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Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationWed, 06 Jan 2016 11:06:19 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/06/t1452078827wz5zmzi5tc30f99.htm/, Retrieved Thu, 02 May 2024 14:23:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287345, Retrieved Thu, 02 May 2024 14:23:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2016-01-06 11:06:19] [9c6885c821bcaafa868d1b0892651286] [Current]
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Dataseries X:
4.2 "'VC'" 0.5
11.5 "'VC'" 0.5
7.3 "'VC'" 0.5
5.8 "'VC'" 0.5
6.4 "'VC'" 0.5
10 "'VC'" 0.5
11.2 "'VC'" 0.5
11.2 "'VC'" 0.5
5.2 "'VC'" 0.5
7 "'VC'" 0.5
16.5 "'VC'" 1
16.5 "'VC'" 1
15.2 "'VC'" 1
17.3 "'VC'" 1
22.5 "'VC'" 1
17.3 "'VC'" 1
13.6 "'VC'" 1
14.5 "'VC'" 1
18.8 "'VC'" 1
15.5 "'VC'" 1
23.6 "'VC'" 2
18.5 "'VC'" 2
33.9 "'VC'" 2
25.5 "'VC'" 2
26.4 "'VC'" 2
32.5 "'VC'" 2
26.7 "'VC'" 2
21.5 "'VC'" 2
23.3 "'VC'" 2
29.5 "'VC'" 2
15.2 "'OJ'" 0.5
21.5 "'OJ'" 0.5
17.6 "'OJ'" 0.5
9.7 "'OJ'" 0.5
14.5 "'OJ'" 0.5
10 "'OJ'" 0.5
8.2 "'OJ'" 0.5
9.4 "'OJ'" 0.5
16.5 "'OJ'" 0.5
9.7 "'OJ'" 0.5
19.7 "'OJ'" 1
23.3 "'OJ'" 1
23.6 "'OJ'" 1
26.4 "'OJ'" 1
20 "'OJ'" 1
25.2 "'OJ'" 1
25.8 "'OJ'" 1
21.2 "'OJ'" 1
14.5 "'OJ'" 1
27.3 "'OJ'" 1
25.5 "'OJ'" 2
26.4 "'OJ'" 2
22.4 "'OJ'" 2
24.5 "'OJ'" 2
24.8 "'OJ'" 2
30.9 "'OJ'" 2
26.4 "'OJ'" 2
27.3 "'OJ'" 2
29.4 "'OJ'" 2
23 "'OJ'" 2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287345&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287345&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B - 1
means13.237.989.4712.83-0.685.33

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B - 1 \tabularnewline
means & 13.23 & 7.98 & 9.47 & 12.83 & -0.68 & 5.33 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287345&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B - 1[/C][/ROW]
[ROW][C]means[/C][C]13.23[/C][C]7.98[/C][C]9.47[/C][C]12.83[/C][C]-0.68[/C][C]5.33[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287345&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 - 1
means13.237.989.4712.83-0.685.33







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A221441.84110720.92812.9820
Treatment_B22426.4341213.217920
Treatment_A:Treatment_B2108.31954.164.1070.022
Residuals54712.10613.187

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 21441.841 & 10720.92 & 812.982 & 0 \tabularnewline
Treatment_B & 2 & 2426.434 & 1213.217 & 92 & 0 \tabularnewline
Treatment_A:Treatment_B & 2 & 108.319 & 54.16 & 4.107 & 0.022 \tabularnewline
Residuals & 54 & 712.106 & 13.187 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287345&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]21441.841[/C][C]10720.92[/C][C]812.982[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]2426.434[/C][C]1213.217[/C][C]92[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]108.319[/C][C]54.16[/C][C]4.107[/C][C]0.022[/C][/ROW]
[ROW][C]Residuals[/C][C]54[/C][C]712.106[/C][C]13.187[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287345&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287345&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
DfSum SqMean SqF valuePr(>F)
2
Treatment_A221441.84110720.92812.9820
Treatment_B22426.4341213.217920
Treatment_A:Treatment_B2108.31954.164.1070.022
Residuals54712.10613.187







Must Include Intercept to use Tukey Test

\begin{tabular}{lllllllll}
\hline
Must Include Intercept to use Tukey Test  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287345&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287345&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287345&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Must Include Intercept to use Tukey Test







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group51.7090.148
54

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 1.709 & 0.148 \tabularnewline
  & 54 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287345&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]5[/C][C]1.709[/C][C]0.148[/C][/ROW]
[ROW][C] [/C][C]54[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287345&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287345&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
DfF valuePr(>F)
Group51.7090.148
54



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = FALSE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = FALSE ;
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')