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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 computationFri, 15 Dec 2017 16:17:02 +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/15/t1513353126lqyla9t7pblf5cb.htm/, Retrieved Wed, 15 May 2024 03:58:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309800, Retrieved Wed, 15 May 2024 03:58:43 +0000
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Original text written by user:Zie Word
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User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [2-way ANOVA] [2017-12-15 15:17:02] [0624292ea623603b59620a7164665963] [Current]
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Dataseries X:
'Duitsland'	'Hoog'	0.906254702
'Duitsland'	'Hoog'	0.932174273
'Duitsland'	'Hoog'	0.95047761
'Duitsland'	'Hoog'	0.905040122
'Duitsland'	'Hoog'	0.935701169
'Duitsland'	'Hoog'	0.928122976
'Duitsland'	'Hoog'	0.925229653
'Duitsland'	'Hoog'	1.005198582
'Duitsland'	'Hoog'	0.858249066
'Duitsland'	'Laag'	0.87390453
'Duitsland'	'Hoog'	0.793216269
'Duitsland'	'Hoog'	0.935246502
'Duitsland'	'Hoog'	0.856936345
'Duitsland'	'Hoog'	0.915428869
'Duitsland'	'Hoog'	1.075757571
'Duitsland'	'Laag'	0.788143717
'Duitsland'	'Hoog'	0.96010508
'Duitsland'	'Hoog'	1.092140127
'Duitsland'	'Hoog'	0.929912574
'Duitsland'	'Hoog'	0.97910217
'Duitsland'	'Hoog'	0.845502942
'Duitsland'	'Hoog'	0.843280778
'Duitsland'	'Hoog'	0.834862146
'Duitsland'	'Hoog'	0.858438783
'Duitsland'	'Laag'	0.837773845
'Duitsland'	'Laag'	0.855699741
'Duitsland'	'Laag'	0.838191755
'Duitsland'	'Laag'	0.887797976
'Duitsland'	'Hoog'	0.909181688
'Duitsland'	'Hoog'	0.901979135
'Duitsland'	'Hoog'	0.94155375
'Duitsland'	'Hoog'	0.903287355
'Duitsland'	'Hoog'	0.929059143
'Duitsland'	'Hoog'	0.872655219
'Duitsland'	'Hoog'	0.873148781
'Duitsland'	'Hoog'	0.835310971
'Duitsland'	'Hoog'	0.89616399
'Duitsland'	'Hoog'	0.894831133
'Duitsland'	'Hoog'	0.764164617
'Duitsland'	'Hoog'	0.903043954
'Duitsland'	'Laag'	0.92390972
'Duitsland'	'Laag'	0.809695881
'Duitsland'	'Laag'	1.004736912
'Duitsland'	'Laag'	0.792395356
'Duitsland'	'Laag'	0.831877551
'Duitsland'	'Laag'	0.839677636
'Frankrijk'	'Hoog'	1.140075749
'Frankrijk'	'Hoog'	1.420117037
'Frankrijk'	'Hoog'	1.048961075
'Frankrijk'	'Laag'	1.04496375
'Frankrijk'	'Laag'	1.148400903
'Frankrijk'	'Laag'	1.132816984
'Frankrijk'	'Laag'	1.028139114
'Frankrijk'	'Laag'	0.9576556
'Frankrijk'	'Hoog'	0.95478413
'Frankrijk'	'Laag'	1.229013361
'Frankrijk'	'Laag'	0.990363762
'Frankrijk'	'Laag'	1.079649407
'Frankrijk'	'Laag'	1.060226459
'Frankrijk'	'Laag'	1.078958179
'Frankrijk'	'Hoog'	0.971863624
'Frankrijk'	'Laag'	0.888589105
'Frankrijk'	'Hoog'	0.94336986
'Frankrijk'	'Hoog'	0.997000278
'Frankrijk'	'Laag'	0.844150987
'Frankrijk'	'Laag'	1.187277062
'Frankrijk'	'Laag'	0.908163146
'Frankrijk'	'Laag'	1.024194714
'Frankrijk'	'Laag'	1.124121053
'Frankrijk'	'Laag'	0.831834941




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309800&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309800&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 time4 seconds
R ServerBig Analytics Cloud Computing Center







ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.9090.159-0.0520.016

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.909 & 0.159 & -0.052 & 0.016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309800&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.909[/C][C]0.159[/C][C]-0.052[/C][C]0.016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309800&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
means0.9090.159-0.0520.016







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.3460.34639.2750
Treatment_B10.0290.0293.2810.075
Treatment_A:Treatment_B10.0010.0010.0970.756
Residuals660.5810.009

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.346 & 0.346 & 39.275 & 0 \tabularnewline
Treatment_B & 1 & 0.029 & 0.029 & 3.281 & 0.075 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.001 & 0.001 & 0.097 & 0.756 \tabularnewline
Residuals & 66 & 0.581 & 0.009 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309800&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]0.346[/C][C]0.346[/C][C]39.275[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.029[/C][C]0.029[/C][C]3.281[/C][C]0.075[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.001[/C][C]0.001[/C][C]0.097[/C][C]0.756[/C][/ROW]
[ROW][C]Residuals[/C][C]66[/C][C]0.581[/C][C]0.009[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309800&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309800&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_A10.3460.34639.2750
Treatment_B10.0290.0293.2810.075
Treatment_A:Treatment_B10.0010.0010.0970.756
Residuals660.5810.009







Tukey Honest Significant Difference Comparisons
difflwruprp adj
Frankrijk-Duitsland0.1480.1010.1950
Laag-Hoog-0.037-0.0830.0080.107
Frankrijk:Hoog-Duitsland:Hoog0.1590.0570.2620.001
Duitsland:Laag-Duitsland:Hoog-0.052-0.1350.0310.365
Frankrijk:Laag-Duitsland:Hoog0.1240.0510.1980
Duitsland:Laag-Frankrijk:Hoog-0.211-0.329-0.0930
Frankrijk:Laag-Frankrijk:Hoog-0.035-0.1460.0760.838
Frankrijk:Laag-Duitsland:Laag0.1760.0830.2690

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
Frankrijk-Duitsland & 0.148 & 0.101 & 0.195 & 0 \tabularnewline
Laag-Hoog & -0.037 & -0.083 & 0.008 & 0.107 \tabularnewline
Frankrijk:Hoog-Duitsland:Hoog & 0.159 & 0.057 & 0.262 & 0.001 \tabularnewline
Duitsland:Laag-Duitsland:Hoog & -0.052 & -0.135 & 0.031 & 0.365 \tabularnewline
Frankrijk:Laag-Duitsland:Hoog & 0.124 & 0.051 & 0.198 & 0 \tabularnewline
Duitsland:Laag-Frankrijk:Hoog & -0.211 & -0.329 & -0.093 & 0 \tabularnewline
Frankrijk:Laag-Frankrijk:Hoog & -0.035 & -0.146 & 0.076 & 0.838 \tabularnewline
Frankrijk:Laag-Duitsland:Laag & 0.176 & 0.083 & 0.269 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309800&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]Frankrijk-Duitsland[/C][C]0.148[/C][C]0.101[/C][C]0.195[/C][C]0[/C][/ROW]
[ROW][C]Laag-Hoog[/C][C]-0.037[/C][C]-0.083[/C][C]0.008[/C][C]0.107[/C][/ROW]
[ROW][C]Frankrijk:Hoog-Duitsland:Hoog[/C][C]0.159[/C][C]0.057[/C][C]0.262[/C][C]0.001[/C][/ROW]
[ROW][C]Duitsland:Laag-Duitsland:Hoog[/C][C]-0.052[/C][C]-0.135[/C][C]0.031[/C][C]0.365[/C][/ROW]
[ROW][C]Frankrijk:Laag-Duitsland:Hoog[/C][C]0.124[/C][C]0.051[/C][C]0.198[/C][C]0[/C][/ROW]
[ROW][C]Duitsland:Laag-Frankrijk:Hoog[/C][C]-0.211[/C][C]-0.329[/C][C]-0.093[/C][C]0[/C][/ROW]
[ROW][C]Frankrijk:Laag-Frankrijk:Hoog[/C][C]-0.035[/C][C]-0.146[/C][C]0.076[/C][C]0.838[/C][/ROW]
[ROW][C]Frankrijk:Laag-Duitsland:Laag[/C][C]0.176[/C][C]0.083[/C][C]0.269[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309800&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309800&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
Frankrijk-Duitsland0.1480.1010.1950
Laag-Hoog-0.037-0.0830.0080.107
Frankrijk:Hoog-Duitsland:Hoog0.1590.0570.2620.001
Duitsland:Laag-Duitsland:Hoog-0.052-0.1350.0310.365
Frankrijk:Laag-Duitsland:Hoog0.1240.0510.1980
Duitsland:Laag-Frankrijk:Hoog-0.211-0.329-0.0930
Frankrijk:Laag-Frankrijk:Hoog-0.035-0.1460.0760.838
Frankrijk:Laag-Duitsland:Laag0.1760.0830.2690







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group33.0030.037
66

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.003 & 0.037 \tabularnewline
  & 66 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309800&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]3.003[/C][C]0.037[/C][/ROW]
[ROW][C] [/C][C]66[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309800&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309800&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)
Group33.0030.037
66



Parameters (Session):
Parameters (R input):
par1 = 3 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- 'TRUE'
par3 <- '2'
par2 <- '1'
par1 <- '3'
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')