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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 computationSat, 05 Nov 2011 19:38:09 -0400
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/Nov/05/t1320536305fyh3e59nlhu4aji.htm/, Retrieved Sat, 20 Apr 2024 07:07:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=139878, Retrieved Sat, 20 Apr 2024 07:07:21 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [Workshop 5 Taak 8] [2011-11-05 23:38:09] [5c44e6aad476a1bab98fc6774eca4c08] [Current]
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Dataseries X:
0	1	'E'
1	0	'F'
0	1	'F'
0	1	'H'
0	1	'H'
0	1	'H'
1	1	'E'
1	1	'F'
0	1	'E'
1	0	'F'
0	0	'H'
0	0	'E'
1	1	'F'
0	0	'H'
1	0	'E'
0	0	'H'
0	1	'E'
0	1	'F'
0	0	'H'
1	0	'F'
0	0	'H'
0	1	'H'
0	0	'H'
0	0	'E'
1	0	'F'
1	0	'E'
1	0	'E'
1	1	'F'
0	0	'F'
0	0	'H'
0	1	'E'
1	1	'E'
0	1	'H'
1	1	'E'
1	1	'F'
0	1	'E'
1	0	'F'
0	0	'H'
1	0	'E'
1	0	'F'
1	0	'F'
0	0	'F'
1	0	'F'
1	1	'H'
1	0	'E'
0	0	'E'
0	0	'H'
1	1	'E'
0	1	'F'
0	0	'F'
0	0	'H'
0	1	'E'
1	1	'F'
1	1	'E'
0	1	'H'
0	1	'H'
0	1	'H'
0	1	'E'
0	0	'H'
1	0	'E'
0	1	'H'
0	1	'F'
0	1	'H'
1	0	'F'
0	1	'E'
1	1	'E'
0	0	'F'
0	1	'H'
0	0	'F'
0	1	'E'
0	1	'E'
0	0	'H'
0	1	'H'
0	1	'F'
0	1	'H'
1	0	'E'
0	1	'F'
1	0	'E'
0	0	'E'
0	0	'E'
0	1	'F'
0	1	'E'
1	1	'F'
0	1	'H'
1	1	'H'
0	1	'H'
0	0	'F'
0	1	'H'
0	1	'H'
1	1	'F'
1	1	'F'
0	0	'H'
0	1	'F'
0	1	'H'
0	0	'E'
1	1	'F'
0	0	'E'
0	1	'H'
1	1	'F'
1	1	'F'
0	1	'H'
1	1	'E'
0	0	'F'
0	1	'H'
0	1	'E'
0	0	'F'
0	0	'H'
0	1	'H'
1	1	'F'
1	1	'F'
0	1	'H'
0	0	'E'
0	1	'H'
0	1	'E'
0	0	'E'
0	1	'F'
0	1	'F'




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=139878&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=139878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=139878&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.471-0.1210.059-0.4710.1560.198

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.471 & -0.121 & 0.059 & -0.471 & 0.156 & 0.198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=139878&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.471[/C][C]-0.121[/C][C]0.059[/C][C]-0.471[/C][C]0.156[/C][C]0.198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=139878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=139878&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
means0.471-0.1210.059-0.4710.1560.198







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.0350.0350.1910.663
Treatment_B15.2462.62314.1890
Treatment_A:Treatment_B10.20.10.5410.584
Residuals11120.5190.185

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.035 & 0.035 & 0.191 & 0.663 \tabularnewline
Treatment_B & 1 & 5.246 & 2.623 & 14.189 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.2 & 0.1 & 0.541 & 0.584 \tabularnewline
Residuals & 111 & 20.519 & 0.185 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=139878&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]0.035[/C][C]0.035[/C][C]0.191[/C][C]0.663[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]5.246[/C][C]2.623[/C][C]14.189[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.2[/C][C]0.1[/C][C]0.541[/C][C]0.584[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]20.519[/C][C]0.185[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=139878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=139878&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_A10.0350.0350.1910.663
Treatment_B15.2462.62314.1890
Treatment_A:Treatment_B10.20.10.5410.584
Residuals11120.5190.185







Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.035-0.1950.1250.663
F-E0.146-0.0870.3790.301
H-E-0.352-0.585-0.1190.001
H-F-0.497-0.726-0.2690
1:E-0:E-0.121-0.5320.2910.957
0:F-0:E0.059-0.3690.4870.999
1:F-0:E0.095-0.3040.4930.983
0:H-0:E-0.471-0.921-0.0210.035
1:H-0:E-0.394-0.783-0.0050.045
0:F-1:E0.179-0.2320.5910.803
1:F-1:E0.215-0.1660.5960.576
0:H-1:E-0.35-0.7850.0850.189
1:H-1:E-0.273-0.6440.0980.277
1:F-0:F0.036-0.3630.4351
0:H-0:F-0.529-0.979-0.0790.011
1:H-0:F-0.452-0.841-0.0640.013
0:H-1:F-0.565-0.988-0.1430.002
1:H-1:F-0.488-0.845-0.1310.002
1:H-0:H0.077-0.3360.490.994

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.035 & -0.195 & 0.125 & 0.663 \tabularnewline
F-E & 0.146 & -0.087 & 0.379 & 0.301 \tabularnewline
H-E & -0.352 & -0.585 & -0.119 & 0.001 \tabularnewline
H-F & -0.497 & -0.726 & -0.269 & 0 \tabularnewline
1:E-0:E & -0.121 & -0.532 & 0.291 & 0.957 \tabularnewline
0:F-0:E & 0.059 & -0.369 & 0.487 & 0.999 \tabularnewline
1:F-0:E & 0.095 & -0.304 & 0.493 & 0.983 \tabularnewline
0:H-0:E & -0.471 & -0.921 & -0.021 & 0.035 \tabularnewline
1:H-0:E & -0.394 & -0.783 & -0.005 & 0.045 \tabularnewline
0:F-1:E & 0.179 & -0.232 & 0.591 & 0.803 \tabularnewline
1:F-1:E & 0.215 & -0.166 & 0.596 & 0.576 \tabularnewline
0:H-1:E & -0.35 & -0.785 & 0.085 & 0.189 \tabularnewline
1:H-1:E & -0.273 & -0.644 & 0.098 & 0.277 \tabularnewline
1:F-0:F & 0.036 & -0.363 & 0.435 & 1 \tabularnewline
0:H-0:F & -0.529 & -0.979 & -0.079 & 0.011 \tabularnewline
1:H-0:F & -0.452 & -0.841 & -0.064 & 0.013 \tabularnewline
0:H-1:F & -0.565 & -0.988 & -0.143 & 0.002 \tabularnewline
1:H-1:F & -0.488 & -0.845 & -0.131 & 0.002 \tabularnewline
1:H-0:H & 0.077 & -0.336 & 0.49 & 0.994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=139878&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]1-0[/C][C]-0.035[/C][C]-0.195[/C][C]0.125[/C][C]0.663[/C][/ROW]
[ROW][C]F-E[/C][C]0.146[/C][C]-0.087[/C][C]0.379[/C][C]0.301[/C][/ROW]
[ROW][C]H-E[/C][C]-0.352[/C][C]-0.585[/C][C]-0.119[/C][C]0.001[/C][/ROW]
[ROW][C]H-F[/C][C]-0.497[/C][C]-0.726[/C][C]-0.269[/C][C]0[/C][/ROW]
[ROW][C]1:E-0:E[/C][C]-0.121[/C][C]-0.532[/C][C]0.291[/C][C]0.957[/C][/ROW]
[ROW][C]0:F-0:E[/C][C]0.059[/C][C]-0.369[/C][C]0.487[/C][C]0.999[/C][/ROW]
[ROW][C]1:F-0:E[/C][C]0.095[/C][C]-0.304[/C][C]0.493[/C][C]0.983[/C][/ROW]
[ROW][C]0:H-0:E[/C][C]-0.471[/C][C]-0.921[/C][C]-0.021[/C][C]0.035[/C][/ROW]
[ROW][C]1:H-0:E[/C][C]-0.394[/C][C]-0.783[/C][C]-0.005[/C][C]0.045[/C][/ROW]
[ROW][C]0:F-1:E[/C][C]0.179[/C][C]-0.232[/C][C]0.591[/C][C]0.803[/C][/ROW]
[ROW][C]1:F-1:E[/C][C]0.215[/C][C]-0.166[/C][C]0.596[/C][C]0.576[/C][/ROW]
[ROW][C]0:H-1:E[/C][C]-0.35[/C][C]-0.785[/C][C]0.085[/C][C]0.189[/C][/ROW]
[ROW][C]1:H-1:E[/C][C]-0.273[/C][C]-0.644[/C][C]0.098[/C][C]0.277[/C][/ROW]
[ROW][C]1:F-0:F[/C][C]0.036[/C][C]-0.363[/C][C]0.435[/C][C]1[/C][/ROW]
[ROW][C]0:H-0:F[/C][C]-0.529[/C][C]-0.979[/C][C]-0.079[/C][C]0.011[/C][/ROW]
[ROW][C]1:H-0:F[/C][C]-0.452[/C][C]-0.841[/C][C]-0.064[/C][C]0.013[/C][/ROW]
[ROW][C]0:H-1:F[/C][C]-0.565[/C][C]-0.988[/C][C]-0.143[/C][C]0.002[/C][/ROW]
[ROW][C]1:H-1:F[/C][C]-0.488[/C][C]-0.845[/C][C]-0.131[/C][C]0.002[/C][/ROW]
[ROW][C]1:H-0:H[/C][C]0.077[/C][C]-0.336[/C][C]0.49[/C][C]0.994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=139878&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=139878&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
1-0-0.035-0.1950.1250.663
F-E0.146-0.0870.3790.301
H-E-0.352-0.585-0.1190.001
H-F-0.497-0.726-0.2690
1:E-0:E-0.121-0.5320.2910.957
0:F-0:E0.059-0.3690.4870.999
1:F-0:E0.095-0.3040.4930.983
0:H-0:E-0.471-0.921-0.0210.035
1:H-0:E-0.394-0.783-0.0050.045
0:F-1:E0.179-0.2320.5910.803
1:F-1:E0.215-0.1660.5960.576
0:H-1:E-0.35-0.7850.0850.189
1:H-1:E-0.273-0.6440.0980.277
1:F-0:F0.036-0.3630.4351
0:H-0:F-0.529-0.979-0.0790.011
1:H-0:F-0.452-0.841-0.0640.013
0:H-1:F-0.565-0.988-0.1430.002
1:H-1:F-0.488-0.845-0.1310.002
1:H-0:H0.077-0.3360.490.994







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group54.340.001
111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 4.34 & 0.001 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=139878&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]5[/C][C]4.34[/C][C]0.001[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=139878&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=139878&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)
Group54.340.001
111



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')