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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationSun, 10 Jan 2016 14:49:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/10/t14524373940xro1s5hzrpfili.htm/, Retrieved Fri, 17 May 2024 03:04:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287886, Retrieved Fri, 17 May 2024 03:04:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Kendall tau Correlation Matrix] [] [2015-11-22 21:46:49] [32b17a345b130fdf5cc88718ed94a974]
- RMP     [Two-Way ANOVA] [ffgd] [2016-01-10 14:49:37] [556542498df17f6b6bb31371ed648c6f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41 38 13 12 14 12 53 32 9
39 32 16 11 18 11 83 51 9
30 35 19 15 11 14 66 42 9
31 33 15 6 12 12 67 41 9
34 37 14 13 16 21 76 46 9
35 29 13 10 18 12 78 47 9
39 31 19 12 14 22 53 37 9
34 36 15 14 14 11 80 49 9
36 35 14 12 15 10 74 45 9
37 38 15 9 15 13 76 47 9
38 31 16 10 17 10 79 49 9
36 34 16 12 19 8 54 33 9
38 35 16 12 10 15 67 42 9
39 38 16 11 16 14 54 33 9
33 37 17 15 18 10 87 53 9
32 33 15 12 14 14 58 36 9
36 32 15 10 14 14 75 45 9
38 38 20 12 17 11 88 54 9
39 38 18 11 14 10 64 41 9
32 32 16 12 16 13 57 36 9
32 33 16 11 18 9.5 66 41 9
31 31 16 12 11 14 68 44 9
39 38 19 13 14 12 54 33 9
37 39 16 11 12 14 56 37 9
39 32 17 12 17 11 86 52 9
41 32 17 13 9 9 80 47 9
36 35 16 10 16 11 76 43 9
33 37 15 14 14 15 69 44 9
33 33 16 12 15 14 78 45 9
34 33 14 10 11 13 67 44 9
31 31 15 12 16 9 80 49 9
27 32 12 8 13 15 54 33 9
37 31 14 10 17 10 71 43 9
34 37 16 12 15 11 84 54 9
34 30 14 12 14 13 74 42 9
32 33 10 7 16 8 71 44 9
29 31 10 9 9 20 63 37 9
36 33 14 12 15 12 71 43 9
29 31 16 10 17 10 76 46 9
35 33 16 10 13 10 69 42 9
37 32 16 10 15 9 74 45 9
34 33 14 12 16 14 75 44 9
38 32 20 15 16 8 54 33 9
35 33 14 10 12 14 52 31 9
38 28 14 10 15 11 69 42 9
37 35 11 12 11 13 68 40 9
38 39 14 13 15 9 65 43 9
33 34 15 11 15 11 75 46 9
36 38 16 11 17 15 74 42 9
38 32 14 12 13 11 75 45 9
32 38 16 14 16 10 72 44 9
32 30 14 10 14 14 67 40 9
32 33 12 12 11 18 63 37 9
34 38 16 13 12 14 62 46 9
32 32 9 5 12 11 63 36 9
37 35 14 6 15 14.5 76 47 9
39 34 16 12 16 13 74 45 9
29 34 16 12 15 9 67 42 9
37 36 15 11 12 10 73 43 9
35 34 16 10 12 15 70 43 9
30 28 12 7 8 20 53 32 9
38 34 16 12 13 12 77 45 9
34 35 16 14 11 12 80 48 9
31 35 14 11 14 14 52 31 9
34 31 16 12 15 13 54 33 9
35 37 17 13 10 11 80 49 10
36 35 18 14 11 17 66 42 10
30 27 18 11 12 12 73 41 10
39 40 12 12 15 13 63 38 10
35 37 16 12 15 14 69 42 10
38 36 10 8 14 13 67 44 10
31 38 14 11 16 15 54 33 10
34 39 18 14 15 13 81 48 10
38 41 18 14 15 10 69 40 10
34 27 16 12 13 11 84 50 10
39 30 17 9 12 19 80 49 10
37 37 16 13 17 13 70 43 10
34 31 16 11 13 17 69 44 10
28 31 13 12 15 13 77 47 10
37 27 16 12 13 9 54 33 10
33 36 16 12 15 11 79 46 10
35 37 16 12 15 9 71 45 10
37 33 15 12 16 12 73 43 10
32 34 15 11 15 12 72 44 10
33 31 16 10 14 13 77 47 10
38 39 14 9 15 13 75 45 10
33 34 16 12 14 12 69 42 10
29 32 16 12 13 15 54 33 10
33 33 15 12 7 22 70 43 10
31 36 12 9 17 13 73 46 10
36 32 17 15 13 15 54 33 10
35 41 16 12 15 13 77 46 10
32 28 15 12 14 15 82 48 10
29 30 13 12 13 12.5 80 47 10
39 36 16 10 16 11 80 47 10
37 35 16 13 12 16 69 43 10
35 31 16 9 14 11 78 46 10
37 34 16 12 17 11 81 48 10
32 36 14 10 15 10 76 46 10
38 36 16 14 17 10 76 45 10
37 35 16 11 12 16 73 45 10
36 37 20 15 16 12 85 52 10
32 28 15 11 11 11 66 42 10
33 39 16 11 15 16 79 47 10
40 32 13 12 9 19 68 41 10
38 35 17 12 16 11 76 47 10
41 39 16 12 15 16 71 43 10
36 35 16 11 10 15 54 33 10
43 42 12 7 10 24 46 30 10
30 34 16 12 15 14 85 52 10
31 33 16 14 11 15 74 44 10
32 41 17 11 13 11 88 55 10
32 33 13 11 14 15 38 11 10
37 34 12 10 18 12 76 47 10
37 32 18 13 16 10 86 53 10
33 40 14 13 14 14 54 33 10
34 40 14 8 14 13 67 44 10
33 35 13 11 14 9 69 42 10
38 36 16 12 14 15 90 55 10
33 37 13 11 12 15 54 33 10
31 27 16 13 14 14 76 46 10
38 39 13 12 15 11 89 54 10
37 38 16 14 15 8 76 47 10
36 31 15 13 15 11 73 45 10
31 33 16 15 13 11 79 47 10
39 32 15 10 17 8 90 55 10
44 39 17 11 17 10 74 44 10
33 36 15 9 19 11 81 53 10
35 33 12 11 15 13 72 44 10
32 33 16 10 13 11 71 42 10
28 32 10 11 9 20 66 40 10
40 37 16 8 15 10 77 46 10
27 30 12 11 15 15 65 40 10
37 38 14 12 15 12 74 46 10
32 29 15 12 16 14 85 53 10
28 22 13 9 11 23 54 33 10
34 35 15 11 14 14 63 42 10
30 35 11 10 11 16 54 35 10
35 34 12 8 15 11 64 40 10
31 35 11 9 13 12 69 41 10
32 34 16 8 15 10 54 33 10
30 37 15 9 16 14 84 51 10
30 35 17 15 14 12 86 53 10
31 23 16 11 15 12 77 46 10
40 31 10 8 16 11 89 55 10
32 27 18 13 16 12 76 47 10
36 36 13 12 11 13 60 38 10
32 31 16 12 12 11 75 46 10
35 32 13 9 9 19 73 46 10
38 39 10 7 16 12 85 53 10
42 37 15 13 13 17 79 47 10
34 38 16 9 16 9 71 41 10
35 39 16 6 12 12 72 44 10
38 34 14 8 9 19 69 43 9
33 31 10 8 13 18 78 51 10
36 32 17 15 13 15 54 33 10
32 37 13 6 14 14 69 43 10
33 36 15 9 19 11 81 53 10
34 32 16 11 13 9 84 51 10
32 38 12 8 12 18 84 50 10
34 36 13 8 13 16 69 46 10
27 26 13 10 10 24 66 43 11
31 26 12 8 14 14 81 47 11
38 33 17 14 16 20 82 50 11
34 39 15 10 10 18 72 43 11
24 30 10 8 11 23 54 33 11
30 33 14 11 14 12 78 48 11
26 25 11 12 12 14 74 44 11
34 38 13 12 9 16 82 50 11
27 37 16 12 9 18 73 41 11
37 31 12 5 11 20 55 34 11
36 37 16 12 16 12 72 44 11
41 35 12 10 9 12 78 47 11
29 25 9 7 13 17 59 35 11
36 28 12 12 16 13 72 44 11
32 35 15 11 13 9 78 44 11
37 33 12 8 9 16 68 43 11
30 30 12 9 12 18 69 41 11
31 31 14 10 16 10 67 41 11
38 37 12 9 11 14 74 42 11
36 36 16 12 14 11 54 33 11
35 30 11 6 13 9 67 41 11
31 36 19 15 15 11 70 44 11
38 32 15 12 14 10 80 48 11
22 28 8 12 16 11 89 55 11
32 36 16 12 13 19 76 44 11
36 34 17 11 14 14 74 43 11
39 31 12 7 15 12 87 52 11
28 28 11 7 13 14 54 30 11
32 36 11 5 11 21 61 39 11
32 36 14 12 11 13 38 11 11
38 40 16 12 14 10 75 44 11
32 33 12 3 15 15 69 42 11
35 37 16 11 11 16 62 41 11
32 32 13 10 15 14 72 44 11
37 38 15 12 12 12 70 44 11
34 31 16 9 14 19 79 48 11
33 37 16 12 14 15 87 53 11
33 33 14 9 8 19 62 37 11
26 32 16 12 13 13 77 44 11
30 30 16 12 9 17 69 44 11
24 30 14 10 15 12 69 40 11
34 31 11 9 17 11 75 42 11
34 32 12 12 13 14 54 35 11
33 34 15 8 15 11 72 43 11
34 36 15 11 15 13 74 45 11
35 37 16 11 14 12 85 55 11
35 36 16 12 16 15 52 31 11
36 33 11 10 13 14 70 44 11
34 33 15 10 16 12 84 50 11
34 33 12 12 9 17 64 40 11
41 44 12 12 16 11 84 53 11
32 39 15 11 11 18 87 54 11
30 32 15 8 10 13 79 49 11
35 35 16 12 11 17 67 40 11
28 25 14 10 15 13 65 41 11
33 35 17 11 17 11 85 52 11
39 34 14 10 14 12 83 52 11
36 35 13 8 8 22 61 36 11
36 39 15 12 15 14 82 52 11
35 33 13 12 11 12 76 46 11
38 36 14 10 16 12 58 31 11
33 32 15 12 10 17 72 44 11
31 32 12 9 15 9 72 44 11
34 36 13 9 9 21 38 11 11
32 36 8 6 16 10 78 46 11
31 32 14 10 19 11 54 33 11
33 34 14 9 12 12 63 34 11
34 33 11 9 8 23 66 42 11
34 35 12 9 11 13 70 43 11
34 30 13 6 14 12 71 43 11
33 38 10 10 9 16 67 44 11
32 34 16 6 15 9 58 36 11
41 33 18 14 13 17 72 46 11
34 32 13 10 16 9 72 44 11
36 31 11 10 11 14 70 43 11
37 30 4 6 12 17 76 50 11
36 27 13 12 13 13 50 33 11
29 31 16 12 10 11 72 43 11
37 30 10 7 11 12 72 44 11
27 32 12 8 12 10 88 53 11
35 35 12 11 8 19 53 34 11
28 28 10 3 12 16 58 35 11
35 33 13 6 12 16 66 40 11
37 31 15 10 15 14 82 53 11
29 35 12 8 11 20 69 42 11
32 35 14 9 13 15 68 43 11
36 32 10 9 14 23 44 29 11
19 21 12 8 10 20 56 36 11
21 20 12 9 12 16 53 30 11
31 34 11 7 15 14 70 42 11
33 32 10 7 13 17 78 47 11
36 34 12 6 13 11 71 44 11
33 32 16 9 13 13 72 45 11
37 33 12 10 12 17 68 44 11
34 33 14 11 12 15 67 43 11
35 37 16 12 9 21 75 43 11
31 32 14 8 9 18 62 40 11
37 34 13 11 15 15 67 41 11
35 30 4 3 10 8 83 52 11
27 30 15 11 14 12 64 38 11
34 38 11 12 15 12 68 41 11
40 36 11 7 7 22 62 39 11
29 32 14 9 14 12 72 43 11

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287886&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]2 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=287886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287886&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.99 ; par4 = two.sided ; par5 = paired ;
Parameters (R input):
par1 = ; par2 = ; par3 = ; 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')