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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, 18 Nov 2020 16:02:43 +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/Nov/18/t16057118439a0wzznj7dmk7w2.htm/, Retrieved Wed, 21 Apr 2021 07:33:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319292, Retrieved Wed, 21 Apr 2021 07:33:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsANOVA, 2way
Estimated Impact21
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [Curry 2-way ANOVA] [2020-11-18 15:02:43] [cf5c3d94c26454c6c14f113bfcafa766] [Current]
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Dataseries X:
4 "'SMK'" "'hot'" 1 1 1
5 "'SMK'" "'hot'" 1 1 1
3 "'SMK'" "'hot'" 1 1 1
4 "'SMK'" "'hot'" 1 1 1
5 "'SMK'" "'hot'" 1 1 1
3 "'SMK'" "'hot'" 1 1 1
7 "'SMK'" "'hot'" 1 1 1
5 "'SMK'" "'hot'" 1 1 1
6 "'SMK'" "'hot'" 1 1 1
3 "'SMK'" "'hot'" 1 1 1
2 "'SMK'" "'hot'" 1 1 1
4 "'SMK'" "'hot'" 1 1 1
5 "'SMK'" "'hot'" 1 1 1
2 "'SMK'" "'hot'" 1 1 1
3 "'SMK'" "'hot'" 1 1 1
6 "'SMK'" "'hot'" 1 1 1
4 "'SMK'" "'hot'" 1 1 1
4 "'SMK'" "'hot'" 1 1 1
6 "'SMK'" "'hot'" 1 1 1
2 "'SMK'" "'hot'" 1 1 1
3 "'SMK'" "'mild'" 1 0 0
5 "'SMK'" "'mild'" 1 0 0
4 "'SMK'" "'mild'" 1 0 0
2 "'SMK'" "'mild'" 1 0 0
7 "'SMK'" "'mild'" 1 0 0
1 "'SMK'" "'mild'" 1 0 0
4 "'SMK'" "'mild'" 1 0 0
4 "'SMK'" "'mild'" 1 0 0
7 "'SMK'" "'mild'" 1 0 0
4 "'SMK'" "'mild'" 1 0 0
3 "'SMK'" "'mild'" 1 0 0
3 "'SMK'" "'mild'" 1 0 0
3 "'SMK'" "'mild'" 1 0 0
3 "'SMK'" "'mild'" 1 0 0
2 "'SMK'" "'mild'" 1 0 0
5 "'SMK'" "'mild'" 1 0 0
5 "'SMK'" "'mild'" 1 0 0
3 "'SMK'" "'mild'" 1 0 0
6 "'SMK'" "'mild'" 1 0 0
2 "'SMK'" "'mild'" 1 0 0
8 "'NS'" "'hot'" 0 1 0
9 "'NS'" "'hot'" 0 1 0
10 "'NS'" "'hot'" 0 1 0
7 "'NS'" "'hot'" 0 1 0
8 "'NS'" "'hot'" 0 1 0
9 "'NS'" "'hot'" 0 1 0
10 "'NS'" "'hot'" 0 1 0
6 "'NS'" "'hot'" 0 1 0
6 "'NS'" "'hot'" 0 1 0
7 "'NS'" "'hot'" 0 1 0
8 "'NS'" "'hot'" 0 1 0
9 "'NS'" "'hot'" 0 1 0
8 "'NS'" "'hot'" 0 1 0
7 "'NS'" "'hot'" 0 1 0
5 "'NS'" "'hot'" 0 1 0
11 "'NS'" "'hot'" 0 1 0
7 "'NS'" "'hot'" 0 1 0
8 "'NS'" "'hot'" 0 1 0
10 "'NS'" "'hot'" 0 1 0
9 "'NS'" "'hot'" 0 1 0
3 "'NS'" "'mild'" 0 0 0
5 "'NS'" "'mild'" 0 0 0
4 "'NS'" "'mild'" 0 0 0
2 "'NS'" "'mild'" 0 0 0
6 "'NS'" "'mild'" 0 0 0
1 "'NS'" "'mild'" 0 0 0
4 "'NS'" "'mild'" 0 0 0
4 "'NS'" "'mild'" 0 0 0
5 "'NS'" "'mild'" 0 0 0
4 "'NS'" "'mild'" 0 0 0
3 "'NS'" "'mild'" 0 0 0
3 "'NS'" "'mild'" 0 0 0
4 "'NS'" "'mild'" 0 0 0
3 "'NS'" "'mild'" 0 0 0
2 "'NS'" "'mild'" 0 0 0
5 "'NS'" "'mild'" 0 0 0
4 "'NS'" "'mild'" 0 0 0
3 "'NS'" "'mild'" 0 0 0
6 "'NS'" "'mild'" 0 0 0
2 "'NS'" "'mild'" 0 0 0




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319292&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319292&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319292&T=0

As an alternative you can also use a 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 time2 seconds
R ServerBig Analytics Cloud Computing Center







ANOVA Model
Response ~ Treatment_A * Treatment_B
means8.1-3.95-4.454.1

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 8.1 & -3.95 & -4.45 & 4.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319292&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]8.1[/C][C]-3.95[/C][C]-4.45[/C][C]4.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319292&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319292&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means8.1-3.95-4.454.1







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A172.272.231.8840
Treatment_B1115.2115.250.8730
Treatment_A:Treatment_B184.0584.0537.1170
Residuals76172.12.264

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 72.2 & 72.2 & 31.884 & 0 \tabularnewline
Treatment_B & 1 & 115.2 & 115.2 & 50.873 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 84.05 & 84.05 & 37.117 & 0 \tabularnewline
Residuals & 76 & 172.1 & 2.264 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319292&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]72.2[/C][C]72.2[/C][C]31.884[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]115.2[/C][C]115.2[/C][C]50.873[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]84.05[/C][C]84.05[/C][C]37.117[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]76[/C][C]172.1[/C][C]2.264[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319292&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319292&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A172.272.231.8840
Treatment_B1115.2115.250.8730
Treatment_A:Treatment_B184.0584.0537.1170
Residuals76172.12.264







Tukey Honest Significant Difference Comparisons
difflwruprp adj
'SMK'-'NS'-1.9-2.57-1.230
'mild'-'hot'-2.4-3.07-1.730
'SMK':'hot'-'NS':'hot'-3.95-5.2-2.70
'NS':'mild'-'NS':'hot'-4.45-5.7-3.20
'SMK':'mild'-'NS':'hot'-4.3-5.55-3.050
'NS':'mild'-'SMK':'hot'-0.5-1.750.750.72
'SMK':'mild'-'SMK':'hot'-0.35-1.60.90.882
'SMK':'mild'-'NS':'mild'0.15-1.11.40.989

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
'SMK'-'NS' & -1.9 & -2.57 & -1.23 & 0 \tabularnewline
'mild'-'hot' & -2.4 & -3.07 & -1.73 & 0 \tabularnewline
'SMK':'hot'-'NS':'hot' & -3.95 & -5.2 & -2.7 & 0 \tabularnewline
'NS':'mild'-'NS':'hot' & -4.45 & -5.7 & -3.2 & 0 \tabularnewline
'SMK':'mild'-'NS':'hot' & -4.3 & -5.55 & -3.05 & 0 \tabularnewline
'NS':'mild'-'SMK':'hot' & -0.5 & -1.75 & 0.75 & 0.72 \tabularnewline
'SMK':'mild'-'SMK':'hot' & -0.35 & -1.6 & 0.9 & 0.882 \tabularnewline
'SMK':'mild'-'NS':'mild' & 0.15 & -1.1 & 1.4 & 0.989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319292&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]'SMK'-'NS'[/C][C]-1.9[/C][C]-2.57[/C][C]-1.23[/C][C]0[/C][/ROW]
[ROW][C]'mild'-'hot'[/C][C]-2.4[/C][C]-3.07[/C][C]-1.73[/C][C]0[/C][/ROW]
[ROW][C]'SMK':'hot'-'NS':'hot'[/C][C]-3.95[/C][C]-5.2[/C][C]-2.7[/C][C]0[/C][/ROW]
[ROW][C]'NS':'mild'-'NS':'hot'[/C][C]-4.45[/C][C]-5.7[/C][C]-3.2[/C][C]0[/C][/ROW]
[ROW][C]'SMK':'mild'-'NS':'hot'[/C][C]-4.3[/C][C]-5.55[/C][C]-3.05[/C][C]0[/C][/ROW]
[ROW][C]'NS':'mild'-'SMK':'hot'[/C][C]-0.5[/C][C]-1.75[/C][C]0.75[/C][C]0.72[/C][/ROW]
[ROW][C]'SMK':'mild'-'SMK':'hot'[/C][C]-0.35[/C][C]-1.6[/C][C]0.9[/C][C]0.882[/C][/ROW]
[ROW][C]'SMK':'mild'-'NS':'mild'[/C][C]0.15[/C][C]-1.1[/C][C]1.4[/C][C]0.989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319292&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319292&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
'SMK'-'NS'-1.9-2.57-1.230
'mild'-'hot'-2.4-3.07-1.730
'SMK':'hot'-'NS':'hot'-3.95-5.2-2.70
'NS':'mild'-'NS':'hot'-4.45-5.7-3.20
'SMK':'mild'-'NS':'hot'-4.3-5.55-3.050
'NS':'mild'-'SMK':'hot'-0.5-1.750.750.72
'SMK':'mild'-'SMK':'hot'-0.35-1.60.90.882
'SMK':'mild'-'NS':'mild'0.15-1.11.40.989







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.250.861
76

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.25 & 0.861 \tabularnewline
  & 76 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319292&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]0.25[/C][C]0.861[/C][/ROW]
[ROW][C] [/C][C]76[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319292&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319292&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.250.861
76



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<-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')