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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationThu, 07 Dec 2017 17:30:06 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/07/t151266425739wxpphrbtkek19.htm/, Retrieved Wed, 15 May 2024 02:59:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308739, Retrieved Wed, 15 May 2024 02:59:48 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDataset 1
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [Two-way ANOVA] [2017-12-07 16:30:06] [79eb5143bcf363cf12f20cb866038ece] [Current]
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Dataseries X:
'S' "'F'" 10
'S' "'M'" 8
'S' "'M'" 6
'S' "'M'" 10
'S' "'F'" 8
'S' "'M'" 10
'S' "'M'" 7
'S' "'M'" 10
'S' "'F'" 6
'S' "'F'" 7
'S' "'F'" 9
'S' "'F'" 6
'S' "'M'" 7
'S' "'F'" 6
'S' "'M'" 4
'S' "'M'" 6
'S' "'M'" 8
'S' "'M'" 9
'S' "'F'" 8
'S' "'F'" 6
'S' "'M'" 6
'S' "'F'" 10
'S' "'M'" 8
'S' "'M'" 8
'S' "'M'" 7
'S' "'F'" 4
'S' "'F'" 9
'S' "'M'" 8
'S' "'M'" 10
'S' "'F'" 8
'B' "'M'" 6
'S' "'M'" 7
'S' "'F'" 8
'S' "'F'" 5
'S' "'F'" 10
'S' "'F'" 2
'S' "'F'" 6
'S' "'M'" 7
'S' "'M'" 5
'S' "'M'" 8
'S' "'M'" 7
'B' "'F'" 7
'S' "'F'" 10
'S' "'F'" 7
'S' "'M'" 6
'S' "'M'" 10
'S' "'M'" 6
'S' "'M'" 5
'S' "'M'" 8
'S' "'M'" 8
'S' "'F'" 5
'S' "'F'" 8
'S' "'F'" 10
'S' "'F'" 7
'S' "'F'" 7
'S' "'F'" 7
'S' "'M'" 7
'B' "'F'" 2
'S' "'F'" 4
'S' "'M'" 6
'B' "'M'" 7
'B' "'F'" 9
'S' "'F'" 9
'S' "'F'" 4
'S' "'F'" 9
'S' "'F'" 9
'S' "'F'" 8
'S' "'F'" 7
'S' "'M'" 9
'S' "'M'" 7
'S' "'M'" 6
'B' "'F'" 7
'B' "'M'" 2
'B' "'M'" 3
'B' "'M'" 4
'B' "'M'" 5
'B' "'F'" 2
'B' "'F'" 6
'S' "'F'" 8
'S' "'F'" 5
'B' "'F'" 4
'S' "'M'" 10
'S' "'M'" 10
'S' "'M'" 10
'S' "'M'" 9
'S' "'M'" 5
'S' "'F'" 5
'S' "'M'" 7
'S' "'M'" 10
'S' "'F'" 9
'S' "'M'" 8
'S' "'M'" 8
'S' "'M'" 8
'S' "'F'" 8
'S' "'M'" 8
'S' "'F'" 7
'S' "'M'" 6
'S' "'F'" 8
'S' "'F'" 2
'S' "'M'" 5
'S' "'F'" 4
'S' "'M'" 9
'S' "'M'" 10
'S' "'F'" 6
'B' "'F'" 4
'S' "'M'" 10
'S' "'F'" 6
'B' "'M'" 7
'B' "'M'" 7
'S' "'F'" 8
'S' "'M'" 6
'S' "'F'" 5
'S' "'M'" 6
'S' "'F'" 7
'S' "'F'" 6
'S' "'M'" 9
'S' "'M'" 9
'S' "'M'" 7
'B' "'F'" 6
'S' "'F'" 7
'S' "'F'" 7
'S' "'F'" 8
'S' "'F'" 7
'S' "'M'" 8
'S' "'F'" 7
'B' "'M'" 4
'S' "'F'" 10
'B' "'M'" 8
'S' "'F'" 8
'B' "'M'" 2
'S' "'F'" 6
'S' "'M'" 4
'B' "'F'" 4
'S' "'F'" 9
'B' "'F'" 2
'B' "'F'" 6
'B' "'M'" 7
'B' "'M'" 4
'S' "'F'" 10
'B' "'F'" 3
'B' "'M'" 7
'B' "'M'" 4
'B' "'F'" 8
'B' "'F'" 4
'B' "'F'" 5
'S' "'F'" 6
'B' "'M'" 5
'B' "'M'" 9
'B' "'F'" 6
'B' "'M'" 8
'S' "'F'" 4
'B' "'M'" 4
'B' "'F'" 8
'B' "'M'" 4
'S' "'M'" 10
'S' "'M'" 8
'S' "'F'" 5
'B' "'M'" 3
'B' "'M'" 7
'S' "'M'" 6
'S' "'F'" 5
'B' "'M'" 5
'S' "'F'" 9
'B' "'M'" 2
'B' "'F'" 7
'S' "'M'" 7
'B' "'F'" 5
'S' "'M'" 9
'S' "'M'" 4
'B' "'M'" 5
'B' "'M'" 9
'S' "'M'" 7
'S' "'M'" 6
'S' "'F'" 8
'B' "'F'" 7
'S' "'F'" 6
'S' "'M'" 8
'B' "'F'" 6
'B' "'F'" 7




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308739&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308739&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308739&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 Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center







ANOVA Model
Response ~ Treatment_A * Treatment_B
means5.4351.565-0.1270.681

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 5.435 & 1.565 & -0.127 & 0.681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308739&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]5.435[/C][C]1.565[/C][C]-0.127[/C][C]0.681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308739&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308739&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
means5.4351.565-0.1270.681







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1129.766129.76635.9750
Treatment_B16.0526.0521.6780.197
Treatment_A:Treatment_B14.1144.1141.140.287
Residuals175631.2523.607

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 129.766 & 129.766 & 35.975 & 0 \tabularnewline
Treatment_B & 1 & 6.052 & 6.052 & 1.678 & 0.197 \tabularnewline
Treatment_A:Treatment_B & 1 & 4.114 & 4.114 & 1.14 & 0.287 \tabularnewline
Residuals & 175 & 631.252 & 3.607 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308739&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]129.766[/C][C]129.766[/C][C]35.975[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]6.052[/C][C]6.052[/C][C]1.678[/C][C]0.197[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]4.114[/C][C]4.114[/C][C]1.14[/C][C]0.287[/C][/ROW]
[ROW][C]Residuals[/C][C]175[/C][C]631.252[/C][C]3.607[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308739&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308739&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_A1129.766129.76635.9750
Treatment_B16.0526.0521.6780.197
Treatment_A:Treatment_B14.1144.1141.140.287
Residuals175631.2523.607







Tukey Honest Significant Difference Comparisons
difflwruprp adj
S-B1.911.2812.5380
'M'-'F'0.368-0.1930.9280.197
S:'F'-B:'F'1.5650.372.760.005
B:'M'-B:'F'-0.127-1.5371.2830.995
S:'M'-B:'F'2.1190.9243.3140
B:'M'-S:'F'-1.692-2.835-0.5490.001
S:'M'-S:'F'0.554-0.311.4180.347
S:'M'-B:'M'2.2461.1033.3890

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
S-B & 1.91 & 1.281 & 2.538 & 0 \tabularnewline
'M'-'F' & 0.368 & -0.193 & 0.928 & 0.197 \tabularnewline
S:'F'-B:'F' & 1.565 & 0.37 & 2.76 & 0.005 \tabularnewline
B:'M'-B:'F' & -0.127 & -1.537 & 1.283 & 0.995 \tabularnewline
S:'M'-B:'F' & 2.119 & 0.924 & 3.314 & 0 \tabularnewline
B:'M'-S:'F' & -1.692 & -2.835 & -0.549 & 0.001 \tabularnewline
S:'M'-S:'F' & 0.554 & -0.31 & 1.418 & 0.347 \tabularnewline
S:'M'-B:'M' & 2.246 & 1.103 & 3.389 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308739&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]S-B[/C][C]1.91[/C][C]1.281[/C][C]2.538[/C][C]0[/C][/ROW]
[ROW][C]'M'-'F'[/C][C]0.368[/C][C]-0.193[/C][C]0.928[/C][C]0.197[/C][/ROW]
[ROW][C]S:'F'-B:'F'[/C][C]1.565[/C][C]0.37[/C][C]2.76[/C][C]0.005[/C][/ROW]
[ROW][C]B:'M'-B:'F'[/C][C]-0.127[/C][C]-1.537[/C][C]1.283[/C][C]0.995[/C][/ROW]
[ROW][C]S:'M'-B:'F'[/C][C]2.119[/C][C]0.924[/C][C]3.314[/C][C]0[/C][/ROW]
[ROW][C]B:'M'-S:'F'[/C][C]-1.692[/C][C]-2.835[/C][C]-0.549[/C][C]0.001[/C][/ROW]
[ROW][C]S:'M'-S:'F'[/C][C]0.554[/C][C]-0.31[/C][C]1.418[/C][C]0.347[/C][/ROW]
[ROW][C]S:'M'-B:'M'[/C][C]2.246[/C][C]1.103[/C][C]3.389[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308739&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308739&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
S-B1.911.2812.5380
'M'-'F'0.368-0.1930.9280.197
S:'F'-B:'F'1.5650.372.760.005
B:'M'-B:'F'-0.127-1.5371.2830.995
S:'M'-B:'F'2.1190.9243.3140
B:'M'-S:'F'-1.692-2.835-0.5490.001
S:'M'-S:'F'0.554-0.311.4180.347
S:'M'-B:'M'2.2461.1033.3890







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.6880.561
175

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.688 & 0.561 \tabularnewline
  & 175 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308739&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]0.688[/C][C]0.561[/C][/ROW]
[ROW][C] [/C][C]175[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308739&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308739&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)
Group30.6880.561
175



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')