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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 computationMon, 18 Dec 2017 21:51:07 +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/2017/Dec/18/t15136308342lhh0r45631upuj.htm/, Retrieved Tue, 14 May 2024 23:09:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310249, Retrieved Tue, 14 May 2024 23:09:38 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact38
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2017-12-18 20:51:07] [5370b2258acb413c12b88dfd0545a67d] [Current]
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Dataseries X:
30	'M'	'18-22'
25	'M'	'18-22'
25	'F'	'18-22'
22	'F'	'18-22'
21	'F'	'18-22'
28	'F'	'18-22'
27	'M'	'18-22'
25	'F'	'18-22'
25	'M'	'18-22'
22	'F'	'18-22'
24	'M'	'18-22'
22	'F'	'18-22'
25	'F'	'18-22'
26	'F'	'18-22'
29	'F'	'18-22'
23	'F'	'18-22'
25	'F'	'18-22'
29	'M'	'18-22'
28	'M'	'18-22'
28	'M'	'18-22'
28	'F'	'18-22'
29	'F'	'18-22'
21	'F'	'18-22'
31	'F'	'18-22'
24	'F'	'18-22'
28	'F'	'18-22'
28	'F'	'18-22'
19	'F'	'18-22'
31	'F'	'18-22'
21	'F'	'18-22'
25	'M'	'18-22'
31	'F'	'18-22'
29	'F'	'18-22'
27	'M'	'18-22'
27	'M'	'18-22'
29	'F'	'18-22'
32	'M'	'18-22'
22	'M'	'18-22'
22	'F'	'18-22'
27	'F'	'18-22'
22	'F'	'18-22'
25	'F'	'18-22'
27	'M'	'18-22'
31	'M'	'18-22'
27	'M'	'18-22'
23	'F'	'18-22'
27	'M'	'18-22'
22	'F'	'18-22'
24	'F'	'18-22'
36	'M'	'18-22'
26	'F'	'18-22'
28	'M'	'18-22'
26	'M'	'18-22'
27	'M'	'18-22'
29	'F'	'18-22'
28	'M'	'18-22'
34	'M'	'18-22'
31	'M'	'18-22'
32	'M'	'18-22'
24	'F'	'18-22'
27	'M'	'18-22'
21	'F'	'18-22'
31	'F'	'18-22'
27	'M'	'18-22'
29	'M'	'18-22'
28	'M'	'18-22'
25	'M'	'18-22'
34	'M'	'18-22'
31	'M'	'18-22'
34	'F'	'18-22'
27	'M'	'18-22'
30	'M'	'18-22'
29	'M'	'18-22'
33	'M'	'18-22'
27	'F'	'23-25'
26	'F'	'23-25'
27	'F'	'23-25'
22	'F'	'23-25'
25	'F'	'23-25'
28	'F'	'23-25'
27	'M'	'23-25'
22	'M'	'23-25'
21	'F'	'23-25'
22	'M'	'23-25'
31	'M'	'23-25'
26	'M'	'23-25'
26	'F'	'23-25'
25	'M'	'23-25'
26	'M'	'23-25'




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310249&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310249&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310249&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 time5 seconds
R ServerBig Analytics Cloud Computing Center







ANOVA Model
Response ~ Treatment_A * Treatment_B
means25.5792.838-0.329-2.516

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 25.579 & 2.838 & -0.329 & -2.516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310249&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]25.579[/C][C]2.838[/C][C]-0.329[/C][C]-2.516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310249&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310249&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
means25.5792.838-0.329-2.516







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1131.424131.42412.0480.001
Treatment_B128.49128.4912.6120.11
Treatment_A:Treatment_B119.66719.6671.8030.183
Residuals85927.22710.909

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 131.424 & 131.424 & 12.048 & 0.001 \tabularnewline
Treatment_B & 1 & 28.491 & 28.491 & 2.612 & 0.11 \tabularnewline
Treatment_A:Treatment_B & 1 & 19.667 & 19.667 & 1.803 & 0.183 \tabularnewline
Residuals & 85 & 927.227 & 10.909 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310249&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]131.424[/C][C]131.424[/C][C]12.048[/C][C]0.001[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]28.491[/C][C]28.491[/C][C]2.612[/C][C]0.11[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]19.667[/C][C]19.667[/C][C]1.803[/C][C]0.183[/C][/ROW]
[ROW][C]Residuals[/C][C]85[/C][C]927.227[/C][C]10.909[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310249&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310249&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_A1131.424131.42412.0480.001
Treatment_B128.49128.4912.6120.11
Treatment_A:Treatment_B119.66719.6671.8030.183
Residuals85927.22710.909







Tukey Honest Significant Difference Comparisons
difflwruprp adj
M-F2.4321.0393.8250.001
23-25-18-22-1.511-3.3710.3480.11
M:18-22-F:18-222.8380.8254.8510.002
F:23-25-F:18-22-0.329-3.6963.0380.994
M:23-25-F:18-22-0.008-3.5683.5521
F:23-25-M:18-22-3.167-6.550.2160.075
M:23-25-M:18-22-2.845-6.4210.730.166
M:23-25-F:23-250.321-4.1584.8010.998

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
M-F & 2.432 & 1.039 & 3.825 & 0.001 \tabularnewline
23-25-18-22 & -1.511 & -3.371 & 0.348 & 0.11 \tabularnewline
M:18-22-F:18-22 & 2.838 & 0.825 & 4.851 & 0.002 \tabularnewline
F:23-25-F:18-22 & -0.329 & -3.696 & 3.038 & 0.994 \tabularnewline
M:23-25-F:18-22 & -0.008 & -3.568 & 3.552 & 1 \tabularnewline
F:23-25-M:18-22 & -3.167 & -6.55 & 0.216 & 0.075 \tabularnewline
M:23-25-M:18-22 & -2.845 & -6.421 & 0.73 & 0.166 \tabularnewline
M:23-25-F:23-25 & 0.321 & -4.158 & 4.801 & 0.998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310249&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]M-F[/C][C]2.432[/C][C]1.039[/C][C]3.825[/C][C]0.001[/C][/ROW]
[ROW][C]23-25-18-22[/C][C]-1.511[/C][C]-3.371[/C][C]0.348[/C][C]0.11[/C][/ROW]
[ROW][C]M:18-22-F:18-22[/C][C]2.838[/C][C]0.825[/C][C]4.851[/C][C]0.002[/C][/ROW]
[ROW][C]F:23-25-F:18-22[/C][C]-0.329[/C][C]-3.696[/C][C]3.038[/C][C]0.994[/C][/ROW]
[ROW][C]M:23-25-F:18-22[/C][C]-0.008[/C][C]-3.568[/C][C]3.552[/C][C]1[/C][/ROW]
[ROW][C]F:23-25-M:18-22[/C][C]-3.167[/C][C]-6.55[/C][C]0.216[/C][C]0.075[/C][/ROW]
[ROW][C]M:23-25-M:18-22[/C][C]-2.845[/C][C]-6.421[/C][C]0.73[/C][C]0.166[/C][/ROW]
[ROW][C]M:23-25-F:23-25[/C][C]0.321[/C][C]-4.158[/C][C]4.801[/C][C]0.998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310249&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310249&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
M-F2.4321.0393.8250.001
23-25-18-22-1.511-3.3710.3480.11
M:18-22-F:18-222.8380.8254.8510.002
F:23-25-F:18-22-0.329-3.6963.0380.994
M:23-25-F:18-22-0.008-3.5683.5521
F:23-25-M:18-22-3.167-6.550.2160.075
M:23-25-M:18-22-2.845-6.4210.730.166
M:23-25-F:23-250.321-4.1584.8010.998







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.4590.231
85

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.459 & 0.231 \tabularnewline
  & 85 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310249&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]1.459[/C][C]0.231[/C][/ROW]
[ROW][C] [/C][C]85[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310249&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310249&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)
Group31.4590.231
85



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')