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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 13:32:21 +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/t1418391281nzsoguxre57bfnj.htm/, Retrieved Sun, 19 May 2024 15:27:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266683, Retrieved Sun, 19 May 2024 15:27:08 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
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] [2b74e5be20a95dee0bfccc444f4c1798] [Current]
-    D      [Two-Way ANOVA] [] [2014-12-12 13:50:17] [fa1b8827d7de91b8b87087311d3d9fa1]
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Dataseries X:
26	'S'	'F'
57	'S'	'M'
37	'S'	'F'
67	'S'	'M'
43	'S'	'M'
52	'S'	'M'
52	'S'	'F'
43	'S'	'M'
84	'S'	'M'
67	'S'	'M'
49	'S'	'M'
70	'S'	'M'
52	'S'	'M'
58	'S'	'F'
68	'S'	'F'
62	'B'	'F'
43	'S'	'M'
56	'S'	'F'
56	'B'	'M'
74	'S'	'F'
65	'S'	'M'
63	'S'	'M'
58	'S'	'F'
57	'S'	'M'
63	'S'	'M'
53	'S'	'M'
57	'B'	'M'
51	'B'	'F'
64	'S'	'M'
53	'S'	'F'
29	'S'	'F'
54	'S'	'F'
58	'S'	'M'
43	'S'	'M'
51	'S'	'M'
53	'S'	'M'
54	'S'	'F'
56	'B'	'M'
61	'S'	'M'
47	'S'	'F'
39	'S'	'M'
48	'S'	'M'
50	'S'	'M'
35	'S'	'M'
30	'B'	'M'
68	'S'	'F'
49	'S'	'M'
61	'B'	'M'
67	'S'	'F'
47	'B'	'M'
56	'B'	'M'
50	'B'	'M'
43	'S'	'M'
67	'B'	'M'
62	'S'	'M'
57	'S'	'M'
41	'B'	'F'
54	'S'	'M'
45	'B'	'F'
48	'B'	'M'
61	'S'	'M'
56	'S'	'F'
41	'S'	'F'
43	'S'	'M'
53	'S'	'F'
44	'B'	'M'
66	'S'	'F'
58	'S'	'M'
46	'S'	'M'
37	'B'	'F'
51	'S'	'F'
51	'S'	'F'
56	'B'	'F'
66	'B'	'M'
37	'S'	'F'
59	'S'	'M'
42	'S'	'F'
38	'B'	'M'
66	'S'	'F'
34	'B'	'F'
53	'S'	'M'
49	'B'	'F'
55	'B'	'F'
49	'B'	'F'
59	'B'	'M'
40	'B'	'F'
58	'B'	'M'
60	'B'	'M'
63	'B'	'F'
56	'B'	'F'
54	'B'	'F'
52	'B'	'M'
34	'B'	'M'
69	'B'	'M'
32	'B'	'F'
48	'B'	'M'
67	'B'	'F'
58	'B'	'M'
57	'B'	'M'
42	'B'	'M'
64	'B'	'M'
58	'B'	'M'
66	'B'	'F'
26	'B'	'M'
61	'B'	'M'
52	'B'	'M'
51	'B'	'F'
55	'B'	'F'
50	'B'	'F'
60	'B'	'F'
56	'B'	'F'
63	'B'	'F'
61	'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=266683&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=266683&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266683&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
means51.8260.8411.1050.688

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 51.826 & 0.841 & 1.105 & 0.688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266683&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]51.826[/C][C]0.841[/C][C]1.105[/C][C]0.688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266683&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266683&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
means51.8260.8411.1050.688







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A148.30448.3040.4140.521
Treatment_B159.22359.2230.5080.478
Treatment_A:Treatment_B13.2263.2260.0280.868
Residuals10912711.689116.621

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 48.304 & 48.304 & 0.414 & 0.521 \tabularnewline
Treatment_B & 1 & 59.223 & 59.223 & 0.508 & 0.478 \tabularnewline
Treatment_A:Treatment_B & 1 & 3.226 & 3.226 & 0.028 & 0.868 \tabularnewline
Residuals & 109 & 12711.689 & 116.621 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266683&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]48.304[/C][C]48.304[/C][C]0.414[/C][C]0.521[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]59.223[/C][C]59.223[/C][C]0.508[/C][C]0.478[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]3.226[/C][C]3.226[/C][C]0.028[/C][C]0.868[/C][/ROW]
[ROW][C]Residuals[/C][C]109[/C][C]12711.689[/C][C]116.621[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266683&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266683&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_A148.30448.3040.4140.521
Treatment_B159.22359.2230.5080.478
Treatment_A:Treatment_B13.2263.2260.0280.868
Residuals10912711.689116.621







Tukey Honest Significant Difference Comparisons
difflwruprp adj
S-B1.312-2.7285.3520.521
M-F1.467-2.6185.5520.478
S:F-B:F0.841-7.3819.0620.993
B:M-B:F1.105-6.7628.9720.983
S:M-B:F2.633-4.84810.1150.795
B:M-S:F0.264-7.5118.041
S:M-S:F1.793-5.5929.1780.921
S:M-B:M1.528-5.468.5160.941

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
S-B & 1.312 & -2.728 & 5.352 & 0.521 \tabularnewline
M-F & 1.467 & -2.618 & 5.552 & 0.478 \tabularnewline
S:F-B:F & 0.841 & -7.381 & 9.062 & 0.993 \tabularnewline
B:M-B:F & 1.105 & -6.762 & 8.972 & 0.983 \tabularnewline
S:M-B:F & 2.633 & -4.848 & 10.115 & 0.795 \tabularnewline
B:M-S:F & 0.264 & -7.511 & 8.04 & 1 \tabularnewline
S:M-S:F & 1.793 & -5.592 & 9.178 & 0.921 \tabularnewline
S:M-B:M & 1.528 & -5.46 & 8.516 & 0.941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266683&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]1.312[/C][C]-2.728[/C][C]5.352[/C][C]0.521[/C][/ROW]
[ROW][C]M-F[/C][C]1.467[/C][C]-2.618[/C][C]5.552[/C][C]0.478[/C][/ROW]
[ROW][C]S:F-B:F[/C][C]0.841[/C][C]-7.381[/C][C]9.062[/C][C]0.993[/C][/ROW]
[ROW][C]B:M-B:F[/C][C]1.105[/C][C]-6.762[/C][C]8.972[/C][C]0.983[/C][/ROW]
[ROW][C]S:M-B:F[/C][C]2.633[/C][C]-4.848[/C][C]10.115[/C][C]0.795[/C][/ROW]
[ROW][C]B:M-S:F[/C][C]0.264[/C][C]-7.511[/C][C]8.04[/C][C]1[/C][/ROW]
[ROW][C]S:M-S:F[/C][C]1.793[/C][C]-5.592[/C][C]9.178[/C][C]0.921[/C][/ROW]
[ROW][C]S:M-B:M[/C][C]1.528[/C][C]-5.46[/C][C]8.516[/C][C]0.941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266683&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266683&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-B1.312-2.7285.3520.521
M-F1.467-2.6185.5520.478
S:F-B:F0.841-7.3819.0620.993
B:M-B:F1.105-6.7628.9720.983
S:M-B:F2.633-4.84810.1150.795
B:M-S:F0.264-7.5118.041
S:M-S:F1.793-5.5929.1780.921
S:M-B:M1.528-5.468.5160.941







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.2850.836
109

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.285 & 0.836 \tabularnewline
  & 109 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266683&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]0.285[/C][C]0.836[/C][/ROW]
[ROW][C] [/C][C]109[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266683&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266683&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)
Group30.2850.836
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')