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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 computationFri, 22 Jan 2016 09:21:58 +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/2016/Jan/22/t1453454535n9m1iqfu0wa1mci.htm/, Retrieved Tue, 07 May 2024 06:12:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=290648, Retrieved Tue, 07 May 2024 06:12:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

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] [Vraag 3 - Examen] [2016-01-22 09:21:58] [39661ea0cc1af7d66f31b3ef3719ea7a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1 1 0 0 0 3.2 3.2
0 0 1 0 1 3.3 0
1 0 1 1 1 3 3
0 0 1 0 1 3.5 0
1 0 1 0 0 3.7 3.7
0 1 0 0 0 2.7 0
1 0 1 1 1 3.6 3.6
0 0 1 0 1 3.5 0
1 1 0 0 0 3.8 3.8
0 0 1 0 0 3.4 0
1 0 0 0 1 3.7 3.7
0 0 1 0 0 3.5 0
1 0 0 1 0 2.8 2.8
0 1 0 1 0 3.8 0
1 0 1 0 0 4.3 4.3
0 0 0 0 1 3.3 0
1 0 0 0 0 3.6 3.6
0 1 0 1 0 3.6 0
1 1 1 0 0 3.3 3.3
0 0 0 0 0 2.8 0

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=290648&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=290648&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=290648&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'George Udny Yule' @ yule.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.6-0.2-0.1560.756

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.6 & -0.2 & -0.156 & 0.756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=290648&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.6[/C][C]-0.2[/C][C]-0.156[/C][C]0.756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=290648&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=290648&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
means0.6-0.2-0.1560.756






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10001
Treatment_B10001
Treatment_A:Treatment_B10.3780.3781.3080.27
Residuals164.6220.289 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0 & 0 & 0 & 1 \tabularnewline
Treatment_B & 1 & 0 & 0 & 0 & 1 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.378 & 0.378 & 1.308 & 0.27 \tabularnewline
Residuals & 16 & 4.622 & 0.289 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=290648&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[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.378[/C][C]0.378[/C][C]1.308[/C][C]0.27[/C][/ROW]
[ROW][C]Residuals[/C][C]16[/C][C]4.622[/C][C]0.289[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=290648&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=290648&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_A10001
Treatment_B10001
Treatment_A:Treatment_B10.3780.3781.3080.27
Residuals164.6220.289






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00-0.5560.5561
1-00-0.510.511
1:0-0:0-0.2-1.1730.7730.934
0:1-0:0-0.156-1.0130.7020.953
1:1-0:00.4-1.2852.0850.903
0:1-1:00.044-0.8130.9020.999
1:1-1:00.6-1.0852.2850.741
1:1-0:10.556-1.0652.1760.762

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0 & -0.556 & 0.556 & 1 \tabularnewline
1-0 & 0 & -0.51 & 0.51 & 1 \tabularnewline
1:0-0:0 & -0.2 & -1.173 & 0.773 & 0.934 \tabularnewline
0:1-0:0 & -0.156 & -1.013 & 0.702 & 0.953 \tabularnewline
1:1-0:0 & 0.4 & -1.285 & 2.085 & 0.903 \tabularnewline
0:1-1:0 & 0.044 & -0.813 & 0.902 & 0.999 \tabularnewline
1:1-1:0 & 0.6 & -1.085 & 2.285 & 0.741 \tabularnewline
1:1-0:1 & 0.556 & -1.065 & 2.176 & 0.762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=290648&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[/C][C]-0.556[/C][C]0.556[/C][C]1[/C][/ROW]
[ROW][C]1-0[/C][C]0[/C][C]-0.51[/C][C]0.51[/C][C]1[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.2[/C][C]-1.173[/C][C]0.773[/C][C]0.934[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-0.156[/C][C]-1.013[/C][C]0.702[/C][C]0.953[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.4[/C][C]-1.285[/C][C]2.085[/C][C]0.903[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]0.044[/C][C]-0.813[/C][C]0.902[/C][C]0.999[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.6[/C][C]-1.085[/C][C]2.285[/C][C]0.741[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.556[/C][C]-1.065[/C][C]2.176[/C][C]0.762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=290648&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=290648&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
1-00-0.5560.5561
1-00-0.510.511
1:0-0:0-0.2-1.1730.7730.934
0:1-0:0-0.156-1.0130.7020.953
1:1-0:00.4-1.2852.0850.903
0:1-1:00.044-0.8130.9020.999
1:1-1:00.6-1.0852.2850.741
1:1-0:10.556-1.0652.1760.762






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.2050.891
16 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.205 & 0.891 \tabularnewline
  & 16 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=290648&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]0.205[/C][C]0.891[/C][/ROW]
[ROW][C] [/C][C]16[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=290648&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=290648&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)
Group30.2050.891
16


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')