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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 13:38:23 +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/t141890991941qpcc6nskhqym2.htm/, Retrieved Sun, 19 May 2024 18:49:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270920, Retrieved Sun, 19 May 2024 18:49:23 +0000
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User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2014-12-18 13:38:23] [c98c6a6156d025200627852118e8b268] [Current]
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Dataseries X:
'S' "'Female'" 12.9
'S' "'Female'" 7.4
'S' "'Male'" 12.2
'S' "'Female'" 12.8
'S' "'Male'" 7.4
'S' "'Male'" 6.7
'S' "'Male'" 12.6
'S' "'Female'" 14.8
'S' "'Male'" 13.3
'S' "'Male'" 11.1
'S' "'Male'" 8.2
'S' "'Male'" 11.4
'S' "'Male'" 6.4
'S' "'Male'" 10.6
'S' "'Female'" 12.0
'S' "'Female'" 6.3
'B' "'Female'" 11.3
'S' "'Male'" 11.9
'S' "'Female'" 9.3
'B' "'Male'" 9.6
'S' "'Female'" 10.0
'S' "'Male'" 6.4
'S' "'Male'" 13.8
'S' "'Female'" 10.8
'S' "'Male'" 13.8
'S' "'Male'" 11.7
'S' "'Male'" 10.9
'B' "'Male'" 16.1
'B' "'Female'" 13.4
'S' "'Male'" 9.9
'S' "'Female'" 11.5
'S' "'Female'" 8.3
'S' "'Female'" 11.7
'S' "'Male'" 6.1
'S' "'Male'" 9.0
'S' "'Male'" 9.7
'S' "'Male'" 10.8
'S' "'Male'" 10.3
'S' "'Female'" 10.4
'B' "'Male'" 12.7
'S' "'Male'" 9.3
'S' "'Female'" 11.8
'S' "'Male'" 5.9
'S' "'Male'" 11.4
'S' "'Male'" 13.0
'S' "'Male'" 10.8
'B' "'Male'" 12.3
'S' "'Female'" 11.3
'S' "'Male'" 11.8
'B' "'Male'" 7.9
'S' "'Female'" 12.7
'B' "'Male'" 12.3
'B' "'Male'" 11.6
'B' "'Male'" 6.7
'S' "'Male'" 10.9
'B' "'Male'" 12.1
'S' "'Male'" 13.3
'S' "'Male'" 10.1
'B' "'Female'" 5.7
'S' "'Male'" 14.3
'B' "'Female'" 8.0
'B' "'Male'" 13.3
'S' "'Male'" 9.3
'S' "'Female'" 12.5
'S' "'Female'" 7.6
'S' "'Male'" 15.9
'S' "'Female'" 9.2
'B' "'Male'" 9.1
'S' "'Female'" 11.1
'S' "'Male'" 13.0
'S' "'Male'" 14.5
'B' "'Female'" 12.2
'S' "'Female'" 12.3
'S' "'Female'" 11.4
'B' "'Female'" 8.8
'B' "'Male'" 14.6
'S' "'Male'" 7.3
'S' "'Female'" 12.6
'S' "'Male'" NA
'S' "'Female'" 13.0
'B' "'Male'" 12.6
'S' "'Female'" 13.2
'B' "'Female'" 9.9
'S' "'Male'" 7.7
'B' "'Female'" 10.5
'B' "'Female'" 13.4
'B' "'Female'" 10.9
'B' "'Male'" 4.3
'B' "'Female'" 10.3
'B' "'Male'" 11.8
'B' "'Male'" 11.2
'B' "'Female'" 11.4
'B' "'Female'" 8.6
'B' "'Female'" 13.2
'B' "'Male'" 12.6
'B' "'Male'" 5.6
'B' "'Male'" 9.9
'B' "'Female'" 8.8
'B' "'Male'" 7.7
'B' "'Female'" 9.0
'B' "'Male'" 7.3
'B' "'Male'" 11.4
'B' "'Male'" 13.6
'B' "'Male'" 7.9
'B' "'Male'" 10.7
'B' "'Female'" 10.3
'B' "'Male'" 8.3
'B' "'Male'" 9.6
'B' "'Male'" 14.2
'B' "'Female'" 8.5
'B' "'Female'" 13.5
'B' "'Female'" 4.9
'B' "'Female'" 6.4
'B' "'Female'" 9.6
'B' "'Female'" 11.6
'B' "'Male'" 11.1




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=270920&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=270920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270920&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
means10.0091.0670.615-1.094

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 10.009 & 1.067 & 0.615 & -1.094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270920&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]10.009[/C][C]1.067[/C][C]0.615[/C][C]-1.094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270920&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
means10.0091.0670.615-1.094







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A15.45.40.8480.359
Treatment_B10.0160.0160.0030.96
Treatment_A:Treatment_B18.2978.2971.3040.256
Residuals111706.4676.365

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 5.4 & 5.4 & 0.848 & 0.359 \tabularnewline
Treatment_B & 1 & 0.016 & 0.016 & 0.003 & 0.96 \tabularnewline
Treatment_A:Treatment_B & 1 & 8.297 & 8.297 & 1.304 & 0.256 \tabularnewline
Residuals & 111 & 706.467 & 6.365 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270920&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]5.4[/C][C]5.4[/C][C]0.848[/C][C]0.359[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.016[/C][C]0.016[/C][C]0.003[/C][C]0.96[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]8.297[/C][C]8.297[/C][C]1.304[/C][C]0.256[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]706.467[/C][C]6.365[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270920&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270920&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_A15.45.40.8480.359
Treatment_B10.0160.0160.0030.96
Treatment_A:Treatment_B18.2978.2971.3040.256
Residuals111706.4676.365







Tukey Honest Significant Difference Comparisons
difflwruprp adj
S-B0.435-0.5011.3720.359
'Male'-'Female'0.024-0.9210.970.96
S:'Female'-B:'Female'1.067-0.8342.9690.463
B:'Male'-B:'Female'0.615-1.2222.4530.818
S:'Male'-B:'Female'0.589-1.152.3270.814
B:'Male'-S:'Female'-0.452-2.2481.3440.913
S:'Male'-S:'Female'-0.479-2.1731.2160.882
S:'Male'-B:'Male'-0.027-1.6491.5961

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
S-B & 0.435 & -0.501 & 1.372 & 0.359 \tabularnewline
'Male'-'Female' & 0.024 & -0.921 & 0.97 & 0.96 \tabularnewline
S:'Female'-B:'Female' & 1.067 & -0.834 & 2.969 & 0.463 \tabularnewline
B:'Male'-B:'Female' & 0.615 & -1.222 & 2.453 & 0.818 \tabularnewline
S:'Male'-B:'Female' & 0.589 & -1.15 & 2.327 & 0.814 \tabularnewline
B:'Male'-S:'Female' & -0.452 & -2.248 & 1.344 & 0.913 \tabularnewline
S:'Male'-S:'Female' & -0.479 & -2.173 & 1.216 & 0.882 \tabularnewline
S:'Male'-B:'Male' & -0.027 & -1.649 & 1.596 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270920&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]S-B[/C][C]0.435[/C][C]-0.501[/C][C]1.372[/C][C]0.359[/C][/ROW]
[ROW][C]'Male'-'Female'[/C][C]0.024[/C][C]-0.921[/C][C]0.97[/C][C]0.96[/C][/ROW]
[ROW][C]S:'Female'-B:'Female'[/C][C]1.067[/C][C]-0.834[/C][C]2.969[/C][C]0.463[/C][/ROW]
[ROW][C]B:'Male'-B:'Female'[/C][C]0.615[/C][C]-1.222[/C][C]2.453[/C][C]0.818[/C][/ROW]
[ROW][C]S:'Male'-B:'Female'[/C][C]0.589[/C][C]-1.15[/C][C]2.327[/C][C]0.814[/C][/ROW]
[ROW][C]B:'Male'-S:'Female'[/C][C]-0.452[/C][C]-2.248[/C][C]1.344[/C][C]0.913[/C][/ROW]
[ROW][C]S:'Male'-S:'Female'[/C][C]-0.479[/C][C]-2.173[/C][C]1.216[/C][C]0.882[/C][/ROW]
[ROW][C]S:'Male'-B:'Male'[/C][C]-0.027[/C][C]-1.649[/C][C]1.596[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270920&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270920&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
S-B0.435-0.5011.3720.359
'Male'-'Female'0.024-0.9210.970.96
S:'Female'-B:'Female'1.067-0.8342.9690.463
B:'Male'-B:'Female'0.615-1.2222.4530.818
S:'Male'-B:'Female'0.589-1.152.3270.814
B:'Male'-S:'Female'-0.452-2.2481.3440.913
S:'Male'-S:'Female'-0.479-2.1731.2160.882
S:'Male'-B:'Male'-0.027-1.6491.5961







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.9650.412
111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.965 & 0.412 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270920&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]0.965[/C][C]0.412[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270920&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270920&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)
Group30.9650.412
111



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):
par4 <- 'FALSE'
par3 <- '2'
par2 <- '1'
par1 <- '3'
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')