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Author's title

Author*Unverified author*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationTue, 31 May 2011 09:38:31 +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/2011/May/31/t13068345267uu5deu9mq6uju4.htm/, Retrieved Fri, 10 May 2024 04:48:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122665, Retrieved Fri, 10 May 2024 04:48:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram, QQplot and Density] [Workshop 1 ] [2010-09-29 15:04:17] [98fd0e87c3eb04e0cc2efde01dbafab6]
-   P   [Histogram, QQplot and Density] [Bin - 07] [2010-10-08 14:22:31] [920d86197c99e892f7cfc71aadebcde0]
- RMPD      [Two-Way ANOVA] [two-way] [2011-05-31 09:38:31] [0f3712da4b0a7219366accad1294c2b7] [Current]
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Dataseries X:
"f"	3.555348061	"n"
"f"	3.784189634	"n"
"f"	2.995732274	"p"
"f"	3.63758616	"n"
"f"	3.761200116	"n"
"f"	3.465735903	"p"
"f"	3.17805383	"n"
"f"	4.077537444	"p"
"f"	3.713572067	"p"
"f"	3.784189634	"n"
"f"	4.189654742	"n"
"f"	3.688879454	"n"
"f"	3.17805383	"n"
"f"	4.094344562	"n"
"f"	3.555348061	"n"
"m"	3.36729583	"p"
"m"	3.044522438	"p"
"m"	3.912023005	"n"
"m"	3.135494216	"p"
"m"	3.583518938	"p"
"m"	3.465735903	"n"
"m"	3.737669618	"n"
"m"	3.663561646	"p"
"m"	4.290459441	"n"
"m"	3.912023005	"n"
"m"	3.17805383	"n"
"m"	3.17805383	"p"
"m"	3.433987204	"p"
"m"	3.80666249	"n"
"m"	3.663561646	"n"




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122665&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122665&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122665&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 time4 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







ANOVA Model
Response ~ Treatment_A * Treatment_B
means3.673-0.110.072-0.292

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 3.673 & -0.11 & 0.072 & -0.292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122665&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]3.673[/C][C]-0.11[/C][C]0.072[/C][C]-0.292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122665&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122665&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
means3.673-0.110.072-0.292







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.5470.5475.2570.03
Treatment_B10.0070.0070.0670.798
Treatment_A:Treatment_B10.140.141.3430.257
Residuals262.7070.104

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.547 & 0.547 & 5.257 & 0.03 \tabularnewline
Treatment_B & 1 & 0.007 & 0.007 & 0.067 & 0.798 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.14 & 0.14 & 1.343 & 0.257 \tabularnewline
Residuals & 26 & 2.707 & 0.104 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122665&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]0.547[/C][C]0.547[/C][C]5.257[/C][C]0.03[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.007[/C][C]0.007[/C][C]0.067[/C][C]0.798[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.14[/C][C]0.14[/C][C]1.343[/C][C]0.257[/C][/ROW]
[ROW][C]Residuals[/C][C]26[/C][C]2.707[/C][C]0.104[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122665&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122665&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_A10.5470.5475.2570.03
Treatment_B10.0070.0070.0670.798
Treatment_A:Treatment_B10.140.141.3430.257
Residuals262.7070.104







Tukey Honest Significant Difference Comparisons
difflwruprp adj
p-n-0.28-0.532-0.0290.03
m-f-0.03-0.2720.2120.803
p:f-n:f-0.11-0.6270.4070.936
n:m-n:f0.072-0.3390.4840.962
p:m-n:f-0.33-0.7580.0980.176
n:m-p:f0.183-0.3590.7250.792
p:m-p:f-0.219-0.7740.3350.702
p:m-n:m-0.402-0.860.0560.101

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
p-n & -0.28 & -0.532 & -0.029 & 0.03 \tabularnewline
m-f & -0.03 & -0.272 & 0.212 & 0.803 \tabularnewline
p:f-n:f & -0.11 & -0.627 & 0.407 & 0.936 \tabularnewline
n:m-n:f & 0.072 & -0.339 & 0.484 & 0.962 \tabularnewline
p:m-n:f & -0.33 & -0.758 & 0.098 & 0.176 \tabularnewline
n:m-p:f & 0.183 & -0.359 & 0.725 & 0.792 \tabularnewline
p:m-p:f & -0.219 & -0.774 & 0.335 & 0.702 \tabularnewline
p:m-n:m & -0.402 & -0.86 & 0.056 & 0.101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122665&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]p-n[/C][C]-0.28[/C][C]-0.532[/C][C]-0.029[/C][C]0.03[/C][/ROW]
[ROW][C]m-f[/C][C]-0.03[/C][C]-0.272[/C][C]0.212[/C][C]0.803[/C][/ROW]
[ROW][C]p:f-n:f[/C][C]-0.11[/C][C]-0.627[/C][C]0.407[/C][C]0.936[/C][/ROW]
[ROW][C]n:m-n:f[/C][C]0.072[/C][C]-0.339[/C][C]0.484[/C][C]0.962[/C][/ROW]
[ROW][C]p:m-n:f[/C][C]-0.33[/C][C]-0.758[/C][C]0.098[/C][C]0.176[/C][/ROW]
[ROW][C]n:m-p:f[/C][C]0.183[/C][C]-0.359[/C][C]0.725[/C][C]0.792[/C][/ROW]
[ROW][C]p:m-p:f[/C][C]-0.219[/C][C]-0.774[/C][C]0.335[/C][C]0.702[/C][/ROW]
[ROW][C]p:m-n:m[/C][C]-0.402[/C][C]-0.86[/C][C]0.056[/C][C]0.101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122665&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122665&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
p-n-0.28-0.532-0.0290.03
m-f-0.03-0.2720.2120.803
p:f-n:f-0.11-0.6270.4070.936
n:m-n:f0.072-0.3390.4840.962
p:m-n:f-0.33-0.7580.0980.176
n:m-p:f0.183-0.3590.7250.792
p:m-p:f-0.219-0.7740.3350.702
p:m-n:m-0.402-0.860.0560.101







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.4540.717
26

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.454 & 0.717 \tabularnewline
  & 26 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122665&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]0.454[/C][C]0.717[/C][/ROW]
[ROW][C] [/C][C]26[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122665&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122665&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)
Group30.4540.717
26



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