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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

Tue, 19 Feb 2013 09:05:23 -0500

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/2013/Feb/19/t1361282832englzajpi0hnhp8.htm/, Retrieved Fri, 03 May 2024 23:01:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206579, Retrieved Fri, 03 May 2024 23:01:50 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

136

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

-     [Variability] [Two-Way ANOVA] [2010-11-30 21:42:30] [74be16979710d4c4e7c6647856088456]
- RM    [Two-Way ANOVA] [Two-Way ANOVA - C...] [2011-11-28 17:22:56] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R PD      [Two-Way ANOVA] [Recognising faces] [2013-02-19 14:05:23] [4e2c5629241a1e636d9839a5af4aa431] [Current]
-   P         [Two-Way ANOVA] [Reaction time] [2013-02-19 14:11:05] [f3df66176306f4bc7dbd536cdf32fa04] 

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Dataseries X:

Download CSV

Histogram

Boxplots

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1.00	881.00	1.00	1.00
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1.00	666.00	1.00	1.00
1.00	1025.00	1.00	.00
1.00	758.00	1.00	1.00
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1.00	667.00	1.00	.00
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1.00	1422.00	1.00	1.00
1.00	1469.00	1.00	1.00
1.00	1247.00	1.00	.00
1.00	678.00	1.00	1.00
1.00	1261.00	1.00	1.00
1.00	933.00	1.00	.00
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1.00	673.00	1.00	1.00
1.00	660.00	1.00	1.00
1.00	768.00	1.00	1.00
1.00	591.00	1.00	.00
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1.00	1271.00	1.00	.00
1.00	745.00	1.00	1.00
1.00	738.00	1.00	.00
1.00	792.00	1.00	.00
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1.00	755.00	1.00	1.00
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1.00	782.00	1.00	.00
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1.00	667.00	1.00	1.00
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1.00	1100.00	1.00	.00
1.00	910.00	1.00	.00
1.00	685.00	1.00	1.00
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1.00	750.00	1.00	1.00
1.00	711.00	1.00	1.00
1.00	1175.00	1.00	.00
1.00	747.00	1.00	.00
1.00	712.00	1.00	1.00
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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206579&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]3 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=206579&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206579&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.833	-0.111	0.139	0.025

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.833 & -0.111 & 0.139 & 0.025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206579&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.833[/C][C]-0.111[/C][C]0.139[/C][C]0.025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206579&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206579&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
means	0.833	-0.111	0.139	0.025

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.357	0.357	2.966	0.087
Treatment_B	1	0.816	0.816	6.778	0.01
Treatment_A:Treatment_B	1	0.005	0.005	0.045	0.832
Residuals	139	16.737	0.12

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.357 & 0.357 & 2.966 & 0.087 \tabularnewline
Treatment_B & 1 & 0.816 & 0.816 & 6.778 & 0.01 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.005 & 0.005 & 0.045 & 0.832 \tabularnewline
Residuals & 139 & 16.737 & 0.12 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206579&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]0.357[/C][C]0.357[/C][C]2.966[/C][C]0.087[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.816[/C][C]0.816[/C][C]6.778[/C][C]0.01[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.005[/C][C]0.005[/C][C]0.045[/C][C]0.832[/C][/ROW]
[ROW][C]Residuals[/C][C]139[/C][C]16.737[/C][C]0.12[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206579&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206579&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)
	1
Treatment_A	1	0.357	0.357	2.966	0.087
Treatment_B	1	0.816	0.816	6.778	0.01
Treatment_A:Treatment_B	1	0.005	0.005	0.045	0.832
Residuals	139	16.737	0.12

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	-0.1	-0.215	0.015	0.087
1-0	0.151	0.036	0.266	0.01
1:0-0:0	-0.111	-0.324	0.102	0.527
0:1-0:0	0.139	-0.074	0.352	0.329
1:1-0:0	0.052	-0.162	0.267	0.92
0:1-1:0	0.25	0.037	0.463	0.014
1:1-1:0	0.163	-0.051	0.378	0.199
1:1-0:1	-0.087	-0.301	0.128	0.72

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.1 & -0.215 & 0.015 & 0.087 \tabularnewline
1-0 & 0.151 & 0.036 & 0.266 & 0.01 \tabularnewline
1:0-0:0 & -0.111 & -0.324 & 0.102 & 0.527 \tabularnewline
0:1-0:0 & 0.139 & -0.074 & 0.352 & 0.329 \tabularnewline
1:1-0:0 & 0.052 & -0.162 & 0.267 & 0.92 \tabularnewline
0:1-1:0 & 0.25 & 0.037 & 0.463 & 0.014 \tabularnewline
1:1-1:0 & 0.163 & -0.051 & 0.378 & 0.199 \tabularnewline
1:1-0:1 & -0.087 & -0.301 & 0.128 & 0.72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206579&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]1-0[/C][C]-0.1[/C][C]-0.215[/C][C]0.015[/C][C]0.087[/C][/ROW]
[ROW][C]1-0[/C][C]0.151[/C][C]0.036[/C][C]0.266[/C][C]0.01[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.111[/C][C]-0.324[/C][C]0.102[/C][C]0.527[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.139[/C][C]-0.074[/C][C]0.352[/C][C]0.329[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.052[/C][C]-0.162[/C][C]0.267[/C][C]0.92[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]0.25[/C][C]0.037[/C][C]0.463[/C][C]0.014[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.163[/C][C]-0.051[/C][C]0.378[/C][C]0.199[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.087[/C][C]-0.301[/C][C]0.128[/C][C]0.72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206579&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206579&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
	diff	lwr	upr	p adj
1-0	-0.1	-0.215	0.015	0.087
1-0	0.151	0.036	0.266	0.01
1:0-0:0	-0.111	-0.324	0.102	0.527
0:1-0:0	0.139	-0.074	0.352	0.329
1:1-0:0	0.052	-0.162	0.267	0.92
0:1-1:0	0.25	0.037	0.463	0.014
1:1-1:0	0.163	-0.051	0.378	0.199
1:1-0:1	-0.087	-0.301	0.128	0.72

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	3.263	0.023
	139

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.263 & 0.023 \tabularnewline
  & 139 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206579&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]3.263[/C][C]0.023[/C][/ROW]
[ROW][C] [/C][C]139[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206579&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206579&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	3.263	0.023
	139

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):

par1 = 1 ; par2 = 3 ; par3 = 4 ; par4 = TRUE ;

Parameters (R input):

par1 = 1 ; par2 = 3 ; par3 = 4 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code