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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 computationWed, 17 Dec 2014 13:32:33 +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/2014/Dec/17/t1418823986tucfcv83kfqrhzv.htm/, Retrieved Sun, 19 May 2024 18:21:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270259, Retrieved Sun, 19 May 2024 18:21:13 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56

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] [hbjtey] [2014-12-17 13:32:33] [ec52aa8040970d621dae982cb6b68c16] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270259&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270259&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means13.222-1.0060.4180.26

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 13.222 & -1.006 & 0.418 & 0.26 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270259&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]13.222[/C][C]-1.006[/C][C]0.418[/C][C]0.26[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270259&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
means13.222-1.0060.4180.26






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A146.77646.7764.170.042
Treatment_B122.06422.0641.9670.162
Treatment_A:Treatment_B11.1441.1440.1020.75
Residuals2743073.69311.218 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 46.776 & 46.776 & 4.17 & 0.042 \tabularnewline
Treatment_B & 1 & 22.064 & 22.064 & 1.967 & 0.162 \tabularnewline
Treatment_A:Treatment_B & 1 & 1.144 & 1.144 & 0.102 & 0.75 \tabularnewline
Residuals & 274 & 3073.693 & 11.218 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270259&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]46.776[/C][C]46.776[/C][C]4.17[/C][C]0.042[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]22.064[/C][C]22.064[/C][C]1.967[/C][C]0.162[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]1.144[/C][C]1.144[/C][C]0.102[/C][C]0.75[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]3073.693[/C][C]11.218[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270259&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270259&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_A146.77646.7764.170.042
Treatment_B122.06422.0641.9670.162
Treatment_A:Treatment_B11.1441.1440.1020.75
Residuals2743073.69311.218






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.828-1.627-0.030.042
'S'-'B'0.562-0.231.3530.163
1:'B'-0:'B'-1.006-2.4990.4860.303
0:'S'-0:'B'0.418-1.1662.0020.904
1:'S'-0:'B'-0.328-1.7541.0980.934
0:'S'-1:'B'1.425-0.1232.9720.083
1:'S'-1:'B'0.678-0.7062.0630.585
1:'S'-0:'S'-0.747-2.230.7370.563

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.828 & -1.627 & -0.03 & 0.042 \tabularnewline
'S'-'B' & 0.562 & -0.23 & 1.353 & 0.163 \tabularnewline
1:'B'-0:'B' & -1.006 & -2.499 & 0.486 & 0.303 \tabularnewline
0:'S'-0:'B' & 0.418 & -1.166 & 2.002 & 0.904 \tabularnewline
1:'S'-0:'B' & -0.328 & -1.754 & 1.098 & 0.934 \tabularnewline
0:'S'-1:'B' & 1.425 & -0.123 & 2.972 & 0.083 \tabularnewline
1:'S'-1:'B' & 0.678 & -0.706 & 2.063 & 0.585 \tabularnewline
1:'S'-0:'S' & -0.747 & -2.23 & 0.737 & 0.563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270259&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]-0.828[/C][C]-1.627[/C][C]-0.03[/C][C]0.042[/C][/ROW]
[ROW][C]'S'-'B'[/C][C]0.562[/C][C]-0.23[/C][C]1.353[/C][C]0.163[/C][/ROW]
[ROW][C]1:'B'-0:'B'[/C][C]-1.006[/C][C]-2.499[/C][C]0.486[/C][C]0.303[/C][/ROW]
[ROW][C]0:'S'-0:'B'[/C][C]0.418[/C][C]-1.166[/C][C]2.002[/C][C]0.904[/C][/ROW]
[ROW][C]1:'S'-0:'B'[/C][C]-0.328[/C][C]-1.754[/C][C]1.098[/C][C]0.934[/C][/ROW]
[ROW][C]0:'S'-1:'B'[/C][C]1.425[/C][C]-0.123[/C][C]2.972[/C][C]0.083[/C][/ROW]
[ROW][C]1:'S'-1:'B'[/C][C]0.678[/C][C]-0.706[/C][C]2.063[/C][C]0.585[/C][/ROW]
[ROW][C]1:'S'-0:'S'[/C][C]-0.747[/C][C]-2.23[/C][C]0.737[/C][C]0.563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270259&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270259&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
1-0-0.828-1.627-0.030.042
'S'-'B'0.562-0.231.3530.163
1:'B'-0:'B'-1.006-2.4990.4860.303
0:'S'-0:'B'0.418-1.1662.0020.904
1:'S'-0:'B'-0.328-1.7541.0980.934
0:'S'-1:'B'1.425-0.1232.9720.083
1:'S'-1:'B'0.678-0.7062.0630.585
1:'S'-0:'S'-0.747-2.230.7370.563






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.7220.539
274 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.722 & 0.539 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270259&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]0.722[/C][C]0.539[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270259&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270259&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)
Group30.7220.539
274


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = TRUE ; par4 = Unknown ;
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')