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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 computationMon, 07 Nov 2011 09:12:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/07/t1320675144wwo9ih490jmknc5.htm/, Retrieved Thu, 28 Mar 2024 11:13:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=140189, Retrieved Thu, 28 Mar 2024 11:13:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [Question 8] [2011-11-07 14:12:12] [5646b3622df538fb37dafdccb2216e7a] [Current]
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Dataseries X:
0.28	'A'	'M'
0.95	'A'	'M'
0.96	'A'	'M'
0.97	'A'	'M'
0.40	'A'	'M'
0.18	'A'	'M'
0.12	'A'	'M'
0.62	'A'	'M'
1.81	'A'	'F'
1.51	'A'	'F'
1.41	'A'	'F'
1.39	'A'	'F'
1.20	'A'	'F'
1.55	'A'	'F'
1.48	'A'	'F'
1.25	'A'	'F'
0.95	'B'	'M'
1.33	'B'	'M'
0.92	'B'	'M'
0.85	'B'	'M'
1.06	'B'	'M'
0.69	'B'	'M'
0.70	'B'	'M'
0.79	'B'	'M'
2.93	'B'	'F'
3.24	'B'	'F'
3.42	'B'	'F'
2.79	'B'	'F'
2.54	'B'	'F'
3.28	'B'	'F'
2.80	'B'	'F'
3.40	'B'	'F'




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140189&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140189&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140189&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means1.451.6-0.89-1.249

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 1.45 & 1.6 & -0.89 & -1.249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140189&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]1.45[/C][C]1.6[/C][C]-0.89[/C][C]-1.249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140189&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140189&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
means1.451.6-0.89-1.249







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A17.6157.61595.1130
Treatment_B118.34718.347229.1610
Treatment_A:Treatment_B13.1193.11938.9550
Residuals282.2420.08

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 7.615 & 7.615 & 95.113 & 0 \tabularnewline
Treatment_B & 1 & 18.347 & 18.347 & 229.161 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 3.119 & 3.119 & 38.955 & 0 \tabularnewline
Residuals & 28 & 2.242 & 0.08 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140189&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]7.615[/C][C]7.615[/C][C]95.113[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]18.347[/C][C]18.347[/C][C]229.161[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]3.119[/C][C]3.119[/C][C]38.955[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]28[/C][C]2.242[/C][C]0.08[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140189&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140189&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_A17.6157.61595.1130
Treatment_B118.34718.347229.1610
Treatment_A:Treatment_B13.1193.11938.9550
Residuals282.2420.08







Tukey Honest Significant Difference Comparisons
difflwruprp adj
B-A0.9760.7711.1810
M-F-1.514-1.719-1.3090
B:F-A:F1.61.2141.9860
A:M-A:F-0.89-1.276-0.5040
B:M-A:F-0.539-0.925-0.1520.004
A:M-B:F-2.49-2.876-2.1040
B:M-B:F-2.139-2.525-1.7520
B:M-A:M0.351-0.0350.7380.085

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
B-A & 0.976 & 0.771 & 1.181 & 0 \tabularnewline
M-F & -1.514 & -1.719 & -1.309 & 0 \tabularnewline
B:F-A:F & 1.6 & 1.214 & 1.986 & 0 \tabularnewline
A:M-A:F & -0.89 & -1.276 & -0.504 & 0 \tabularnewline
B:M-A:F & -0.539 & -0.925 & -0.152 & 0.004 \tabularnewline
A:M-B:F & -2.49 & -2.876 & -2.104 & 0 \tabularnewline
B:M-B:F & -2.139 & -2.525 & -1.752 & 0 \tabularnewline
B:M-A:M & 0.351 & -0.035 & 0.738 & 0.085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140189&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]B-A[/C][C]0.976[/C][C]0.771[/C][C]1.181[/C][C]0[/C][/ROW]
[ROW][C]M-F[/C][C]-1.514[/C][C]-1.719[/C][C]-1.309[/C][C]0[/C][/ROW]
[ROW][C]B:F-A:F[/C][C]1.6[/C][C]1.214[/C][C]1.986[/C][C]0[/C][/ROW]
[ROW][C]A:M-A:F[/C][C]-0.89[/C][C]-1.276[/C][C]-0.504[/C][C]0[/C][/ROW]
[ROW][C]B:M-A:F[/C][C]-0.539[/C][C]-0.925[/C][C]-0.152[/C][C]0.004[/C][/ROW]
[ROW][C]A:M-B:F[/C][C]-2.49[/C][C]-2.876[/C][C]-2.104[/C][C]0[/C][/ROW]
[ROW][C]B:M-B:F[/C][C]-2.139[/C][C]-2.525[/C][C]-1.752[/C][C]0[/C][/ROW]
[ROW][C]B:M-A:M[/C][C]0.351[/C][C]-0.035[/C][C]0.738[/C][C]0.085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140189&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140189&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
B-A0.9760.7711.1810
M-F-1.514-1.719-1.3090
B:F-A:F1.61.2141.9860
A:M-A:F-0.89-1.276-0.5040
B:M-A:F-0.539-0.925-0.1520.004
A:M-B:F-2.49-2.876-2.1040
B:M-B:F-2.139-2.525-1.7520
B:M-A:M0.351-0.0350.7380.085







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group33.6960.023
28

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.696 & 0.023 \tabularnewline
  & 28 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140189&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]3.696[/C][C]0.023[/C][/ROW]
[ROW][C] [/C][C]28[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140189&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140189&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)
Group33.6960.023
28



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')