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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 computationSat, 25 Jan 2020 07:43:23 +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/2020/Jan/25/t1579934789d8ssb0gutdrf8mo.htm/, Retrieved Fri, 26 Apr 2024 12:01:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319039, Retrieved Fri, 26 Apr 2024 12:01:06 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [test] [2020-01-25 06:43:23] [91ea98095c3449299d530fa8627eca43] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1 0 10
1 1 8
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1 0 5
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1 1 9
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319039&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319039&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B
means5.3042.2341.003-0.434

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 5.304 & 2.234 & 1.003 & -0.434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319039&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]5.304[/C][C]2.234[/C][C]1.003[/C][C]-0.434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319039&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
means5.3042.2341.003-0.434






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1140.409140.40946.9990
Treatment_B121.14521.1457.0780.009
Treatment_A:Treatment_B11.6721.6720.560.455
Residuals175522.8082.987 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 140.409 & 140.409 & 46.999 & 0 \tabularnewline
Treatment_B & 1 & 21.145 & 21.145 & 7.078 & 0.009 \tabularnewline
Treatment_A:Treatment_B & 1 & 1.672 & 1.672 & 0.56 & 0.455 \tabularnewline
Residuals & 175 & 522.808 & 2.987 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319039&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]140.409[/C][C]140.409[/C][C]46.999[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]21.145[/C][C]21.145[/C][C]7.078[/C][C]0.009[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]1.672[/C][C]1.672[/C][C]0.56[/C][C]0.455[/C][/ROW]
[ROW][C]Residuals[/C][C]175[/C][C]522.808[/C][C]2.987[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319039&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319039&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_A1140.409140.40946.9990
Treatment_B121.14521.1457.0780.009
Treatment_A:Treatment_B11.6721.6720.560.455
Residuals175522.8082.987






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-01.9861.4152.5580
1-00.6870.1771.1970.009
1:0-0:02.2341.1463.3220
0:1-0:01.003-0.282.2870.182
1:1-0:02.8031.7163.8910
0:1-1:0-1.231-2.271-0.190.013
1:1-1:00.569-0.2171.3560.241
1:1-0:11.80.762.840

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 1.986 & 1.415 & 2.558 & 0 \tabularnewline
1-0 & 0.687 & 0.177 & 1.197 & 0.009 \tabularnewline
1:0-0:0 & 2.234 & 1.146 & 3.322 & 0 \tabularnewline
0:1-0:0 & 1.003 & -0.28 & 2.287 & 0.182 \tabularnewline
1:1-0:0 & 2.803 & 1.716 & 3.891 & 0 \tabularnewline
0:1-1:0 & -1.231 & -2.271 & -0.19 & 0.013 \tabularnewline
1:1-1:0 & 0.569 & -0.217 & 1.356 & 0.241 \tabularnewline
1:1-0:1 & 1.8 & 0.76 & 2.84 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319039&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]1.986[/C][C]1.415[/C][C]2.558[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]0.687[/C][C]0.177[/C][C]1.197[/C][C]0.009[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]2.234[/C][C]1.146[/C][C]3.322[/C][C]0[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]1.003[/C][C]-0.28[/C][C]2.287[/C][C]0.182[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]2.803[/C][C]1.716[/C][C]3.891[/C][C]0[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-1.231[/C][C]-2.271[/C][C]-0.19[/C][C]0.013[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.569[/C][C]-0.217[/C][C]1.356[/C][C]0.241[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]1.8[/C][C]0.76[/C][C]2.84[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319039&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319039&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
1-01.9861.4152.5580
1-00.6870.1771.1970.009
1:0-0:02.2341.1463.3220
0:1-0:01.003-0.282.2870.182
1:1-0:02.8031.7163.8910
0:1-1:0-1.231-2.271-0.190.013
1:1-1:00.569-0.2171.3560.241
1:1-0:11.80.762.840






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group35.3690.001
175 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 5.369 & 0.001 \tabularnewline
  & 175 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319039&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]5.369[/C][C]0.001[/C][/ROW]
[ROW][C] [/C][C]175[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319039&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319039&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)
Group35.3690.001
175


Figures (Output of Computation)

Input Parameters & R Code

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