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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Thu, 18 Dec 2014 10:16:28 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/18/t14188978175qqmiizfyk5yxdt.htm/, Retrieved Sat, 18 May 2024 15:22:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270781, Retrieved Sat, 18 May 2024 15:22:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

123

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [Multipleregression] [2014-12-14 15:14:52] [7c87d1c7801dd67c2a0c90c2b6a05b3c]
- RM D    [Two-Way ANOVA] [2wayanova] [2014-12-18 10:16:28] [21b927ddce509724d48ffb8407994bd0] [Current]

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13 "'S'" "'Female'"
14 "'S'" "'Female'"
16 "'S'" "'Male'"
14 "'S'" "'Male'"
13 "'S'" "'Male'"
15 "'S'" "'Female'"
13 "'S'" "'Male'"
20 "'S'" "'Male'"
17 "'S'" "'Male'"
15 "'S'" "'Male'"
16 "'S'" "'Male'"
17 "'S'" "'Female'"
11 "'S'" "'Female'"
16 "'B'" "'Female'"
16 "'S'" "'Male'"
15 "'S'" "'Female'"
14 "'S'" "'Female'"
16 "'S'" "'Male'"
17 "'S'" "'Female'"
15 "'S'" "'Male'"
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14 "'B'" "'Male'"
15 "'S'" "'Male'"
17 "'S'" "'Female'"
14 "'S'" "'Female'"
16 "'S'" "'Female'"
15 "'S'" "'Male'"
16 "'S'" "'Male'"
8 "'S'" "'Female'"
17 "'B'" "'Male'"
10 "'S'" "'Female'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
16 "'B'" "'Male'"
8 "'S'" "'Female'"
14 "'B'" "'Male'"
16 "'S'" "'Male'"
19 "'B'" "'Male'"
19 "'S'" "'Male'"
14 "'S'" "'Male'"
13 "'S'" "'Male'"
15 "'S'" "'Male'"
11 "'S'" "'Female'"
9 "'S'" "'Female'"
12 "'S'" "'Female'"
13 "'S'" "'Male'"
17 "'S'" "'Female'"
7 "'S'" "'Female'"
15 "'S'" "'Female'"
12 "'B'" "'Male'"
15 "'S'" "'Female'"
16 "'S'" "'Male'"
14 "'B'" "'Female'"
16 "'B'" "'Female'"
13 "'B'" "'Male'"
16 "'B'" "'Female'"
10 "'B'" "'Female'"
12 "'B'" "'Male'"
14 "'B'" "'Female'"
16 "'B'" "'Female'"
18 "'B'" "'Male'"
12 "'B'" "'Female'"
15 "'B'" "'Female'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
12 "'B'" "'Female'"
15 "'B'" "'Male'"
14 "'S'" "'Male'"
15 "'S'" "'Female'"
16 "'S'" "'Male'"
13 "'S'" "'Female'"
10 "'S'" "'Female'"
17 "'S'" "'Male'"
15 "'S'" "'Male'"
18 "'S'" "'Male'"
16 "'S'" "'Male'"
20 "'S'" "'Male'"
16 "'B'" "'Male'"
17 "'S'" "'Male'"
16 "'S'" "'Male'"
15 "'S'" "'Female'"
13 "'S'" "'Male'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
17 "'S'" "'Male'"
20 "'S'" "'Male'"
14 "'S'" "'Female'"
17 "'S'" "'Male'"
6 "'B'" "'Male'"
16 "'S'" "'Male'"
15 "'S'" "'Male'"
16 "'S'" "'Male'"
16 "'S'" "'Female'"
14 "'S'" "'Female'"
16 "'S'" "'Male'"
16 "'S'" "'Female'"
16 "'S'" "'Female'"
14 "'S'" "'Male'"
14 "'S'" "'Female'"
16 "'S'" "'Male'"
16 "'S'" "'Male'"
15 "'S'" "'Female'"
16 "'B'" "'Male'"
16 "'B'" "'Male'"
18 "'S'" "'Male'"
15 "'S'" "'Female'"
16 "'B'" "'Female'"
16 "'B'" "'Female'"
16 "'B'" "'Female'"
17 "'B'" "'Male'"
14 "'S'" "'Female'"
18 "'S'" "'Male'"
9 "'B'" "'Female'"
15 "'B'" "'Male'"
14 "'B'" "'Female'"
15 "'B'" "'Male'"
13 "'B'" "'Female'"
16 "'B'" "'Female'"
20 "'B'" "'Male'"
14 "'B'" "'Female'"
12 "'B'" "'Male'"
15 "'S'" "'Male'"
15 "'S'" "'Male'"
15 "'B'" "'Male'"
16 "'S'" "'Male'"
11 "'S'" "'Female'"
16 "'B'" "'Male'"
7 "'S'" "'Female'"
11 "'B'" "'Female'"
9 "'B'" "'Female'"
15 "'S'" "'Male'"
16 "'B'" "'Female'"
14 "'B'" "'Male'"
15 "'B'" "'Female'"
13 "'B'" "'Female'"
13 "'B'" "'Female'"
12 "'B'" "'Female'"
16 "'B'" "'Male'"
14 "'B'" "'Male'"
16 "'B'" "'Male'"
14 "'B'" "'Male'"
15 "'B'" "'Female'"
10 "'B'" "'Female'"
16 "'B'" "'Male'"
14 "'S'" "'Female'"
16 "'B'" "'Female'"
12 "'B'" "'Female'"
16 "'B'" "'Female'"
16 "'B'" "'Male'"
15 "'B'" "'Male'"
14 "'S'" "'Female'"
16 "'B'" "'Female'"
11 "'S'" "'Male'"
15 "'B'" "'Female'"
18 "'S'" "'Male'"
13 "'B'" "'Male'"
7 "'B'" "'Female'"
7 "'B'" "'Male'"
17 "'B'" "'Male'"
18 "'S'" "'Male'"
15 "'S'" "'Female'"
8 "'B'" "'Female'"
13 "'S'" "'Female'"
13 "'S'" "'Male'"
15 "'B'" "'Male'"
18 "'S'" "'Male'"
16 "'B'" "'Male'"
14 "'B'" "'Female'"
15 "'S'" "'Female'"
19 "'B'" "'Female'"
16 "'S'" "'Male'"
12 "'S'" "'Male'"
16 "'S'" "'Female'"
11 "'B'" "'Female'"
16 "'S'" "'Female'"
15 "'B'" "'Male'"
19 "'S'" "'Male'"
15 "'S'" "'Female'"
14 "'S'" "'Female'"
14 "'S'" "'Female'"
17 "'B'" "'Male'"
16 "'S'" "'Male'"
20 "'S'" "'Male'"
16 "'S'" "'Male'"
9 "'B'" "'Female'"
13 "'S'" "'Male'"
15 "'S'" "'Male'"
19 "'B'" "'Male'"
16 "'S'" "'Female'"
17 "'B'" "'Female'"
16 "'B'" "'Male'"
9 "'B'" "'Female'"
11 "'B'" "'Male'"
14 "'B'" "'Male'"
19 "'S'" "'Female'"
13 "'S'" "'Male'"
14 "'S'" "'Female'"
15 "'S'" "'Male'"
15 "'S'" "'Male'"
14 "'S'" "'Female'"
16 "'B'" "'Male'"
17 "'B'" "'Female'"
12 "'S'" "'Male'"
15 "'B'" "'Female'"
17 "'B'" "'Male'"
15 "'S'" "'Female'"
10 "'B'" "'Female'"
16 "'B'" "'Male'"
15 "'B'" "'Male'"
11 "'B'" "'Female'"
16 "'B'" "'Male'"
16 "'B'" "'Male'"
16 "'B'" "'Female'"
14 "'B'" "'Male'"
14 "'B'" "'Female'"
16 "'B'" "'Female'"
16 "'B'" "'Male'"
18 "'B'" "'Male'"
14 "'B'" "'Female'"
20 "'B'" "'Male'"
15 "'B'" "'Female'"
16 "'B'" "'Female'"
16 "'B'" "'Male'"
16 "'S'" "'Female'"
12 "'B'" "'Female'"
8 "'B'" "'Male'"

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270781&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]4 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=270781&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270781&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 Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B - 1
means	13.608	13.846	1.45	0.42

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B - 1 \tabularnewline
means & 13.608 & 13.846 & 1.45 & 0.42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270781&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B - 1[/C][/ROW]
[ROW][C]means[/C][C]13.608[/C][C]13.846[/C][C]1.45[/C][C]0.42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270781&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270781&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 - 1
means	13.608	13.846	1.45	0.42

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	49320.282	24660.141	3949.713	0
Treatment_B	2	158.458	158.458	25.379	0
Treatment_A:Treatment_B	2	2.467	2.467	0.395	0.53
Residuals	225	1404.794	6.244

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 49320.282 & 24660.141 & 3949.713 & 0 \tabularnewline
Treatment_B & 2 & 158.458 & 158.458 & 25.379 & 0 \tabularnewline
Treatment_A:Treatment_B & 2 & 2.467 & 2.467 & 0.395 & 0.53 \tabularnewline
Residuals & 225 & 1404.794 & 6.244 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270781&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]2[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]2[/C][C]49320.282[/C][C]24660.141[/C][C]3949.713[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]158.458[/C][C]158.458[/C][C]25.379[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]2.467[/C][C]2.467[/C][C]0.395[/C][C]0.53[/C][/ROW]
[ROW][C]Residuals[/C][C]225[/C][C]1404.794[/C][C]6.244[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270781&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270781&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
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	49320.282	24660.141	3949.713	0
Treatment_B	2	158.458	158.458	25.379	0
Treatment_A:Treatment_B	2	2.467	2.467	0.395	0.53
Residuals	225	1404.794	6.244

Must Include Intercept to use Tukey Test

\begin{tabular}{lllllllll}
\hline
Must Include Intercept to use Tukey Test  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270781&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270781&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270781&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Must Include Intercept to use Tukey Test

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	2.677	0.048
	225

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 2.677 & 0.048 \tabularnewline
  & 225 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270781&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]2.677[/C][C]0.048[/C][/ROW]
[ROW][C] [/C][C]225[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270781&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270781&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
	Df	F value	Pr(>F)
Group	3	2.677	0.048
	225

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = FALSE ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code