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*Unverified author*

R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Sun, 27 Apr 2014 19:09:05 -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/t1398640339gywah68i09gntvf.htm/, Retrieved Fri, 17 May 2024 01:43:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234639, Retrieved Fri, 17 May 2024 01:43:29 +0000

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Estimated Impact

144

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-       [Two-Way ANOVA] [Rachael Hepburn (...] [2014-04-27 23:09:05] [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=234639&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=234639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234639&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	0.417	0.238	-0.527

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.333 & 0.417 & 0.238 & -0.527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234639&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]0.417[/C][C]0.238[/C][C]-0.527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234639&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	0.417	0.238	-0.527

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.244	0.244	0.992	0.324
Treatment_B	1	0.005	0.005	0.022	0.883
Treatment_A:Treatment_B	1	0.88	0.88	3.573	0.065
Residuals	47	11.576	0.246

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.244 & 0.244 & 0.992 & 0.324 \tabularnewline
Treatment_B & 1 & 0.005 & 0.005 & 0.022 & 0.883 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.88 & 0.88 & 3.573 & 0.065 \tabularnewline
Residuals & 47 & 11.576 & 0.246 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234639&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]0.244[/C][C]0.244[/C][C]0.992[/C][C]0.324[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.005[/C][C]0.005[/C][C]0.022[/C][C]0.883[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.88[/C][C]0.88[/C][C]3.573[/C][C]0.065[/C][/ROW]
[ROW][C]Residuals[/C][C]47[/C][C]11.576[/C][C]0.246[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234639&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	0.244	0.244	0.992	0.324
Treatment_B	1	0.005	0.005	0.022	0.883
Treatment_A:Treatment_B	1	0.88	0.88	3.573	0.065
Residuals	47	11.576	0.246

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
2-1	0.138	-0.141	0.418	0.324
0.6-0.4	-0.021	-0.301	0.26	0.883
2:0.4-1:0.4	0.417	-0.123	0.956	0.182
1:0.6-1:0.4	0.238	-0.282	0.758	0.618
2:0.6-1:0.4	0.128	-0.401	0.657	0.917
1:0.6-2:0.4	-0.179	-0.699	0.341	0.797
2:0.6-2:0.4	-0.288	-0.818	0.241	0.474
2:0.6-1:0.6	-0.11	-0.619	0.399	0.939

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2-1 & 0.138 & -0.141 & 0.418 & 0.324 \tabularnewline
0.6-0.4 & -0.021 & -0.301 & 0.26 & 0.883 \tabularnewline
2:0.4-1:0.4 & 0.417 & -0.123 & 0.956 & 0.182 \tabularnewline
1:0.6-1:0.4 & 0.238 & -0.282 & 0.758 & 0.618 \tabularnewline
2:0.6-1:0.4 & 0.128 & -0.401 & 0.657 & 0.917 \tabularnewline
1:0.6-2:0.4 & -0.179 & -0.699 & 0.341 & 0.797 \tabularnewline
2:0.6-2:0.4 & -0.288 & -0.818 & 0.241 & 0.474 \tabularnewline
2:0.6-1:0.6 & -0.11 & -0.619 & 0.399 & 0.939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234639&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]0.138[/C][C]-0.141[/C][C]0.418[/C][C]0.324[/C][/ROW]
[ROW][C]0.6-0.4[/C][C]-0.021[/C][C]-0.301[/C][C]0.26[/C][C]0.883[/C][/ROW]
[ROW][C]2:0.4-1:0.4[/C][C]0.417[/C][C]-0.123[/C][C]0.956[/C][C]0.182[/C][/ROW]
[ROW][C]1:0.6-1:0.4[/C][C]0.238[/C][C]-0.282[/C][C]0.758[/C][C]0.618[/C][/ROW]
[ROW][C]2:0.6-1:0.4[/C][C]0.128[/C][C]-0.401[/C][C]0.657[/C][C]0.917[/C][/ROW]
[ROW][C]1:0.6-2:0.4[/C][C]-0.179[/C][C]-0.699[/C][C]0.341[/C][C]0.797[/C][/ROW]
[ROW][C]2:0.6-2:0.4[/C][C]-0.288[/C][C]-0.818[/C][C]0.241[/C][C]0.474[/C][/ROW]
[ROW][C]2:0.6-1:0.6[/C][C]-0.11[/C][C]-0.619[/C][C]0.399[/C][C]0.939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234639&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	0.138	-0.141	0.418	0.324
0.6-0.4	-0.021	-0.301	0.26	0.883
2:0.4-1:0.4	0.417	-0.123	0.956	0.182
1:0.6-1:0.4	0.238	-0.282	0.758	0.618
2:0.6-1:0.4	0.128	-0.401	0.657	0.917
1:0.6-2:0.4	-0.179	-0.699	0.341	0.797
2:0.6-2:0.4	-0.288	-0.818	0.241	0.474
2:0.6-1:0.6	-0.11	-0.619	0.399	0.939

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	0.468	0.706
	47

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.468 & 0.706 \tabularnewline
  & 47 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234639&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]0.468[/C][C]0.706[/C][/ROW]
[ROW][C] [/C][C]47[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234639&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234639&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	0.468	0.706
	47

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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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