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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 computationFri, 12 Dec 2014 13:50:17 +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/12/t1418392232tb8rq4b8sd13len.htm/, Retrieved Thu, 16 May 2024 19:12:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266704, Retrieved Thu, 16 May 2024 19:12:52 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [] [2014-12-12 11:43:14] [7b949ef3605c038fc6e10efeab34f433]
- R  D  [Two-Way ANOVA] [] [2014-12-12 13:32:21] [fa1b8827d7de91b8b87087311d3d9fa1]
-    D      [Two-Way ANOVA] [] [2014-12-12 13:50:17] [2b74e5be20a95dee0bfccc444f4c1798] [Current]
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Dataseries X:
50	'S'	'F'
62	'S'	'M'
54	'S'	'F'
71	'S'	'M'
54	'S'	'M'
65	'S'	'M'
73	'S'	'F'
52	'S'	'M'
84	'S'	'M'
42	'S'	'M'
66	'S'	'M'
65	'S'	'M'
78	'S'	'M'
73	'S'	'F'
75	'S'	'F'
72	'B'	'F'
66	'S'	'M'
70	'S'	'F'
61	'B'	'M'
81	'S'	'F'
71	'S'	'M'
69	'S'	'M'
71	'S'	'F'
72	'S'	'M'
68	'S'	'M'
70	'S'	'M'
68	'B'	'M'
61	'B'	'F'
67	'S'	'M'
76	'S'	'F'
70	'S'	'F'
60	'S'	'F'
72	'S'	'M'
69	'S'	'M'
71	'S'	'M'
62	'S'	'M'
70	'S'	'F'
64	'B'	'M'
58	'S'	'M'
76	'S'	'F'
52	'S'	'M'
59	'S'	'M'
68	'S'	'M'
76	'S'	'M'
65	'B'	'M'
67	'S'	'F'
59	'S'	'M'
69	'B'	'M'
76	'S'	'F'
63	'B'	'M'
75	'B'	'M'
63	'B'	'M'
60	'S'	'M'
73	'B'	'M'
63	'S'	'M'
70	'S'	'M'
75	'B'	'F'
66	'S'	'M'
63	'B'	'F'
63	'B'	'M'
64	'S'	'M'
70	'S'	'F'
75	'S'	'F'
61	'S'	'M'
60	'S'	'F'
62	'B'	'M'
73	'S'	'F'
61	'S'	'M'
66	'S'	'M'
64	'B'	'F'
59	'S'	'F'
64	'S'	'F'
60	'B'	'F'
56	'B'	'M'
78	'S'	'F'
53	'S'	'M'
67	'S'	'F'
59	'B'	'M'
66	'S'	'F'
68	'B'	'F'
71	'S'	'M'
66	'B'	'F'
73	'B'	'F'
72	'B'	'F'
71	'B'	'M'
59	'B'	'F'
64	'B'	'M'
66	'B'	'M'
78	'B'	'F'
68	'B'	'F'
73	'B'	'F'
62	'B'	'M'
65	'B'	'M'
68	'B'	'M'
65	'B'	'F'
60	'B'	'M'
71	'B'	'F'
65	'B'	'M'
68	'B'	'M'
64	'B'	'M'
74	'B'	'M'
69	'B'	'M'
76	'B'	'F'
68	'B'	'M'
72	'B'	'M'
67	'B'	'M'
63	'B'	'F'
59	'B'	'F'
73	'B'	'F'
66	'B'	'F'
62	'B'	'F'
69	'B'	'F'
66	'B'	'M'




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=266704&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=266704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266704&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
means67.6521.264-1.79-2.181

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 67.652 & 1.264 & -1.79 & -2.181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266704&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]67.652[/C][C]1.264[/C][C]-1.79[/C][C]-2.181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266704&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
means67.6521.264-1.79-2.181







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.5950.5950.0130.91
Treatment_B1238.201238.2015.1740.025
Treatment_A:Treatment_B132.42432.4240.7040.403
Residuals1095018.39146.04

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.595 & 0.595 & 0.013 & 0.91 \tabularnewline
Treatment_B & 1 & 238.201 & 238.201 & 5.174 & 0.025 \tabularnewline
Treatment_A:Treatment_B & 1 & 32.424 & 32.424 & 0.704 & 0.403 \tabularnewline
Residuals & 109 & 5018.391 & 46.04 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266704&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]0.595[/C][C]0.595[/C][C]0.013[/C][C]0.91[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]238.201[/C][C]238.201[/C][C]5.174[/C][C]0.025[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]32.424[/C][C]32.424[/C][C]0.704[/C][C]0.403[/C][/ROW]
[ROW][C]Residuals[/C][C]109[/C][C]5018.391[/C][C]46.04[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266704&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266704&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_A10.5950.5950.0130.91
Treatment_B1238.201238.2015.1740.025
Treatment_A:Treatment_B132.42432.4240.7040.403
Residuals1095018.39146.04







Tukey Honest Significant Difference Comparisons
difflwruprp adj
S-B-0.146-2.6842.3930.91
M-F-2.942-5.509-0.3750.025
S:F-B:F1.264-3.9016.430.919
B:M-B:F-1.79-6.7333.1530.781
S:M-B:F-2.706-7.4071.9950.44
B:M-S:F-3.055-7.941.8310.365
S:M-S:F-3.971-8.6110.6690.121
S:M-B:M-0.916-5.3073.4750.948

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
S-B & -0.146 & -2.684 & 2.393 & 0.91 \tabularnewline
M-F & -2.942 & -5.509 & -0.375 & 0.025 \tabularnewline
S:F-B:F & 1.264 & -3.901 & 6.43 & 0.919 \tabularnewline
B:M-B:F & -1.79 & -6.733 & 3.153 & 0.781 \tabularnewline
S:M-B:F & -2.706 & -7.407 & 1.995 & 0.44 \tabularnewline
B:M-S:F & -3.055 & -7.94 & 1.831 & 0.365 \tabularnewline
S:M-S:F & -3.971 & -8.611 & 0.669 & 0.121 \tabularnewline
S:M-B:M & -0.916 & -5.307 & 3.475 & 0.948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266704&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]-0.146[/C][C]-2.684[/C][C]2.393[/C][C]0.91[/C][/ROW]
[ROW][C]M-F[/C][C]-2.942[/C][C]-5.509[/C][C]-0.375[/C][C]0.025[/C][/ROW]
[ROW][C]S:F-B:F[/C][C]1.264[/C][C]-3.901[/C][C]6.43[/C][C]0.919[/C][/ROW]
[ROW][C]B:M-B:F[/C][C]-1.79[/C][C]-6.733[/C][C]3.153[/C][C]0.781[/C][/ROW]
[ROW][C]S:M-B:F[/C][C]-2.706[/C][C]-7.407[/C][C]1.995[/C][C]0.44[/C][/ROW]
[ROW][C]B:M-S:F[/C][C]-3.055[/C][C]-7.94[/C][C]1.831[/C][C]0.365[/C][/ROW]
[ROW][C]S:M-S:F[/C][C]-3.971[/C][C]-8.611[/C][C]0.669[/C][C]0.121[/C][/ROW]
[ROW][C]S:M-B:M[/C][C]-0.916[/C][C]-5.307[/C][C]3.475[/C][C]0.948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266704&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266704&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-B-0.146-2.6842.3930.91
M-F-2.942-5.509-0.3750.025
S:F-B:F1.264-3.9016.430.919
B:M-B:F-1.79-6.7333.1530.781
S:M-B:F-2.706-7.4071.9950.44
B:M-S:F-3.055-7.941.8310.365
S:M-S:F-3.971-8.6110.6690.121
S:M-B:M-0.916-5.3073.4750.948







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.9690.123
109

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.969 & 0.123 \tabularnewline
  & 109 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266704&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]1.969[/C][C]0.123[/C][/ROW]
[ROW][C] [/C][C]109[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266704&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266704&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)
Group31.9690.123
109



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')