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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 computationThu, 18 Dec 2014 13:09:20 +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/18/t14189087619fr0xzkxrt7od2t.htm/, Retrieved Sun, 19 May 2024 17:43:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270903, Retrieved Sun, 19 May 2024 17:43:04 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2014-12-18 13:09:20] [58179e1d3a5a39b9daf58e365d8a3352] [Current]
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Dataseries X:
0 "'S'" 96
0 "'S'" 88
1 "'S'" 114
1 "'S'" 69
1 "'S'" 176
0 "'S'" 114
1 "'S'" 121
1 "'S'" 110
1 "'S'" 158
1 "'S'" 116
1 "'S'" 181
0 "'S'" 141
0 "'S'" 35
0 "'B'" 80
1 "'S'" 152
0 "'S'" 97
0 "'S'" 84
1 "'S'" 101
0 "'S'" 107
1 "'S'" 112
1 "'S'" 171
1 "'B'" 137
1 "'S'" 66
0 "'S'" 93
0 "'S'" 105
0 "'S'" 131
1 "'S'" 102
1 "'S'" 120
0 "'S'" 77
1 "'B'" 108
0 "'S'" 168
1 "'S'" 75
1 "'S'" 107
1 "'B'" 62
0 "'S'" 121
1 "'B'" 97
1 "'S'" 126
1 "'B'" 104
1 "'S'" 148
1 "'S'" 146
1 "'S'" 97
1 "'S'" 118
0 "'S'" 58
0 "'S'" 63
0 "'S'" 50
1 "'S'" 94
0 "'S'" 127
0 "'S'" 128
0 "'S'" 146
1 "'B'" 69
0 "'S'" 186
1 "'S'" 85
0 "'B'" 54
0 "'B'" 106
1 "'B'" 34
0 "'B'" 60
0 "'B'" 62
1 "'B'" 64
0 "'B'" 98
0 "'B'" 35
1 "'B'" 55
0 "'B'" 54
0 "'B'" 51




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270903&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270903&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'Gertrude Mary Cox' @ cox.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means66.66714.44438.81-0.546

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 66.667 & 14.444 & 38.81 & -0.546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270903&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]66.667[/C][C]14.444[/C][C]38.81[/C][C]-0.546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270903&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
means66.66714.44438.81-0.546







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A13585.8913585.8913.1880.079
Treatment_B119071.33819071.33816.9550
Treatment_A:Treatment_B10.9560.9560.0010.977
Residuals5966363.7521124.809

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 3585.891 & 3585.891 & 3.188 & 0.079 \tabularnewline
Treatment_B & 1 & 19071.338 & 19071.338 & 16.955 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.956 & 0.956 & 0.001 & 0.977 \tabularnewline
Residuals & 59 & 66363.752 & 1124.809 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270903&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]3585.891[/C][C]3585.891[/C][C]3.188[/C][C]0.079[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]19071.338[/C][C]19071.338[/C][C]16.955[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.956[/C][C]0.956[/C][C]0.001[/C][C]0.977[/C][/ROW]
[ROW][C]Residuals[/C][C]59[/C][C]66363.752[/C][C]1124.809[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270903&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270903&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_A13585.8913585.8913.1880.079
Treatment_B119071.33819071.33816.9550
Treatment_A:Treatment_B10.9560.9560.0010.977
Residuals5966363.7521124.809







Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-015.106-1.82332.0350.079
'S'-'B'38.49619.7857.2120
1:'B'-0:'B'14.444-27.35456.2430.798
0:'S'-0:'B'38.813.48374.1360.026
1:'S'-0:'B'52.70818.05187.3660.001
0:'S'-1:'B'24.365-10.96159.6910.273
1:'S'-1:'B'38.2643.60672.9210.025
1:'S'-0:'S'13.899-12.59640.3930.512

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 15.106 & -1.823 & 32.035 & 0.079 \tabularnewline
'S'-'B' & 38.496 & 19.78 & 57.212 & 0 \tabularnewline
1:'B'-0:'B' & 14.444 & -27.354 & 56.243 & 0.798 \tabularnewline
0:'S'-0:'B' & 38.81 & 3.483 & 74.136 & 0.026 \tabularnewline
1:'S'-0:'B' & 52.708 & 18.051 & 87.366 & 0.001 \tabularnewline
0:'S'-1:'B' & 24.365 & -10.961 & 59.691 & 0.273 \tabularnewline
1:'S'-1:'B' & 38.264 & 3.606 & 72.921 & 0.025 \tabularnewline
1:'S'-0:'S' & 13.899 & -12.596 & 40.393 & 0.512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270903&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]15.106[/C][C]-1.823[/C][C]32.035[/C][C]0.079[/C][/ROW]
[ROW][C]'S'-'B'[/C][C]38.496[/C][C]19.78[/C][C]57.212[/C][C]0[/C][/ROW]
[ROW][C]1:'B'-0:'B'[/C][C]14.444[/C][C]-27.354[/C][C]56.243[/C][C]0.798[/C][/ROW]
[ROW][C]0:'S'-0:'B'[/C][C]38.81[/C][C]3.483[/C][C]74.136[/C][C]0.026[/C][/ROW]
[ROW][C]1:'S'-0:'B'[/C][C]52.708[/C][C]18.051[/C][C]87.366[/C][C]0.001[/C][/ROW]
[ROW][C]0:'S'-1:'B'[/C][C]24.365[/C][C]-10.961[/C][C]59.691[/C][C]0.273[/C][/ROW]
[ROW][C]1:'S'-1:'B'[/C][C]38.264[/C][C]3.606[/C][C]72.921[/C][C]0.025[/C][/ROW]
[ROW][C]1:'S'-0:'S'[/C][C]13.899[/C][C]-12.596[/C][C]40.393[/C][C]0.512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270903&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270903&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
1-015.106-1.82332.0350.079
'S'-'B'38.49619.7857.2120
1:'B'-0:'B'14.444-27.35456.2430.798
0:'S'-0:'B'38.813.48374.1360.026
1:'S'-0:'B'52.70818.05187.3660.001
0:'S'-1:'B'24.365-10.96159.6910.273
1:'S'-1:'B'38.2643.60672.9210.025
1:'S'-0:'S'13.899-12.59640.3930.512







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.810.494
59

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.81 & 0.494 \tabularnewline
  & 59 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270903&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]0.81[/C][C]0.494[/C][/ROW]
[ROW][C] [/C][C]59[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270903&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270903&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)
Group30.810.494
59



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<-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')