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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, 18 Dec 2014 08:44:34 +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/2014/Dec/18/t1418892483xq4swc633ve9nl1.htm/, Retrieved Sun, 19 May 2024 21:33:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270769, Retrieved Sun, 19 May 2024 21:33:02 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi-Squared and McNemar Tests] [] [2010-11-16 14:33:59] [b98453cac15ba1066b407e146608df68]
- RMPD  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-10-29 17:56:37] [272d52cebbec48285fb11674f7e19cee]
- RMPD      [Two-Way ANOVA] [] [2014-12-18 08:44:34] [d22b5684547ea06d48f60665f2dd1986] [Current]
- RMPD        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-18 09:18:55] [272d52cebbec48285fb11674f7e19cee]
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Dataseries X:
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Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270769&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270769&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270769&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means19.077-0.1862.191-0.65

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 19.077 & -0.186 & 2.191 & -0.65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270769&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]19.077[/C][C]-0.186[/C][C]2.191[/C][C]-0.65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270769&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270769&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
means19.077-0.1862.191-0.65







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A110.14110.1410.3950.53
Treatment_B1236.062236.0629.1850.003
Treatment_A:Treatment_B17.1547.1540.2780.598
Residuals2757067.46725.7

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 10.141 & 10.141 & 0.395 & 0.53 \tabularnewline
Treatment_B & 1 & 236.062 & 236.062 & 9.185 & 0.003 \tabularnewline
Treatment_A:Treatment_B & 1 & 7.154 & 7.154 & 0.278 & 0.598 \tabularnewline
Residuals & 275 & 7067.467 & 25.7 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270769&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]10.141[/C][C]10.141[/C][C]0.395[/C][C]0.53[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]236.062[/C][C]236.062[/C][C]9.185[/C][C]0.003[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]7.154[/C][C]7.154[/C][C]0.278[/C][C]0.598[/C][/ROW]
[ROW][C]Residuals[/C][C]275[/C][C]7067.467[/C][C]25.7[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270769&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270769&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_A110.14110.1410.3950.53
Treatment_B1236.062236.0629.1850.003
Treatment_A:Treatment_B17.1547.1540.2780.598
Residuals2757067.46725.7







Tukey Honest Significant Difference Comparisons
difflwruprp adj
'S'-'B'-0.381-1.5770.8140.53
1-01.850.6433.0560.003
'S':0-'B':0-0.186-2.5872.2150.997
'B':1-'B':02.191-0.0594.440.059
'S':1-'B':01.355-0.7883.4980.361
'B':1-'S':02.3770.0234.730.047
'S':1-'S':01.541-0.7113.7930.291
'S':1-'B':1-0.836-2.9261.2550.73

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
'S'-'B' & -0.381 & -1.577 & 0.814 & 0.53 \tabularnewline
1-0 & 1.85 & 0.643 & 3.056 & 0.003 \tabularnewline
'S':0-'B':0 & -0.186 & -2.587 & 2.215 & 0.997 \tabularnewline
'B':1-'B':0 & 2.191 & -0.059 & 4.44 & 0.059 \tabularnewline
'S':1-'B':0 & 1.355 & -0.788 & 3.498 & 0.361 \tabularnewline
'B':1-'S':0 & 2.377 & 0.023 & 4.73 & 0.047 \tabularnewline
'S':1-'S':0 & 1.541 & -0.711 & 3.793 & 0.291 \tabularnewline
'S':1-'B':1 & -0.836 & -2.926 & 1.255 & 0.73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270769&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]-0.381[/C][C]-1.577[/C][C]0.814[/C][C]0.53[/C][/ROW]
[ROW][C]1-0[/C][C]1.85[/C][C]0.643[/C][C]3.056[/C][C]0.003[/C][/ROW]
[ROW][C]'S':0-'B':0[/C][C]-0.186[/C][C]-2.587[/C][C]2.215[/C][C]0.997[/C][/ROW]
[ROW][C]'B':1-'B':0[/C][C]2.191[/C][C]-0.059[/C][C]4.44[/C][C]0.059[/C][/ROW]
[ROW][C]'S':1-'B':0[/C][C]1.355[/C][C]-0.788[/C][C]3.498[/C][C]0.361[/C][/ROW]
[ROW][C]'B':1-'S':0[/C][C]2.377[/C][C]0.023[/C][C]4.73[/C][C]0.047[/C][/ROW]
[ROW][C]'S':1-'S':0[/C][C]1.541[/C][C]-0.711[/C][C]3.793[/C][C]0.291[/C][/ROW]
[ROW][C]'S':1-'B':1[/C][C]-0.836[/C][C]-2.926[/C][C]1.255[/C][C]0.73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270769&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270769&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'-'B'-0.381-1.5770.8140.53
1-01.850.6433.0560.003
'S':0-'B':0-0.186-2.5872.2150.997
'B':1-'B':02.191-0.0594.440.059
'S':1-'B':01.355-0.7883.4980.361
'B':1-'S':02.3770.0234.730.047
'S':1-'S':01.541-0.7113.7930.291
'S':1-'B':1-0.836-2.9261.2550.73







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group33.250.022
275

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.25 & 0.022 \tabularnewline
  & 275 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270769&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]3.25[/C][C]0.022[/C][/ROW]
[ROW][C] [/C][C]275[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270769&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270769&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)
Group33.250.022
275



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')