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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, 30 Oct 2012 14:20:09 -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/2012/Oct/30/t13516212530cv93owow013dso.htm/, Retrieved Fri, 03 May 2024 21:32:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=185275, Retrieved Fri, 03 May 2024 21:32:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

Tree of Dependent Computations

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)] [WS5 Q6] [2012-10-30 17:35:06] [15980d50f043b229c552ae7b9d1fee1e]
- RMPD    [Two-Way ANOVA] [WS5 Q8] [2012-10-30 18:20:09] [6be1b944a7a94a22fefeff86eded5e58] [Current]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185275&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185275&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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.417-0.4170.11-0.3910.891.391

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.417 & -0.417 & 0.11 & -0.391 & 0.89 & 1.391 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185275&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.417[/C][C]-0.417[/C][C]0.11[/C][C]-0.391[/C][C]0.89[/C][C]1.391[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185275&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
means0.417-0.4170.11-0.3910.891.391






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.7190.7194.1570.044
Treatment_B15.1042.55214.7560
Treatment_A:Treatment_B10.9790.4892.8290.063
Residuals11119.1980.173 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.719 & 0.719 & 4.157 & 0.044 \tabularnewline
Treatment_B & 1 & 5.104 & 2.552 & 14.756 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.979 & 0.489 & 2.829 & 0.063 \tabularnewline
Residuals & 111 & 19.198 & 0.173 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185275&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]0.719[/C][C]0.719[/C][C]4.157[/C][C]0.044[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]5.104[/C][C]2.552[/C][C]14.756[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.979[/C][C]0.489[/C][C]2.829[/C][C]0.063[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]19.198[/C][C]0.173[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185275&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)
1
Treatment_A10.7190.7194.1570.044
Treatment_B15.1042.55214.7560
Treatment_A:Treatment_B10.9790.4892.8290.063
Residuals11119.1980.173






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.4310.0120.8510.044
F-E0.135-0.0910.360.334
H-E-0.355-0.58-0.1290.001
H-F-0.489-0.71-0.2680
1:E-0:E-0.417-1.6390.8060.921
0:F-0:E0.11-0.1710.390.866
1:F-0:E0.583-0.2931.460.389
0:H-0:E-0.391-0.67-0.1120.001
1:H-0:E0.583-0.6391.8060.737
0:F-1:E0.526-0.6961.7480.811
1:F-1:E1-0.4772.4770.37
0:H-1:E0.026-1.1961.2471
1:H-1:E1-0.7062.7060.535
1:F-0:F0.474-0.4011.3490.62
0:H-0:F-0.501-0.776-0.2260
1:H-0:F0.474-0.7481.6960.87
0:H-1:F-0.974-1.849-0.10.02
1:H-1:F0-1.4771.4771
1:H-0:H0.974-0.2472.1960.197

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.431 & 0.012 & 0.851 & 0.044 \tabularnewline
F-E & 0.135 & -0.091 & 0.36 & 0.334 \tabularnewline
H-E & -0.355 & -0.58 & -0.129 & 0.001 \tabularnewline
H-F & -0.489 & -0.71 & -0.268 & 0 \tabularnewline
1:E-0:E & -0.417 & -1.639 & 0.806 & 0.921 \tabularnewline
0:F-0:E & 0.11 & -0.171 & 0.39 & 0.866 \tabularnewline
1:F-0:E & 0.583 & -0.293 & 1.46 & 0.389 \tabularnewline
0:H-0:E & -0.391 & -0.67 & -0.112 & 0.001 \tabularnewline
1:H-0:E & 0.583 & -0.639 & 1.806 & 0.737 \tabularnewline
0:F-1:E & 0.526 & -0.696 & 1.748 & 0.811 \tabularnewline
1:F-1:E & 1 & -0.477 & 2.477 & 0.37 \tabularnewline
0:H-1:E & 0.026 & -1.196 & 1.247 & 1 \tabularnewline
1:H-1:E & 1 & -0.706 & 2.706 & 0.535 \tabularnewline
1:F-0:F & 0.474 & -0.401 & 1.349 & 0.62 \tabularnewline
0:H-0:F & -0.501 & -0.776 & -0.226 & 0 \tabularnewline
1:H-0:F & 0.474 & -0.748 & 1.696 & 0.87 \tabularnewline
0:H-1:F & -0.974 & -1.849 & -0.1 & 0.02 \tabularnewline
1:H-1:F & 0 & -1.477 & 1.477 & 1 \tabularnewline
1:H-0:H & 0.974 & -0.247 & 2.196 & 0.197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185275&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]0.431[/C][C]0.012[/C][C]0.851[/C][C]0.044[/C][/ROW]
[ROW][C]F-E[/C][C]0.135[/C][C]-0.091[/C][C]0.36[/C][C]0.334[/C][/ROW]
[ROW][C]H-E[/C][C]-0.355[/C][C]-0.58[/C][C]-0.129[/C][C]0.001[/C][/ROW]
[ROW][C]H-F[/C][C]-0.489[/C][C]-0.71[/C][C]-0.268[/C][C]0[/C][/ROW]
[ROW][C]1:E-0:E[/C][C]-0.417[/C][C]-1.639[/C][C]0.806[/C][C]0.921[/C][/ROW]
[ROW][C]0:F-0:E[/C][C]0.11[/C][C]-0.171[/C][C]0.39[/C][C]0.866[/C][/ROW]
[ROW][C]1:F-0:E[/C][C]0.583[/C][C]-0.293[/C][C]1.46[/C][C]0.389[/C][/ROW]
[ROW][C]0:H-0:E[/C][C]-0.391[/C][C]-0.67[/C][C]-0.112[/C][C]0.001[/C][/ROW]
[ROW][C]1:H-0:E[/C][C]0.583[/C][C]-0.639[/C][C]1.806[/C][C]0.737[/C][/ROW]
[ROW][C]0:F-1:E[/C][C]0.526[/C][C]-0.696[/C][C]1.748[/C][C]0.811[/C][/ROW]
[ROW][C]1:F-1:E[/C][C]1[/C][C]-0.477[/C][C]2.477[/C][C]0.37[/C][/ROW]
[ROW][C]0:H-1:E[/C][C]0.026[/C][C]-1.196[/C][C]1.247[/C][C]1[/C][/ROW]
[ROW][C]1:H-1:E[/C][C]1[/C][C]-0.706[/C][C]2.706[/C][C]0.535[/C][/ROW]
[ROW][C]1:F-0:F[/C][C]0.474[/C][C]-0.401[/C][C]1.349[/C][C]0.62[/C][/ROW]
[ROW][C]0:H-0:F[/C][C]-0.501[/C][C]-0.776[/C][C]-0.226[/C][C]0[/C][/ROW]
[ROW][C]1:H-0:F[/C][C]0.474[/C][C]-0.748[/C][C]1.696[/C][C]0.87[/C][/ROW]
[ROW][C]0:H-1:F[/C][C]-0.974[/C][C]-1.849[/C][C]-0.1[/C][C]0.02[/C][/ROW]
[ROW][C]1:H-1:F[/C][C]0[/C][C]-1.477[/C][C]1.477[/C][C]1[/C][/ROW]
[ROW][C]1:H-0:H[/C][C]0.974[/C][C]-0.247[/C][C]2.196[/C][C]0.197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185275&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185275&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
1-00.4310.0120.8510.044
F-E0.135-0.0910.360.334
H-E-0.355-0.58-0.1290.001
H-F-0.489-0.71-0.2680
1:E-0:E-0.417-1.6390.8060.921
0:F-0:E0.11-0.1710.390.866
1:F-0:E0.583-0.2931.460.389
0:H-0:E-0.391-0.67-0.1120.001
1:H-0:E0.583-0.6391.8060.737
0:F-1:E0.526-0.6961.7480.811
1:F-1:E1-0.4772.4770.37
0:H-1:E0.026-1.1961.2471
1:H-1:E1-0.7062.7060.535
1:F-0:F0.474-0.4011.3490.62
0:H-0:F-0.501-0.776-0.2260
1:H-0:F0.474-0.7481.6960.87
0:H-1:F-0.974-1.849-0.10.02
1:H-1:F0-1.4771.4771
1:H-0:H0.974-0.2472.1960.197






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group55.6910
111 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 5.691 & 0 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185275&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]5.691[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185275&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185275&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)
Group55.6910
111


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = 3 ; par4 = TRUE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; 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')