76	0.221	0.469
2:0.6-2:0.4	-0.308	-0.823	0.207	0.395
2:0.6-1:0.6	-0.038	-0.529	0.452	0.997

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2-1 & 0.187 & -0.083 & 0.457 & 0.171 \tabularnewline
0.6-0.4 & -0.064 & -0.335 & 0.207 & 0.638 \tabularnewline
2:0.4-1:0.4 & 0.436 & -0.09 & 0.962 & 0.136 \tabularnewline
1:0.6-1:0.4 & 0.167 & -0.335 & 0.668 & 0.813 \tabularnewline
2:0.6-1:0.4 & 0.128 & -0.397 & 0.654 & 0.916 \tabularnewline
1:0.6-2:0.4 & -0.269 & -0.76 & 0.221 & 0.469 \tabularnewline
2:0.6-2:0.4 & -0.308 & -0.823 & 0.207 & 0.395 \tabularnewline
2:0.6-1:0.6 & -0.038 & -0.529 & 0.452 & 0.997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234638&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]2-1[/C][C]0.187[/C][C]-0.083[/C][C]0.457[/C][C]0.171[/C][/ROW]
[ROW][C]0.6-0.4[/C][C]-0.064[/C][C]-0.335[/C][C]0.207[/C][C]0.638[/C][/ROW]
[ROW][C]2:0.4-1:0.4[/C][C]0.436[/C][C]-0.09[/C][C]0.962[/C][C]0.136[/C][/ROW]
[ROW][C]1:0.6-1:0.4[/C][C]0.167[/C][C]-0.335[/C][C]0.668[/C][C]0.813[/C][/ROW]
[ROW][C]2:0.6-1:0.4[/C][C]0.128[/C][C]-0.397[/C][C]0.654[/C][C]0.916[/C][/ROW]
[ROW][C]1:0.6-2:0.4[/C][C]-0.269[/C][C]-0.76[/C][C]0.221[/C][C]0.469[/C][/ROW]
[ROW][C]2:0.6-2:0.4[/C][C]-0.308[/C][C]-0.823[/C][C]0.207[/C][C]0.395[/C][/ROW]
[ROW][C]2:0.6-1:0.6[/C][C]-0.038[/C][C]-0.529[/C][C]0.452[/C][C]0.997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234638&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234638&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
2-1	0.187	-0.083	0.457	0.171
0.6-0.4	-0.064	-0.335	0.207	0.638
2:0.4-1:0.4	0.436	-0.09	0.962	0.136
1:0.6-1:0.4	0.167	-0.335	0.668	0.813
2:0.6-1:0.4	0.128	-0.397	0.654	0.916
1:0.6-2:0.4	-0.269	-0.76	0.221	0.469
2:0.6-2:0.4	-0.308	-0.823	0.207	0.395
2:0.6-1:0.6	-0.038	-0.529	0.452	0.997

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	1.276	0.293
	50

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.276 & 0.293 \tabularnewline
  & 50 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234638&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]1.276[/C][C]0.293[/C][/ROW]
[ROW][C] [/C][C]50[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234638&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234638&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	1.276	0.293
	50

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):

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

Parameters (R input):

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