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Description of Statistical Computation

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 computationSun, 21 Nov 2010 21:01:40 +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/2010/Nov/21/t12903736040sxynjlle06q5rv.htm/, Retrieved Thu, 02 May 2024 07:52:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98410, Retrieved Thu, 02 May 2024 07:52:20 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [] [2010-11-02 14:42:14] [b98453cac15ba1066b407e146608df68]
- R PD    [Two-Way ANOVA] [2 way anova Treat...] [2010-11-21 21:01:40] [9ea95e194e0eb2a674315798620d5bc6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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0	0	'H'	0	0	'LO'
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0	0	'F'	0	1	'LO'
0	1	'F'	1	1	'HI'
0	0	'H'	0	0	'LO'
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0	0	'H'	0	1	'HI'
1	0	'E'	-1	1	'HI'
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0	0	'H'	0	1	'LO'
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0	1	'F'	1	1	'HI'
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0	1	'E'	1	1	'HI'
0	1	'F'	1	1	'HI'
0	0	'H'	0	0	'HI'
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0	0	'H'	0	1	'HI'
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0	0	'E'	0	1	'HI'
0	1	'E'	1	0	'HI'
0	0	'H'	0	0	'HI'
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0	0	'E'	0	1	'LO'
0	0	'H'	0	1	'HI'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98410&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98410&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98410&T=0

As an alternative you can also use a QR Code:  
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'RServer@AstonUniversity' @ vre.aston.ac.uk






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.4090.156-0.409-0.1010.0030.173

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.409 & 0.156 & -0.409 & -0.101 & 0.003 & 0.173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98410&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.409[/C][C]0.156[/C][C]-0.409[/C][C]-0.101[/C][C]0.003[/C][C]0.173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98410&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98410&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.4090.156-0.409-0.1010.0030.173






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A25.0592.5313.1430
Treatment_B20.0450.0450.2320.631
Treatment_A:Treatment_B20.1730.0870.450.639
Residuals10620.4010.192 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 5.059 & 2.53 & 13.143 & 0 \tabularnewline
Treatment_B & 2 & 0.045 & 0.045 & 0.232 & 0.631 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.173 & 0.087 & 0.45 & 0.639 \tabularnewline
Residuals & 106 & 20.401 & 0.192 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98410&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]2[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]2[/C][C]5.059[/C][C]2.53[/C][C]13.143[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0.045[/C][C]0.045[/C][C]0.232[/C][C]0.631[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.173[/C][C]0.087[/C][C]0.45[/C][C]0.639[/C][/ROW]
[ROW][C]Residuals[/C][C]106[/C][C]20.401[/C][C]0.192[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98410&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98410&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A25.0592.5313.1430
Treatment_B20.0450.0450.2320.631
Treatment_A:Treatment_B20.1730.0870.450.639
Residuals10620.4010.192






Tukey Honest Significant Difference Comparisons
difflwruprp adj
F-E0.155-0.0890.3990.292
H-E-0.346-0.589-0.1030.003
H-F-0.501-0.738-0.2630
LO-HI-0.041-0.2110.1290.631
F:HI-E:HI0.156-0.2240.5360.839
H:HI-E:HI-0.409-0.781-0.0370.022
E:LO-E:HI-0.101-0.5470.3440.986
F:LO-E:HI0.058-0.3690.4840.999
H:LO-E:HI-0.338-0.7730.0980.224
H:HI-F:HI-0.565-0.933-0.1970
E:LO-F:HI-0.258-0.6990.1840.54
F:LO-F:HI-0.099-0.5210.3240.984
H:LO-F:HI-0.494-0.925-0.0620.015
E:LO-H:HI0.308-0.1280.7430.321
F:LO-H:HI0.4670.0510.8830.018
H:LO-H:HI0.071-0.3540.4960.997
F:LO-E:LO0.159-0.3240.6410.93
H:LO-E:LO-0.236-0.7270.2540.728
H:LO-F:LO-0.395-0.8680.0780.157

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
F-E & 0.155 & -0.089 & 0.399 & 0.292 \tabularnewline
H-E & -0.346 & -0.589 & -0.103 & 0.003 \tabularnewline
H-F & -0.501 & -0.738 & -0.263 & 0 \tabularnewline
LO-HI & -0.041 & -0.211 & 0.129 & 0.631 \tabularnewline
F:HI-E:HI & 0.156 & -0.224 & 0.536 & 0.839 \tabularnewline
H:HI-E:HI & -0.409 & -0.781 & -0.037 & 0.022 \tabularnewline
E:LO-E:HI & -0.101 & -0.547 & 0.344 & 0.986 \tabularnewline
F:LO-E:HI & 0.058 & -0.369 & 0.484 & 0.999 \tabularnewline
H:LO-E:HI & -0.338 & -0.773 & 0.098 & 0.224 \tabularnewline
H:HI-F:HI & -0.565 & -0.933 & -0.197 & 0 \tabularnewline
E:LO-F:HI & -0.258 & -0.699 & 0.184 & 0.54 \tabularnewline
F:LO-F:HI & -0.099 & -0.521 & 0.324 & 0.984 \tabularnewline
H:LO-F:HI & -0.494 & -0.925 & -0.062 & 0.015 \tabularnewline
E:LO-H:HI & 0.308 & -0.128 & 0.743 & 0.321 \tabularnewline
F:LO-H:HI & 0.467 & 0.051 & 0.883 & 0.018 \tabularnewline
H:LO-H:HI & 0.071 & -0.354 & 0.496 & 0.997 \tabularnewline
F:LO-E:LO & 0.159 & -0.324 & 0.641 & 0.93 \tabularnewline
H:LO-E:LO & -0.236 & -0.727 & 0.254 & 0.728 \tabularnewline
H:LO-F:LO & -0.395 & -0.868 & 0.078 & 0.157 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98410&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]F-E[/C][C]0.155[/C][C]-0.089[/C][C]0.399[/C][C]0.292[/C][/ROW]
[ROW][C]H-E[/C][C]-0.346[/C][C]-0.589[/C][C]-0.103[/C][C]0.003[/C][/ROW]
[ROW][C]H-F[/C][C]-0.501[/C][C]-0.738[/C][C]-0.263[/C][C]0[/C][/ROW]
[ROW][C]LO-HI[/C][C]-0.041[/C][C]-0.211[/C][C]0.129[/C][C]0.631[/C][/ROW]
[ROW][C]F:HI-E:HI[/C][C]0.156[/C][C]-0.224[/C][C]0.536[/C][C]0.839[/C][/ROW]
[ROW][C]H:HI-E:HI[/C][C]-0.409[/C][C]-0.781[/C][C]-0.037[/C][C]0.022[/C][/ROW]
[ROW][C]E:LO-E:HI[/C][C]-0.101[/C][C]-0.547[/C][C]0.344[/C][C]0.986[/C][/ROW]
[ROW][C]F:LO-E:HI[/C][C]0.058[/C][C]-0.369[/C][C]0.484[/C][C]0.999[/C][/ROW]
[ROW][C]H:LO-E:HI[/C][C]-0.338[/C][C]-0.773[/C][C]0.098[/C][C]0.224[/C][/ROW]
[ROW][C]H:HI-F:HI[/C][C]-0.565[/C][C]-0.933[/C][C]-0.197[/C][C]0[/C][/ROW]
[ROW][C]E:LO-F:HI[/C][C]-0.258[/C][C]-0.699[/C][C]0.184[/C][C]0.54[/C][/ROW]
[ROW][C]F:LO-F:HI[/C][C]-0.099[/C][C]-0.521[/C][C]0.324[/C][C]0.984[/C][/ROW]
[ROW][C]H:LO-F:HI[/C][C]-0.494[/C][C]-0.925[/C][C]-0.062[/C][C]0.015[/C][/ROW]
[ROW][C]E:LO-H:HI[/C][C]0.308[/C][C]-0.128[/C][C]0.743[/C][C]0.321[/C][/ROW]
[ROW][C]F:LO-H:HI[/C][C]0.467[/C][C]0.051[/C][C]0.883[/C][C]0.018[/C][/ROW]
[ROW][C]H:LO-H:HI[/C][C]0.071[/C][C]-0.354[/C][C]0.496[/C][C]0.997[/C][/ROW]
[ROW][C]F:LO-E:LO[/C][C]0.159[/C][C]-0.324[/C][C]0.641[/C][C]0.93[/C][/ROW]
[ROW][C]H:LO-E:LO[/C][C]-0.236[/C][C]-0.727[/C][C]0.254[/C][C]0.728[/C][/ROW]
[ROW][C]H:LO-F:LO[/C][C]-0.395[/C][C]-0.868[/C][C]0.078[/C][C]0.157[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98410&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98410&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
F-E0.155-0.0890.3990.292
H-E-0.346-0.589-0.1030.003
H-F-0.501-0.738-0.2630
LO-HI-0.041-0.2110.1290.631
F:HI-E:HI0.156-0.2240.5360.839
H:HI-E:HI-0.409-0.781-0.0370.022
E:LO-E:HI-0.101-0.5470.3440.986
F:LO-E:HI0.058-0.3690.4840.999
H:LO-E:HI-0.338-0.7730.0980.224
H:HI-F:HI-0.565-0.933-0.1970
E:LO-F:HI-0.258-0.6990.1840.54
F:LO-F:HI-0.099-0.5210.3240.984
H:LO-F:HI-0.494-0.925-0.0620.015
E:LO-H:HI0.308-0.1280.7430.321
F:LO-H:HI0.4670.0510.8830.018
H:LO-H:HI0.071-0.3540.4960.997
F:LO-E:LO0.159-0.3240.6410.93
H:LO-E:LO-0.236-0.7270.2540.728
H:LO-F:LO-0.395-0.8680.0780.157






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group55.3540
106 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 5.354 & 0 \tabularnewline
  & 106 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98410&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]5.354[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]106[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98410&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98410&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group55.3540
106


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = 3 ; par3 = 6 ; par4 = TRUE ;
Parameters (R input):
par1 = 4 ; par2 = 3 ; par3 = 6 ; 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')