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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 computationTue, 18 Dec 2012 13:20:27 -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/18/t1355855097eiaidhnhpdf8xtr.htm/, Retrieved Thu, 31 Oct 2024 22:59:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201544, Retrieved Thu, 31 Oct 2024 22:59:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

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] [Two-Way Anova] [2012-12-18 18:20:27] [e5cf4d544f75f57c12196ef0ffd71d75] [Current]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201544&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201544&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201544&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 time7 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.4710.059-0.471-0.1210.1560.198

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.471 & 0.059 & -0.471 & -0.121 & 0.156 & 0.198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201544&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]0.059[/C][C]-0.471[/C][C]-0.121[/C][C]0.156[/C][C]0.198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201544&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201544&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
means0.4710.059-0.471-0.1210.1560.198






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A25.2812.64114.2840
Treatment_B2000.0010.98
Treatment_A:Treatment_B20.20.10.5410.584
Residuals11120.5190.185 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 5.281 & 2.641 & 14.284 & 0 \tabularnewline
Treatment_B & 2 & 0 & 0 & 0.001 & 0.98 \tabularnewline
Treatment_A:Treatment_B & 2 & 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=201544&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]5.281[/C][C]2.641[/C][C]14.284[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0[/C][C]0[/C][C]0.001[/C][C]0.98[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/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=201544&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201544&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_A25.2812.64114.2840
Treatment_B2000.0010.98
Treatment_A:Treatment_B20.20.10.5410.584
Residuals11120.5190.185






Tukey Honest Significant Difference Comparisons
difflwruprp adj
F-E0.145-0.0880.3780.307
H-E-0.355-0.588-0.1220.001
H-F-0.5-0.728-0.2720
1-0-0.002-0.1620.1580.98
F:0-E:00.059-0.3690.4870.999
H:0-E:0-0.471-0.921-0.0210.035
E:1-E:0-0.121-0.5320.2910.957
F:1-E:00.095-0.3040.4930.983
H:1-E:0-0.394-0.783-0.0050.045
H:0-F:0-0.529-0.979-0.0790.011
E:1-F:0-0.179-0.5910.2320.803
F:1-F:00.036-0.3630.4351
H:1-F:0-0.452-0.841-0.0640.013
E:1-H:00.35-0.0850.7850.189
F:1-H:00.5650.1430.9880.002
H:1-H:00.077-0.3360.490.994
F:1-E:10.215-0.1660.5960.576
H:1-E:1-0.273-0.6440.0980.277
H:1-F:1-0.488-0.845-0.1310.002

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
F-E & 0.145 & -0.088 & 0.378 & 0.307 \tabularnewline
H-E & -0.355 & -0.588 & -0.122 & 0.001 \tabularnewline
H-F & -0.5 & -0.728 & -0.272 & 0 \tabularnewline
1-0 & -0.002 & -0.162 & 0.158 & 0.98 \tabularnewline
F:0-E:0 & 0.059 & -0.369 & 0.487 & 0.999 \tabularnewline
H:0-E:0 & -0.471 & -0.921 & -0.021 & 0.035 \tabularnewline
E:1-E:0 & -0.121 & -0.532 & 0.291 & 0.957 \tabularnewline
F:1-E:0 & 0.095 & -0.304 & 0.493 & 0.983 \tabularnewline
H:1-E:0 & -0.394 & -0.783 & -0.005 & 0.045 \tabularnewline
H:0-F:0 & -0.529 & -0.979 & -0.079 & 0.011 \tabularnewline
E:1-F:0 & -0.179 & -0.591 & 0.232 & 0.803 \tabularnewline
F:1-F:0 & 0.036 & -0.363 & 0.435 & 1 \tabularnewline
H:1-F:0 & -0.452 & -0.841 & -0.064 & 0.013 \tabularnewline
E:1-H:0 & 0.35 & -0.085 & 0.785 & 0.189 \tabularnewline
F:1-H:0 & 0.565 & 0.143 & 0.988 & 0.002 \tabularnewline
H:1-H:0 & 0.077 & -0.336 & 0.49 & 0.994 \tabularnewline
F:1-E:1 & 0.215 & -0.166 & 0.596 & 0.576 \tabularnewline
H:1-E:1 & -0.273 & -0.644 & 0.098 & 0.277 \tabularnewline
H:1-F:1 & -0.488 & -0.845 & -0.131 & 0.002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201544&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]0.145[/C][C]-0.088[/C][C]0.378[/C][C]0.307[/C][/ROW]
[ROW][C]H-E[/C][C]-0.355[/C][C]-0.588[/C][C]-0.122[/C][C]0.001[/C][/ROW]
[ROW][C]H-F[/C][C]-0.5[/C][C]-0.728[/C][C]-0.272[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]-0.002[/C][C]-0.162[/C][C]0.158[/C][C]0.98[/C][/ROW]
[ROW][C]F:0-E:0[/C][C]0.059[/C][C]-0.369[/C][C]0.487[/C][C]0.999[/C][/ROW]
[ROW][C]H:0-E:0[/C][C]-0.471[/C][C]-0.921[/C][C]-0.021[/C][C]0.035[/C][/ROW]
[ROW][C]E:1-E:0[/C][C]-0.121[/C][C]-0.532[/C][C]0.291[/C][C]0.957[/C][/ROW]
[ROW][C]F:1-E:0[/C][C]0.095[/C][C]-0.304[/C][C]0.493[/C][C]0.983[/C][/ROW]
[ROW][C]H:1-E:0[/C][C]-0.394[/C][C]-0.783[/C][C]-0.005[/C][C]0.045[/C][/ROW]
[ROW][C]H:0-F:0[/C][C]-0.529[/C][C]-0.979[/C][C]-0.079[/C][C]0.011[/C][/ROW]
[ROW][C]E:1-F:0[/C][C]-0.179[/C][C]-0.591[/C][C]0.232[/C][C]0.803[/C][/ROW]
[ROW][C]F:1-F:0[/C][C]0.036[/C][C]-0.363[/C][C]0.435[/C][C]1[/C][/ROW]
[ROW][C]H:1-F:0[/C][C]-0.452[/C][C]-0.841[/C][C]-0.064[/C][C]0.013[/C][/ROW]
[ROW][C]E:1-H:0[/C][C]0.35[/C][C]-0.085[/C][C]0.785[/C][C]0.189[/C][/ROW]
[ROW][C]F:1-H:0[/C][C]0.565[/C][C]0.143[/C][C]0.988[/C][C]0.002[/C][/ROW]
[ROW][C]H:1-H:0[/C][C]0.077[/C][C]-0.336[/C][C]0.49[/C][C]0.994[/C][/ROW]
[ROW][C]F:1-E:1[/C][C]0.215[/C][C]-0.166[/C][C]0.596[/C][C]0.576[/C][/ROW]
[ROW][C]H:1-E:1[/C][C]-0.273[/C][C]-0.644[/C][C]0.098[/C][C]0.277[/C][/ROW]
[ROW][C]H:1-F:1[/C][C]-0.488[/C][C]-0.845[/C][C]-0.131[/C][C]0.002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201544&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201544&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-E0.145-0.0880.3780.307
H-E-0.355-0.588-0.1220.001
H-F-0.5-0.728-0.2720
1-0-0.002-0.1620.1580.98
F:0-E:00.059-0.3690.4870.999
H:0-E:0-0.471-0.921-0.0210.035
E:1-E:0-0.121-0.5320.2910.957
F:1-E:00.095-0.3040.4930.983
H:1-E:0-0.394-0.783-0.0050.045
H:0-F:0-0.529-0.979-0.0790.011
E:1-F:0-0.179-0.5910.2320.803
F:1-F:00.036-0.3630.4351
H:1-F:0-0.452-0.841-0.0640.013
E:1-H:00.35-0.0850.7850.189
F:1-H:00.5650.1430.9880.002
H:1-H:00.077-0.3360.490.994
F:1-E:10.215-0.1660.5960.576
H:1-E:1-0.273-0.6440.0980.277
H:1-F:1-0.488-0.845-0.1310.002






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=201544&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=201544&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201544&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)
Group54.340.001
111


Figures (Output of Computation)

Input Parameters & R Code

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')