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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 computationFri, 21 Dec 2012 18:28:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356132531yncp97lzt98ka4n.htm/, Retrieved Thu, 31 Oct 2024 23:53:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204401, Retrieved Thu, 31 Oct 2024 23:53:40 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2010-11-02 14:17:22] [b98453cac15ba1066b407e146608df68]
- R P   [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2012-12-16 14:09:23] [147786ccb76fa00e429d4b9f5f28b291]
- RMPD      [Two-Way ANOVA] [] [2012-12-21 23:28:36] [26ce3afa84a4087bb435ca409d5552c3] [Current]
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Dataseries X:
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'Treatment'	1
4	'Treatment'	0
4	'NoTreatment'	0
4	'Treatment'	1
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	1
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'Treatment'	1
4	'NoTreatment'	0
4	'NoTreatment'	1
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	1
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	1
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'Treatment'	1
4	'Treatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	0
4	'NoTreatment'	1
4	'NoTreatment'	0
4	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	1
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'Treatment'	0
2	'Treatment'	0
2	'Treatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	0
2	'NoTreatment'	1
2	'NoTreatment'	1
2	'NoTreatment'	0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204401&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204401&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.059-0.011-0.0590.272

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.059 & -0.011 & -0.059 & 0.272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204401&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.059[/C][C]-0.011[/C][C]-0.059[/C][C]0.272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204401&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
means0.059-0.011-0.0590.272







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.1390.1392.0630.153
Treatment_B10.2730.2734.0490.046
Treatment_A:Treatment_B10.5370.5377.9670.005
Residuals15010.1150.067

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.139 & 0.139 & 2.063 & 0.153 \tabularnewline
Treatment_B & 1 & 0.273 & 0.273 & 4.049 & 0.046 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.537 & 0.537 & 7.967 & 0.005 \tabularnewline
Residuals & 150 & 10.115 & 0.067 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204401&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]0.139[/C][C]0.139[/C][C]2.063[/C][C]0.153[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.273[/C][C]0.273[/C][C]4.049[/C][C]0.046[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.537[/C][C]0.537[/C][C]7.967[/C][C]0.005[/C][/ROW]
[ROW][C]Residuals[/C][C]150[/C][C]10.115[/C][C]0.067[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204401&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_A10.1390.1392.0630.153
Treatment_B10.2730.2734.0490.046
Treatment_A:Treatment_B10.5370.5377.9670.005
Residuals15010.1150.067







Tukey Honest Significant Difference Comparisons
difflwruprp adj
4-20.061-0.0230.1440.153
Treatment-NoTreatment0.0960.0020.190.046
4:NoTreatment-2:NoTreatment-0.011-0.1380.1160.996
2:Treatment-2:NoTreatment-0.059-0.2480.130.85
4:Treatment-2:NoTreatment0.2020.0330.3720.012
2:Treatment-4:NoTreatment-0.048-0.2320.1370.908
4:Treatment-4:NoTreatment0.2130.0490.3780.005
4:Treatment-2:Treatment0.2610.0450.4770.011

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
4-2 & 0.061 & -0.023 & 0.144 & 0.153 \tabularnewline
Treatment-NoTreatment & 0.096 & 0.002 & 0.19 & 0.046 \tabularnewline
4:NoTreatment-2:NoTreatment & -0.011 & -0.138 & 0.116 & 0.996 \tabularnewline
2:Treatment-2:NoTreatment & -0.059 & -0.248 & 0.13 & 0.85 \tabularnewline
4:Treatment-2:NoTreatment & 0.202 & 0.033 & 0.372 & 0.012 \tabularnewline
2:Treatment-4:NoTreatment & -0.048 & -0.232 & 0.137 & 0.908 \tabularnewline
4:Treatment-4:NoTreatment & 0.213 & 0.049 & 0.378 & 0.005 \tabularnewline
4:Treatment-2:Treatment & 0.261 & 0.045 & 0.477 & 0.011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204401&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]4-2[/C][C]0.061[/C][C]-0.023[/C][C]0.144[/C][C]0.153[/C][/ROW]
[ROW][C]Treatment-NoTreatment[/C][C]0.096[/C][C]0.002[/C][C]0.19[/C][C]0.046[/C][/ROW]
[ROW][C]4:NoTreatment-2:NoTreatment[/C][C]-0.011[/C][C]-0.138[/C][C]0.116[/C][C]0.996[/C][/ROW]
[ROW][C]2:Treatment-2:NoTreatment[/C][C]-0.059[/C][C]-0.248[/C][C]0.13[/C][C]0.85[/C][/ROW]
[ROW][C]4:Treatment-2:NoTreatment[/C][C]0.202[/C][C]0.033[/C][C]0.372[/C][C]0.012[/C][/ROW]
[ROW][C]2:Treatment-4:NoTreatment[/C][C]-0.048[/C][C]-0.232[/C][C]0.137[/C][C]0.908[/C][/ROW]
[ROW][C]4:Treatment-4:NoTreatment[/C][C]0.213[/C][C]0.049[/C][C]0.378[/C][C]0.005[/C][/ROW]
[ROW][C]4:Treatment-2:Treatment[/C][C]0.261[/C][C]0.045[/C][C]0.477[/C][C]0.011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204401&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204401&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
4-20.061-0.0230.1440.153
Treatment-NoTreatment0.0960.0020.190.046
4:NoTreatment-2:NoTreatment-0.011-0.1380.1160.996
2:Treatment-2:NoTreatment-0.059-0.2480.130.85
4:Treatment-2:NoTreatment0.2020.0330.3720.012
2:Treatment-4:NoTreatment-0.048-0.2320.1370.908
4:Treatment-4:NoTreatment0.2130.0490.3780.005
4:Treatment-2:Treatment0.2610.0450.4770.011







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group34.6930.004
150

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 4.693 & 0.004 \tabularnewline
  & 150 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204401&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]4.693[/C][C]0.004[/C][/ROW]
[ROW][C] [/C][C]150[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204401&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204401&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)
Group34.6930.004
150



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