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workshop 5 Vraag 8

*The author of this computation has been verified*

R Software Module: /rwasp_Two Factor ANOVA.wasp (opens new window with default values)

Title produced by software: Two-Way ANOVA

Date of computation: Sun, 30 Oct 2011 10:04:53 -0400

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t.htm/, Retrieved Thu, 23 May 2013 08:21:00 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1288645075cgfsqx0t70qx6tj (pk = 91119)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

0	'E'	'M'
1	'F'	'V'
0	'F'	'M'
0	'H'	'M'
0	'H'	'M'
0	'H'	'M'
1	'E'	'M'
1	'F'	'M'
0	'E'	'M'
1	'F'	'V'
0	'H'	'V'
0	'E'	'V'
1	'F'	'M'
0	'H'	'V'
1	'E'	'V'
0	'H'	'V'
0	'E'	'M'
0	'F'	'M'
0	'H'	'V'
1	'F'	'V'
0	'H'	'V'
0	'H'	'M'
0	'H'	'V'
0	'E'	'V'
1	'F'	'V'
1	'E'	'V'
1	'E'	'V'
0	'F'	'M'
0	'F'	'V'
0	'H'	'V'
0	'E'	'M'
1	'E'	'M'
0	'H'	'M'
1	'E'	'M'
1	'F'	'M'
0	'E'	'M'
1	'F'	'V'
0	'H'	'V'
1	'E'	'V'
1	'F'	'V'
1	'F'	'V'
0	'F'	'V'
1	'F'	'V'
1	'H'	'M'
1	'E'	'V'
0	'E'	'V'
0	'H'	'V'
1	'E'	'M'
0	'F'	'M'
0	'F'	'V'
0	'H'	'V'
0	'E'	'M'
1	'F'	'M'
1	'E'	'M'
0	'H'	'M'
0	'H'	'M'
0	'H'	'M'
0	'E'	'M'
0	'H'	'V'
1	'E'	'V'
0	'H'	'M'
0	'F'	'M'
0	'H'	'M'
1	'F'	'V'
0	'E'	'M'
1	'E'	'M'
0	'F'	'V'
0	'H'	'M'
0	'F'	'V'
0	'E'	'M'
-1	'E'	'M'
0	'H'	'V'
0	'H'	'M'
0	'F'	'M'
0	'H'	'M'
1	'E'	'V'
0	'F'	'M'
1	'E'	'V'
0	'E'	'V'
0	'E'	'V'
0	'F'	'M'
0	'E'	'M'
1	'F'	'M'
0	'H'	'M'
0	'H'	'M'
0	'H'	'M'
0	'F'	'V'
0	'H'	'M'
0	'H'	'M'
1	'F'	'M'
1	'F'	'M'
0	'H'	'V'
0	'F'	'M'
0	'H'	'M'
0	'E'	'V'
1	'F'	'M'
0	'E'	'V'
0	'H'	'M'
1	'F'	'M'
0	'F'	'M'
0	'H'	'M'
1	'E'	'M'
0	'F'	'V'
0	'H'	'M'
0	'E'	'M'
0	'F'	'V'
0	'H'	'V'
0	'H'	'M'
1	'F'	'M'
1	'F'	'M'
0	'H'	'M'
0	'E'	'V'
0	'H'	'M'
0	'E'	'M'
0	'E'	'V'
0	'F'	'M'
0	'F'	'M'

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.3	0.178	-0.262	0.171	-0.119	-0.209

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	4.852	2.426	12.601	0
Treatment_B	2	0.105	0.105	0.546	0.462
Treatment_A:Treatment_B	2	0.201	0.101	0.523	0.594
Residuals	111	21.371	0.193

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
F-E	0.122	-0.116	0.359	0.447
H-E	-0.353	-0.591	-0.116	0.002
H-F	-0.475	-0.708	-0.242	0
V-M	0.061	-0.103	0.224	0.463
F:M-E:M	0.178	-0.211	0.567	0.768
H:M-E:M	-0.262	-0.64	0.117	0.347
E:V-E:M	0.171	-0.249	0.59	0.846
F:V-E:M	0.229	-0.19	0.649	0.61
H:V-E:M	-0.3	-0.743	0.143	0.371
H:M-F:M	-0.44	-0.804	-0.076	0.009
E:V-F:M	-0.008	-0.415	0.399	1
F:V-F:M	0.051	-0.356	0.458	0.999
H:V-F:M	-0.478	-0.91	-0.047	0.021
E:V-H:M	0.432	0.035	0.829	0.024
F:V-H:M	0.491	0.094	0.888	0.006
H:V-H:M	-0.038	-0.46	0.383	1
F:V-E:V	0.059	-0.378	0.495	0.999
H:V-E:V	-0.471	-0.93	-0.011	0.041
H:V-F:V	-0.529	-0.989	-0.07	0.014

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	5.504	0
	111

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/3xo7x1319983491.png (opens in new window)

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/3xo7x1319983491.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/4v2ca1319983491.png (opens in new window)

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/4v2ca1319983491.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/5qgi41319983491.png (opens in new window)

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/5qgi41319983491.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/60x0g1319983491.png (opens in new window)

http://www.freestatistics.org/blog/date/2011/Oct/30/t1319983521zup68bh7mhwrf0t/60x0g1319983491.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

Parameters (R input):

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')