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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, 30 Jan 2019 12:50:35 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Jan/30/t1548849172ahvpanpwdvrawmo.htm/, Retrieved Sun, 28 Apr 2024 09:03:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=317036, Retrieved Sun, 28 Apr 2024 09:03:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

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] [] [2019-01-30 11:50:35] [e1673e5a5acd2a07f04f1ca35d927222] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6 1 0
7 0 0
2 1 0
11 0 0
13 1 0
3 0 0
17 1 0
10 0 0
4 1 0
12 0 0
7 1 1
11 0 1
3 1 1
5 0 1
1 1 1
12 0 1
18 1 1
8 0 1
6 1 1
1 0 1

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317036&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=317036&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317036&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B
means8.6-0.2-1.2-0.2

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 8.6 & -0.2 & -1.2 & -0.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317036&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]8.6[/C][C]-0.2[/C][C]-1.2[/C][C]-0.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317036&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317036&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
means8.6-0.2-1.2-0.2






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.450.450.0150.903
Treatment_B18.458.450.2880.599
Treatment_A:Treatment_B10.050.050.0020.968
Residuals16469.629.35 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.45 & 0.45 & 0.015 & 0.903 \tabularnewline
Treatment_B & 1 & 8.45 & 8.45 & 0.288 & 0.599 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.05 & 0.05 & 0.002 & 0.968 \tabularnewline
Residuals & 16 & 469.6 & 29.35 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317036&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]0.45[/C][C]0.45[/C][C]0.015[/C][C]0.903[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]8.45[/C][C]8.45[/C][C]0.288[/C][C]0.599[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.05[/C][C]0.05[/C][C]0.002[/C][C]0.968[/C][/ROW]
[ROW][C]Residuals[/C][C]16[/C][C]469.6[/C][C]29.35[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317036&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317036&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_A10.450.450.0150.903
Treatment_B18.458.450.2880.599
Treatment_A:Treatment_B10.050.050.0020.968
Residuals16469.629.35






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.3-5.4364.8360.903
1-0-1.3-6.4363.8360.599
1:0-0:0-0.2-10.0039.6031
0:1-0:0-1.2-11.0038.6030.985
1:1-0:0-1.6-11.4038.2030.965
0:1-1:0-1-10.8038.8030.991
1:1-1:0-1.4-11.2038.4030.976
1:1-0:1-0.4-10.2039.4030.999

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.3 & -5.436 & 4.836 & 0.903 \tabularnewline
1-0 & -1.3 & -6.436 & 3.836 & 0.599 \tabularnewline
1:0-0:0 & -0.2 & -10.003 & 9.603 & 1 \tabularnewline
0:1-0:0 & -1.2 & -11.003 & 8.603 & 0.985 \tabularnewline
1:1-0:0 & -1.6 & -11.403 & 8.203 & 0.965 \tabularnewline
0:1-1:0 & -1 & -10.803 & 8.803 & 0.991 \tabularnewline
1:1-1:0 & -1.4 & -11.203 & 8.403 & 0.976 \tabularnewline
1:1-0:1 & -0.4 & -10.203 & 9.403 & 0.999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317036&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]-0.3[/C][C]-5.436[/C][C]4.836[/C][C]0.903[/C][/ROW]
[ROW][C]1-0[/C][C]-1.3[/C][C]-6.436[/C][C]3.836[/C][C]0.599[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.2[/C][C]-10.003[/C][C]9.603[/C][C]1[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-1.2[/C][C]-11.003[/C][C]8.603[/C][C]0.985[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-1.6[/C][C]-11.403[/C][C]8.203[/C][C]0.965[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-1[/C][C]-10.803[/C][C]8.803[/C][C]0.991[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-1.4[/C][C]-11.203[/C][C]8.403[/C][C]0.976[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.4[/C][C]-10.203[/C][C]9.403[/C][C]0.999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317036&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317036&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
1-0-0.3-5.4364.8360.903
1-0-1.3-6.4363.8360.599
1:0-0:0-0.2-10.0039.6031
0:1-0:0-1.2-11.0038.6030.985
1:1-0:0-1.6-11.4038.2030.965
0:1-1:0-1-10.8038.8030.991
1:1-1:0-1.4-11.2038.4030.976
1:1-0:1-0.4-10.2039.4030.999






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.3330.801
16 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.333 & 0.801 \tabularnewline
  & 16 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317036&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]0.333[/C][C]0.801[/C][/ROW]
[ROW][C] [/C][C]16[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317036&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317036&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)
Group30.3330.801
16


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Seasonal Dummies ; par3 = Linear Trend ; par4 = 3 ; par6 = 12 ;
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')