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Author's title

Author

*The author of this computation has been verified*

R Software Module

Ian.Hollidayrwasp_Two Factor ANOVA -V4.wasp

Title produced by software

Variability

Date of computation

Fri, 03 Dec 2010 16:51:43 +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/2010/Dec/03/t129139574229k80bvbh01po8u.htm/, Retrieved Tue, 02 Sep 2025 09:40:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104925, Retrieved Tue, 02 Sep 2025 09:40:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

336

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]
-    D    [Variability] [W9 Compendium EX 1B] [2010-12-03 16:51:43] [a2cca81b2088ee964389f3d2c6477f39] [Current]

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Dataseries X:

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Histogram

Boxplots

1	'SMK'	'hot'
2	'SMK'	'hot'
2	'SMK'	'hot'
2	'SMK'	'hot'
2	'SMK'	'hot'
2	'SMK'	'hot'
2	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
3	'SMK'	'hot'
4	'SMK'	'hot'
4	'SMK'	'hot'
4	'SMK'	'hot'
4	'SMK'	'mild'
4	'SMK'	'mild'
4	'SMK'	'mild'
4	'SMK'	'mild'
4	'SMK'	'mild'
4	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
6	'SMK'	'mild'
6	'SMK'	'mild'
6	'SMK'	'mild'
6	'SMK'	'mild'
7	'SMK'	'mild'
7	'SMK'	'mild'
7	'SMK'	'mild'
5	'NS'	'hot'
6	'NS'	'hot'
6	'NS'	'hot'
7	'NS'	'hot'
7	'NS'	'hot'
7	'NS'	'hot'
7	'NS'	'hot'
8	'NS'	'hot'
8	'NS'	'hot'
8	'NS'	'hot'
8	'NS'	'hot'
8	'NS'	'hot'
9	'NS'	'hot'
9	'NS'	'hot'
9	'NS'	'hot'
9	'NS'	'hot'
10	'NS'	'hot'
10	'NS'	'hot'
10	'NS'	'hot'
11	'NS'	'hot'
1	'NS'	'mild'
2	'NS'	'mild'
2	'NS'	'mild'
2	'NS'	'mild'
3	'NS'	'mild'
3	'NS'	'mild'
3	'NS'	'mild'
3	'NS'	'mild'
3	'NS'	'mild'
4	'NS'	'mild'
4	'NS'	'mild'
4	'NS'	'mild'
4	'NS'	'mild'
4	'NS'	'mild'
4	'NS'	'mild'
5	'NS'	'mild'
5	'NS'	'mild'
5	'NS'	'mild'
6	'NS'	'mild'
6	'NS'	'mild'

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104925&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104925&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

ANOVA Model
xdf2$rate ~ xdf2$status * xdf2$curry
names	(Intercept)	xdf2$statusSMK	xdf2$currymild	xdf2$statusSMK:xdf2$currymild
means	8.1	-5.35	-4.45	6.9

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
xdf2$rate ~ xdf2$status * xdf2$curry \tabularnewline
names & (Intercept) & xdf2$statusSMK & xdf2$currymild & xdf2$statusSMK:xdf2$currymild \tabularnewline
means & 8.1 & -5.35 & -4.45 & 6.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104925&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]xdf2$rate ~ xdf2$status * xdf2$curry[/C][/ROW]
[ROW][C]names[/C][C](Intercept)[/C][C]xdf2$statusSMK[/C][C]xdf2$currymild[/C][C]xdf2$statusSMK:xdf2$currymild[/C][/ROW]
[ROW][C]means[/C][C]8.1[/C][C]-5.35[/C][C]-4.45[/C][C]6.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104925&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
xdf2$rate ~ xdf2$status * xdf2$curry
names	(Intercept)	xdf2$statusSMK	xdf2$currymild	xdf2$statusSMK:xdf2$currymild
means	8.1	-5.35	-4.45	6.9

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
xdf2$status	1	72.2	72.2	48.431	1.0479e-09
xdf2$curry	1	20	20	13.416	0.0004591
xdf2$status:xdf2$curry	1	238.05	238.05	159.68	2.3155e-20
Residuals	76	113.3	1.4908

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
xdf2$status & 1 & 72.2 & 72.2 & 48.431 & 1.0479e-09 \tabularnewline
xdf2$curry & 1 & 20 & 20 & 13.416 & 0.0004591 \tabularnewline
xdf2$status:xdf2$curry & 1 & 238.05 & 238.05 & 159.68 & 2.3155e-20 \tabularnewline
Residuals & 76 & 113.3 & 1.4908 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104925&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]xdf2$status[/C][C]1[/C][C]72.2[/C][C]72.2[/C][C]48.431[/C][C]1.0479e-09[/C][/ROW]
[ROW][C]xdf2$curry[/C][C]1[/C][C]20[/C][C]20[/C][C]13.416[/C][C]0.0004591[/C][/ROW]
[ROW][C]xdf2$status:xdf2$curry[/C][C]1[/C][C]238.05[/C][C]238.05[/C][C]159.68[/C][C]2.3155e-20[/C][/ROW]
[ROW][C]Residuals[/C][C]76[/C][C]113.3[/C][C]1.4908[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104925&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
xdf2$status	1	72.2	72.2	48.431	1.0479e-09
xdf2$curry	1	20	20	13.416	0.0004591
xdf2$status:xdf2$curry	1	238.05	238.05	159.68	2.3155e-20
Residuals	76	113.3	1.4908

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
SMK-NS	-1.9	-2.4438	-1.3562	9.5685e-10
mild-hot	-1	-1.5438	-0.45624	0.0004591
SMK:hot-NS:hot	-5.35	-6.3642	-4.3358	0
NS:mild-NS:hot	-4.45	-5.4642	-3.4358	0
SMK:mild-NS:hot	-2.9	-3.9142	-1.8858	4.7494e-10
NS:mild-SMK:hot	0.9	-0.11423	1.9142	0.10003
SMK:mild-SMK:hot	2.45	1.4358	3.4642	8.6974e-08
SMK:mild-NS:mild	1.55	0.53577	2.5642	0.00078528

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
SMK-NS & -1.9 & -2.4438 & -1.3562 & 9.5685e-10 \tabularnewline
mild-hot & -1 & -1.5438 & -0.45624 & 0.0004591 \tabularnewline
SMK:hot-NS:hot & -5.35 & -6.3642 & -4.3358 & 0 \tabularnewline
NS:mild-NS:hot & -4.45 & -5.4642 & -3.4358 & 0 \tabularnewline
SMK:mild-NS:hot & -2.9 & -3.9142 & -1.8858 & 4.7494e-10 \tabularnewline
NS:mild-SMK:hot & 0.9 & -0.11423 & 1.9142 & 0.10003 \tabularnewline
SMK:mild-SMK:hot & 2.45 & 1.4358 & 3.4642 & 8.6974e-08 \tabularnewline
SMK:mild-NS:mild & 1.55 & 0.53577 & 2.5642 & 0.00078528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104925&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]SMK-NS[/C][C]-1.9[/C][C]-2.4438[/C][C]-1.3562[/C][C]9.5685e-10[/C][/ROW]
[ROW][C]mild-hot[/C][C]-1[/C][C]-1.5438[/C][C]-0.45624[/C][C]0.0004591[/C][/ROW]
[ROW][C]SMK:hot-NS:hot[/C][C]-5.35[/C][C]-6.3642[/C][C]-4.3358[/C][C]0[/C][/ROW]
[ROW][C]NS:mild-NS:hot[/C][C]-4.45[/C][C]-5.4642[/C][C]-3.4358[/C][C]0[/C][/ROW]
[ROW][C]SMK:mild-NS:hot[/C][C]-2.9[/C][C]-3.9142[/C][C]-1.8858[/C][C]4.7494e-10[/C][/ROW]
[ROW][C]NS:mild-SMK:hot[/C][C]0.9[/C][C]-0.11423[/C][C]1.9142[/C][C]0.10003[/C][/ROW]
[ROW][C]SMK:mild-SMK:hot[/C][C]2.45[/C][C]1.4358[/C][C]3.4642[/C][C]8.6974e-08[/C][/ROW]
[ROW][C]SMK:mild-NS:mild[/C][C]1.55[/C][C]0.53577[/C][C]2.5642[/C][C]0.00078528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104925&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104925&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
SMK-NS	-1.9	-2.4438	-1.3562	9.5685e-10
mild-hot	-1	-1.5438	-0.45624	0.0004591
SMK:hot-NS:hot	-5.35	-6.3642	-4.3358	0
NS:mild-NS:hot	-4.45	-5.4642	-3.4358	0
SMK:mild-NS:hot	-2.9	-3.9142	-1.8858	4.7494e-10
NS:mild-SMK:hot	0.9	-0.11423	1.9142	0.10003
SMK:mild-SMK:hot	2.45	1.4358	3.4642	8.6974e-08
SMK:mild-NS:mild	1.55	0.53577	2.5642	0.00078528

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	2.57	0.060418
	76

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 2.57 & 0.060418 \tabularnewline
  & 76 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104925&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]2.57[/C][C]0.060418[/C][/ROW]
[ROW][C] [/C][C]76[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104925&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104925&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	2.57	0.060418
	76

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 = 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])
mynames<- c(V1, V2, V3)
xdf2<-xdf
names(xdf2)<-mynames
names(xdf)<-c('R', 'A', 'B')
mynames <- c(V1, V2, V3)
if(intercept == FALSE)eval (substitute(lmout<-lm(xdf$R ~ xdf$A * xdf$B- 1, data = xdf), list(xdf=quote(xdf2),R=mynames[1],A=mynames[2],B=mynames[3]) ))else eval(substitute(lmout<-lm(xdf$R ~ xdf$A * xdf$B, data = xdf), list(xdf=quote(xdf2),R=mynames[1],A=mynames[2],B=mynames[3]) ))
oldnames<-names(lmout$coeff)
newnames<-gsub('xdf2$', '', oldnames)
(names(lmout$coeff)<-newnames)
(names(lmout$coefficients)<-newnames)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmout$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
callstr<-gsub('xdf2$', '',as.character(lmout$call$formula))
callstr<-paste(callstr[2], callstr[1], callstr[3])
a<-table.element(a,callstr ,length(lmout$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'names',,TRUE)
for(i in 1:length(lmout$coefficients)){
a<-table.element(a, names(lmout$coefficients[i]),,FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmout$coefficients)){
a<-table.element(a, signif(lmout$coefficients[i], digits=5),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
(aov.xdf<-aov(lmout) )
(anova.xdf<-anova(lmout) )
rownames(anova.xdf)<-gsub('xdf2$','',rownames(anova.xdf))
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$Df[1],,FALSE)
a<-table.element(a, signif(anova.xdf$'Sum Sq'[i], digits=5),,FALSE)
a<-table.element(a, signif(anova.xdf$'Mean Sq'[i], digits=5),,FALSE)
a<-table.element(a, signif(anova.xdf$'F value'[i], digits=5),,FALSE)
a<-table.element(a, signif(anova.xdf$'Pr(>F)'[i], digits=5),,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$'Df'[i+1],,FALSE)
a<-table.element(a, signif(anova.xdf$'Sum Sq'[i+1], digits=5),,FALSE)
a<-table.element(a, signif(anova.xdf$'Mean Sq'[i+1], digits=5),,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(R ~ A + 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$A, xdf$B, xdf$R, 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(0,0,1,2,1,2,0,0,3,3,3,3), 2,6))
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,signif(thsd[[nt]][i,j], digits=5), 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(lmout)
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,signif(lt.lmxdf[[i]][1], digits=5), 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