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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Fri, 12 Dec 2014 11:43:14 +0000

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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/Dec/12/t1418384946lp48bn0v8r2b0hc.htm/, Retrieved Thu, 16 May 2024 12:12:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266557, Retrieved Thu, 16 May 2024 12:12:02 +0000

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-       [Two-Way ANOVA] [] [2014-12-12 11:43:14] [aa823bdb4d51626f3fbc68989a46faf3] [Current]
- R  D    [Two-Way ANOVA] [] [2014-12-12 13:32:21] [fa1b8827d7de91b8b87087311d3d9fa1] 
-    D      [Two-Way ANOVA] [] [2014-12-12 13:50:17] [fa1b8827d7de91b8b87087311d3d9fa1] 
- R  D    [Two-Way ANOVA] [] [2014-12-12 13:57:30] [fa1b8827d7de91b8b87087311d3d9fa1] 

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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	'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266557&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266557&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	'Gwilym Jenkins' @ jenkins.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	23.492	0.199	-0.689	-0.703

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 23.492 & 0.199 & -0.689 & -0.703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266557&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]23.492[/C][C]0.199[/C][C]-0.689[/C][C]-0.703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266557&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	23.492	0.199	-0.689	-0.703

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	6.018	6.018	0.644	0.423
Treatment_B	1	73.086	73.086	7.818	0.006
Treatment_A:Treatment_B	1	8.346	8.346	0.893	0.346
Residuals	274	2561.461	9.348

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 6.018 & 6.018 & 0.644 & 0.423 \tabularnewline
Treatment_B & 1 & 73.086 & 73.086 & 7.818 & 0.006 \tabularnewline
Treatment_A:Treatment_B & 1 & 8.346 & 8.346 & 0.893 & 0.346 \tabularnewline
Residuals & 274 & 2561.461 & 9.348 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266557&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]6.018[/C][C]6.018[/C][C]0.644[/C][C]0.423[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]73.086[/C][C]73.086[/C][C]7.818[/C][C]0.006[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]8.346[/C][C]8.346[/C][C]0.893[/C][C]0.346[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]2561.461[/C][C]9.348[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266557&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266557&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	6.018	6.018	0.644	0.423
Treatment_B	1	73.086	73.086	7.818	0.006
Treatment_A:Treatment_B	1	8.346	8.346	0.893	0.346
Residuals	274	2561.461	9.348

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	-0.294	-1.017	0.428	0.423
1-0	-1.031	-1.76	-0.302	0.006
1:0-0:0	0.199	-1.249	1.647	0.985
0:1-0:0	-0.689	-2.046	0.667	0.555
1:1-0:0	-1.193	-2.489	0.102	0.083
0:1-1:0	-0.888	-2.308	0.532	0.371
1:1-1:0	-1.392	-2.754	-0.031	0.043
1:1-0:1	-0.504	-1.768	0.76	0.732

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.294 & -1.017 & 0.428 & 0.423 \tabularnewline
1-0 & -1.031 & -1.76 & -0.302 & 0.006 \tabularnewline
1:0-0:0 & 0.199 & -1.249 & 1.647 & 0.985 \tabularnewline
0:1-0:0 & -0.689 & -2.046 & 0.667 & 0.555 \tabularnewline
1:1-0:0 & -1.193 & -2.489 & 0.102 & 0.083 \tabularnewline
0:1-1:0 & -0.888 & -2.308 & 0.532 & 0.371 \tabularnewline
1:1-1:0 & -1.392 & -2.754 & -0.031 & 0.043 \tabularnewline
1:1-0:1 & -0.504 & -1.768 & 0.76 & 0.732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266557&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]1-0[/C][C]-0.294[/C][C]-1.017[/C][C]0.428[/C][C]0.423[/C][/ROW]
[ROW][C]1-0[/C][C]-1.031[/C][C]-1.76[/C][C]-0.302[/C][C]0.006[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.199[/C][C]-1.249[/C][C]1.647[/C][C]0.985[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-0.689[/C][C]-2.046[/C][C]0.667[/C][C]0.555[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-1.193[/C][C]-2.489[/C][C]0.102[/C][C]0.083[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.888[/C][C]-2.308[/C][C]0.532[/C][C]0.371[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-1.392[/C][C]-2.754[/C][C]-0.031[/C][C]0.043[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.504[/C][C]-1.768[/C][C]0.76[/C][C]0.732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266557&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266557&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
1-0	-0.294	-1.017	0.428	0.423
1-0	-1.031	-1.76	-0.302	0.006
1:0-0:0	0.199	-1.249	1.647	0.985
0:1-0:0	-0.689	-2.046	0.667	0.555
1:1-0:0	-1.193	-2.489	0.102	0.083
0:1-1:0	-0.888	-2.308	0.532	0.371
1:1-1:0	-1.392	-2.754	-0.031	0.043
1:1-0:1	-0.504	-1.768	0.76	0.732

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	1.312	0.271
	274

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.312 & 0.271 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266557&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]1.312[/C][C]0.271[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266557&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266557&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	1.312	0.271
	274

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

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')

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Input Parameters & R Code