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Author

*The author of this computation has been verified*

R Software Module

Title produced by software

Two-Way ANOVA

Date of computation

Thu, 08 Nov 2012 08:22:23 -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/2012/Nov/08/t1352380972dhm6f5ol4of63ja.htm/, Retrieved Thu, 31 Oct 2024 22:59:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=186698, Retrieved Thu, 31 Oct 2024 22:59:55 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

155

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]
- RM        [Two-Way ANOVA] [workshop 6: smoke...] [2012-11-08 13:22:23] [b9bb0bee71e79baedbda8d04cb7f9b59] [Current]

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Dataseries X:

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Histogram

Boxplots

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

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186698&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186698&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	'Herman Ole Andreas Wold' @ wold.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	8.1	-3.95	-4.45	4.1

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 8.1 & -3.95 & -4.45 & 4.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186698&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]8.1[/C][C]-3.95[/C][C]-4.45[/C][C]4.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186698&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	8.1	-3.95	-4.45	4.1

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	72.2	72.2	31.884	0
Treatment_B	1	115.2	115.2	50.873	0
Treatment_A:Treatment_B	1	84.05	84.05	37.117	0
Residuals	76	172.1	2.264

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 72.2 & 72.2 & 31.884 & 0 \tabularnewline
Treatment_B & 1 & 115.2 & 115.2 & 50.873 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 84.05 & 84.05 & 37.117 & 0 \tabularnewline
Residuals & 76 & 172.1 & 2.264 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186698&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]72.2[/C][C]72.2[/C][C]31.884[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]115.2[/C][C]115.2[/C][C]50.873[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]84.05[/C][C]84.05[/C][C]37.117[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]76[/C][C]172.1[/C][C]2.264[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186698&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186698&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	72.2	72.2	31.884	0
Treatment_B	1	115.2	115.2	50.873	0
Treatment_A:Treatment_B	1	84.05	84.05	37.117	0
Residuals	76	172.1	2.264

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
SMK-NS	-1.9	-2.57	-1.23	0
mild-hot	-2.4	-3.07	-1.73	0
SMK:hot-NS:hot	-3.95	-5.2	-2.7	0
NS:mild-NS:hot	-4.45	-5.7	-3.2	0
SMK:mild-NS:hot	-4.3	-5.55	-3.05	0
NS:mild-SMK:hot	-0.5	-1.75	0.75	0.72
SMK:mild-SMK:hot	-0.35	-1.6	0.9	0.882
SMK:mild-NS:mild	0.15	-1.1	1.4	0.989

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
SMK-NS & -1.9 & -2.57 & -1.23 & 0 \tabularnewline
mild-hot & -2.4 & -3.07 & -1.73 & 0 \tabularnewline
SMK:hot-NS:hot & -3.95 & -5.2 & -2.7 & 0 \tabularnewline
NS:mild-NS:hot & -4.45 & -5.7 & -3.2 & 0 \tabularnewline
SMK:mild-NS:hot & -4.3 & -5.55 & -3.05 & 0 \tabularnewline
NS:mild-SMK:hot & -0.5 & -1.75 & 0.75 & 0.72 \tabularnewline
SMK:mild-SMK:hot & -0.35 & -1.6 & 0.9 & 0.882 \tabularnewline
SMK:mild-NS:mild & 0.15 & -1.1 & 1.4 & 0.989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186698&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]-2.57[/C][C]-1.23[/C][C]0[/C][/ROW]
[ROW][C]mild-hot[/C][C]-2.4[/C][C]-3.07[/C][C]-1.73[/C][C]0[/C][/ROW]
[ROW][C]SMK:hot-NS:hot[/C][C]-3.95[/C][C]-5.2[/C][C]-2.7[/C][C]0[/C][/ROW]
[ROW][C]NS:mild-NS:hot[/C][C]-4.45[/C][C]-5.7[/C][C]-3.2[/C][C]0[/C][/ROW]
[ROW][C]SMK:mild-NS:hot[/C][C]-4.3[/C][C]-5.55[/C][C]-3.05[/C][C]0[/C][/ROW]
[ROW][C]NS:mild-SMK:hot[/C][C]-0.5[/C][C]-1.75[/C][C]0.75[/C][C]0.72[/C][/ROW]
[ROW][C]SMK:mild-SMK:hot[/C][C]-0.35[/C][C]-1.6[/C][C]0.9[/C][C]0.882[/C][/ROW]
[ROW][C]SMK:mild-NS:mild[/C][C]0.15[/C][C]-1.1[/C][C]1.4[/C][C]0.989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186698&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186698&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	-2.57	-1.23	0
mild-hot	-2.4	-3.07	-1.73	0
SMK:hot-NS:hot	-3.95	-5.2	-2.7	0
NS:mild-NS:hot	-4.45	-5.7	-3.2	0
SMK:mild-NS:hot	-4.3	-5.55	-3.05	0
NS:mild-SMK:hot	-0.5	-1.75	0.75	0.72
SMK:mild-SMK:hot	-0.35	-1.6	0.9	0.882
SMK:mild-NS:mild	0.15	-1.1	1.4	0.989

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	0.25	0.861
	76

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.25 & 0.861 \tabularnewline
  & 76 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186698&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]0.25[/C][C]0.861[/C][/ROW]
[ROW][C] [/C][C]76[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186698&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186698&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	0.25	0.861
	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 ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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