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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 computationMon, 19 Jan 2015 11:22:18 +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/2015/Jan/19/t14216665472ati6o2yk9z9r3p.htm/, Retrieved Thu, 16 May 2024 16:08:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=274457, Retrieved Thu, 16 May 2024 16:08:47 +0000
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-       [Two-Way ANOVA] [] [2015-01-19 11:22:18] [99d5c1073827aabbadf7ab1e7da1d584] [Current]
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Dataseries X:
21 2011 0
22 2011 1
22 2011 0
18 2011 1
23 2011 1
12 2011 1
20 2011 0
22 2011 1
21 2011 1
19 2011 1
22 2011 1
15 2011 1
20 2011 1
19 2011 0
18 2011 0
15 2011 0
20 2011 1
21 2011 0
21 2011 1
15 2011 0
16 2011 1
23 2011 1
21 2011 0
18 2011 1
25 2011 1
9 2011 1
30 2011 1
20 2011 0
23 2011 1
16 2011 0
16 2011 0
19 2011 0
25 2011 1
18 2011 1
23 2011 1
21 2011 1
10 2011 0
14 2011 1
22 2011 1
26 2011 0
23 2011 1
23 2011 1
24 2011 1
24 2011 1
18 2011 1
23 2011 0
15 2011 1
19 2011 1
16 2011 0
25 2011 1
23 2011 1
17 2011 1
19 2011 1
21 2011 1
18 2011 1
27 2011 1
21 2011 0
13 2011 1
8 2011 0
29 2011 1
28 2011 1
23 2011 0
21 2011 0
19 2011 1
19 2011 0
20 2011 1
18 2011 0
19 2011 1
17 2011 1
19 2011 0
25 2011 0
19 2011 0
22 2011 0
23 2011 1
14 2011 0
16 2011 0
24 2011 1
20 2011 0
12 2011 0
24 2011 1
22 2011 0
12 2011 0
22 2011 0
20 2011 1
10 2011 0
23 2011 1
17 2011 1
22 2011 0
24 2011 0
18 2011 0
21 2011 1
20 2011 1
20 2011 1
22 2011 0
19 2011 1
20 2011 0
26 2011 1
23 2011 1
24 2011 1
21 2011 1
21 2011 1
19 2011 0
8 2011 1
17 2011 1
20 2011 1
11 2011 0
8 2011 0
15 2011 0
18 2011 0
18 2011 0
19 2011 0
19 2011 1
23 2012 1
22 2012 1
21 2012 1
25 2012 1
30 2012 0
17 2012 1
27 2012 1
23 2012 0
23 2012 1
18 2012 0
18 2012 0
23 2012 1
19 2012 1
15 2012 1
20 2012 1
16 2012 1
24 2012 1
25 2012 1
25 2012 1
19 2012 0
19 2012 1
16 2012 1
19 2012 1
19 2012 1
23 2012 1
21 2012 1
22 2012 0
19 2012 1
20 2012 1
20 2012 1
3 2012 1
23 2012 1
23 2012 0
20 2012 0
15 2012 1
16 2012 0
7 2012 0
24 2012 1
17 2012 0
24 2012 1
24 2012 1
19 2012 0
25 2012 1
20 2012 1
28 2012 1
23 2012 0
27 2012 0
18 2012 0
28 2012 0
21 2012 1
19 2012 0
23 2012 1
27 2012 0
22 2012 1
28 2012 0
25 2012 1
21 2012 0
22 2012 0
28 2012 1
20 2012 0
29 2012 1
25 2012 1
25 2012 1
20 2012 1
20 2012 1
16 2012 0
20 2012 1
20 2012 0
23 2012 0
18 2012 0
25 2012 1
18 2012 0
19 2012 1
25 2012 0
25 2012 0
25 2012 0
24 2012 0
19 2012 1
26 2012 1
10 2012 1
17 2012 1
13 2012 0
17 2012 0
30 2012 1
25 2012 0
4 2012 0
16 2012 0
21 2012 0
23 2012 1
22 2012 1
17 2012 0
20 2012 0
20 2012 1
22 2012 0
16 2012 1
23 2012 1
0 2012 0
18 2012 1
25 2012 1
23 2012 1
12 2012 0
18 2012 0
24 2012 0
11 2012 1
18 2012 1
23 2012 1
24 2012 1
29 2012 0
18 2012 0
15 2012 0
29 2012 1
16 2012 1
19 2012 0
22 2012 0
16 2012 0
23 2012 1
23 2012 1
19 2012 0
4 2012 0
20 2012 0
24 2012 1
20 2012 1
4 2012 1
24 2012 1
22 2012 0
16 2012 1
3 2012 1
15 2012 1
24 2012 0
17 2012 0
20 2012 1
27 2012 0
26 2012 1
23 2012 1
17 2012 0
20 2012 1
22 2012 0
19 2012 1
24 2012 1
19 2012 0
23 2012 1
15 2012 0
27 2012 1
26 2012 0
22 2012 1
22 2012 0
18 2012 0
15 2012 1
22 2012 1
27 2012 0
10 2012 1
20 2012 1
17 2012 0
23 2012 1
19 2012 0
13 2012 0
27 2012 1
23 2012 1
16 2012 0
25 2012 1
2 2012 0
26 2012 0
20 2012 1
23 2012 0
22 2012 0
24 2012 1





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=274457&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=274457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274457&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







ANOVA Model
Response ~ Treatment_A * Treatment_B
means18.1911.3152.316-0.888

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 18.191 & 1.315 & 2.316 & -0.888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274457&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]18.191[/C][C]1.315[/C][C]2.316[/C][C]-0.888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274457&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
means18.1911.3152.316-0.888







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A139.80839.8081.5610.213
Treatment_B1216.916216.9168.5060.004
Treatment_A:Treatment_B112.89112.8910.5050.478
Residuals2746987.38225.501

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 39.808 & 39.808 & 1.561 & 0.213 \tabularnewline
Treatment_B & 1 & 216.916 & 216.916 & 8.506 & 0.004 \tabularnewline
Treatment_A:Treatment_B & 1 & 12.891 & 12.891 & 0.505 & 0.478 \tabularnewline
Residuals & 274 & 6987.382 & 25.501 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274457&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]39.808[/C][C]39.808[/C][C]1.561[/C][C]0.213[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]216.916[/C][C]216.916[/C][C]8.506[/C][C]0.004[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]12.891[/C][C]12.891[/C][C]0.505[/C][C]0.478[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]6987.382[/C][C]25.501[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274457&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274457&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)
1
Treatment_A139.80839.8081.5610.213
Treatment_B1216.916216.9168.5060.004
Treatment_A:Treatment_B112.89112.8910.5050.478
Residuals2746987.38225.501







Tukey Honest Significant Difference Comparisons
difflwruprp adj
2012-20110.772-0.4441.9870.213
1-01.7830.5792.9870.004
2012:0-2011:01.315-1.1263.7570.505
2011:1-2011:02.316-0.1834.8160.08
2012:1-2011:02.7440.4085.080.014
2011:1-2012:01.001-1.2253.2270.651
2012:1-2012:01.429-0.6123.470.271
2012:1-2011:10.428-1.6832.5380.953

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2012-2011 & 0.772 & -0.444 & 1.987 & 0.213 \tabularnewline
1-0 & 1.783 & 0.579 & 2.987 & 0.004 \tabularnewline
2012:0-2011:0 & 1.315 & -1.126 & 3.757 & 0.505 \tabularnewline
2011:1-2011:0 & 2.316 & -0.183 & 4.816 & 0.08 \tabularnewline
2012:1-2011:0 & 2.744 & 0.408 & 5.08 & 0.014 \tabularnewline
2011:1-2012:0 & 1.001 & -1.225 & 3.227 & 0.651 \tabularnewline
2012:1-2012:0 & 1.429 & -0.612 & 3.47 & 0.271 \tabularnewline
2012:1-2011:1 & 0.428 & -1.683 & 2.538 & 0.953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274457&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]2012-2011[/C][C]0.772[/C][C]-0.444[/C][C]1.987[/C][C]0.213[/C][/ROW]
[ROW][C]1-0[/C][C]1.783[/C][C]0.579[/C][C]2.987[/C][C]0.004[/C][/ROW]
[ROW][C]2012:0-2011:0[/C][C]1.315[/C][C]-1.126[/C][C]3.757[/C][C]0.505[/C][/ROW]
[ROW][C]2011:1-2011:0[/C][C]2.316[/C][C]-0.183[/C][C]4.816[/C][C]0.08[/C][/ROW]
[ROW][C]2012:1-2011:0[/C][C]2.744[/C][C]0.408[/C][C]5.08[/C][C]0.014[/C][/ROW]
[ROW][C]2011:1-2012:0[/C][C]1.001[/C][C]-1.225[/C][C]3.227[/C][C]0.651[/C][/ROW]
[ROW][C]2012:1-2012:0[/C][C]1.429[/C][C]-0.612[/C][C]3.47[/C][C]0.271[/C][/ROW]
[ROW][C]2012:1-2011:1[/C][C]0.428[/C][C]-1.683[/C][C]2.538[/C][C]0.953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274457&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274457&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
difflwruprp adj
2012-20110.772-0.4441.9870.213
1-01.7830.5792.9870.004
2012:0-2011:01.315-1.1263.7570.505
2011:1-2011:02.316-0.1834.8160.08
2012:1-2011:02.7440.4085.080.014
2011:1-2012:01.001-1.2253.2270.651
2012:1-2012:01.429-0.6123.470.271
2012:1-2011:10.428-1.6832.5380.953







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.540.204
274

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.54 & 0.204 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274457&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]1.54[/C][C]0.204[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274457&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274457&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)
Group31.540.204
274



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')