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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_One Factor ANOVA.wasp
Title produced by softwareOne-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)
Date of computationWed, 10 Dec 2014 14:47:02 +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/2014/Dec/10/t14182228655wvbczgmv6d5z1w.htm/, Retrieved Tue, 28 May 2024 22:49:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265299, Retrieved Tue, 28 May 2024 22:49:16 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

Tree of Dependent Computations

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-       [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [anova] [2014-12-10 14:47:02] [093d2a2ec26a339da390c0fc5c0644df] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21 12.9
26 7.4
22 12.2
22 12.8
18 7.4
23 6.7
12 12.6
20 14.8
22 13.3
21 11.1
19 8.2
22 11.4
15 6.4
20 10.6
19 12.0
18 6.3
15 11.3
20 11.9
21 9.3
21 9.6
15 10.0
16 6.4
23 13.8
21 10.8
18 13.8
25 11.7
9 10.9
30 16.1
20 13.4
23 9.9
16 11.5
16 8.3
19 11.7
25 6.1
25 9.0
18 9.7
23 10.8
21 10.3
10 10.4
14 12.7
22 9.3
26 11.8
23 5.9
23 11.4
24 13.0
24 10.8
18 12.3
23 11.3
15 11.8
19 7.9
16 12.7
25 12.3
23 11.6
17 6.7
19 10.9
21 12.1
18 13.3
27 10.1
21 5.7
13 14.3
8 8.0
29 13.3
28 9.3
23 12.5
21 7.6
19 15.9
19 9.2
20 9.1
18 11.1
19 13.0
17 14.5
19 12.2
25 12.3
19 11.4
22 8.8
23 14.6
26 7.3
14 12.6
28 NA
16 13.0
24 12.6
20 13.2
12 9.9
24 7.7
22 10.5
12 13.4
22 10.9
20 4.3
10 10.3
23 11.8
17 11.2
22 11.4
24 8.6
18 13.2
21 12.6
20 5.6
20 9.9
22 8.8
19 7.7
20 9.0
26 7.3
23 11.4
24 13.6
21 7.9
21 10.7
19 10.3
8 8.3
17 9.6
20 14.2
11 8.5
8 13.5
15 4.9
18 6.4
18 9.6
19 11.6
19 11.1
23 4.35
22 12.7
21 18.1
25 17.85
30 16.6
17 12.6
27 17.1
23 19.1
23 16.1
18 13.35
18 18.4
23 14.7
19 10.6
15 12.6
20 16.2
16 13.6
24 18.9
25 14.1
25 14.5
19 16.15
19 14.75
16 14.8
19 12.45
19 12.65
23 17.35
21 8.6
22 18.4
19 16.1
20 11.6
20 17.75
3 15.25
23 17.65
14 15.6
23 16.35
20 17.65
15 13.6
13 11.7
16 14.35
7 14.75
24 18.25
17 9.9
24 16
24 18.25
19 16.85
25 14.6
20 13.85
28 18.95
23 15.6
27 14.85
18 11.75
28 18.45
21 15.9
19 17.1
23 16.1
27 19.9
22 10.95
28 18.45
25 15.1
21 15
22 11.35
28 15.95
20 18.1
29 14.6
25 15.4
25 15.4
20 17.6
20 13.35
16 19.1
20 15.35
20 7.6
23 13.4
18 13.9
25 19.1
18 15.25
19 12.9
25 16.1
25 17.35
25 13.15
24 12.15
19 12.6
26 10.35
10 15.4
17 9.6
13 18.2
17 13.6
30 14.85
25 14.75
4 14.1
16 14.9
21 16.25
23 19.25
22 13.6
17 13.6
20 15.65
20 12.75
22 14.6
16 9.85
23 12.65
16 11.9
0 19.2
18 16.6
25 11.2
23 15.25
12 11.9
18 13.2
24 16.35
11 12.4
18 15.85
14 14.35
23 18.15
24 11.15
29 15.65
18 17.75
15 7.65
29 12.35
16 15.6
19 19.3
22 15.2
16 17.1
23 15.6
23 18.4
19 19.05
4 18.55
20 19.1
24 13.1
20 12.85
4 9.5
24 4.5
22 11.85
16 13.6
3 11.7
15 12.4
24 13.35
17 11.4
20 14.9
27 19.9
23 17.75
26 11.2
23 14.6
17 17.6
20 14.05
22 16.1
19 13.35
24 11.85
19 11.95
23 14.75
15 15.15
27 13.2
26 16.85
22 7.85
22 7.7
18 12.6
15 7.85
22 10.95
27 12.35
10 9.95
20 14.9
17 16.65
23 13.4
19 13.95
13 15.7
27 16.85
23 10.95
16 15.35
25 12.2
2 15.1
26 17.75
20 15.2
23 14.6
22 16.65
24 8.1

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=265299&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=265299&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265299&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






ANOVA Model
NUMERACYTOT ~ TOT
means152716.66726102219.52122.66716.66722.33319.3332422.6671922211620.667151821.3332316191921242222.6672813192317.52117.3332022202019.667242520.752320.2519.5818.14320.52018192014.52013152124.1672318.51828.518.6672113.5152114.66718201924.5131820282423.66719202123.52419.52420.6672418.521.521.752520.52313242128424281921023192720232415202123251816.33320262220.51521.66718.52082419121122.52222.5201923.667418.251816181028

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
NUMERACYTOT  ~  TOT \tabularnewline
means & 15 & 27 & 16.667 & 26 & 10 & 22 & 19.5 & 21 & 22.667 & 16.667 & 22.333 & 19.333 & 24 & 22.667 & 19 & 22 & 21 & 16 & 20.667 & 15 & 18 & 21.333 & 23 & 16 & 19 & 19 & 21 & 24 & 22 & 22.667 & 28 & 13 & 19 & 23 & 17.5 & 21 & 17.333 & 20 & 22 & 20 & 20 & 19.667 & 24 & 25 & 20.75 & 23 & 20.25 & 19.5 & 8 & 18.143 & 20.5 & 20 & 18 & 19 & 20 & 14.5 & 20 & 13 & 15 & 21 & 24.167 & 23 & 18.5 & 18 & 28.5 & 18.667 & 21 & 13.5 & 15 & 21 & 14.667 & 18 & 20 & 19 & 24.5 & 13 & 18 & 20 & 28 & 24 & 23.667 & 19 & 20 & 21 & 23.5 & 24 & 19.5 & 24 & 20.667 & 24 & 18.5 & 21.5 & 21.75 & 25 & 20.5 & 23 & 13 & 24 & 21 & 28 & 4 & 24 & 28 & 19 & 21 & 0 & 23 & 19 & 27 & 20 & 23 & 24 & 15 & 20 & 21 & 23 & 25 & 18 & 16.333 & 20 & 26 & 22 & 20.5 & 15 & 21.667 & 18.5 & 20 & 8 & 24 & 19 & 12 & 11 & 22.5 & 22 & 22.5 & 20 & 19 & 23.667 & 4 & 18.25 & 18 & 16 & 18 & 10 & 28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265299&T=1

[TABLE]
[ROW]ANOVA Model[/C][/ROW]
[ROW]NUMERACYTOT  ~  TOT[/C][/ROW]
[ROW][C]means[/C][C]15[/C][C]27[/C][C]16.667[/C][C]26[/C][C]10[/C][C]22[/C][C]19.5[/C][C]21[/C][C]22.667[/C][C]16.667[/C][C]22.333[/C][C]19.333[/C][C]24[/C][C]22.667[/C][C]19[/C][C]22[/C][C]21[/C][C]16[/C][C]20.667[/C][C]15[/C][C]18[/C][C]21.333[/C][C]23[/C][C]16[/C][C]19[/C][C]19[/C][C]21[/C][C]24[/C][C]22[/C][C]22.667[/C][C]28[/C][C]13[/C][C]19[/C][C]23[/C][C]17.5[/C][C]21[/C][C]17.333[/C][C]20[/C][C]22[/C][C]20[/C][C]20[/C][C]19.667[/C][C]24[/C][C]25[/C][C]20.75[/C][C]23[/C][C]20.25[/C][C]19.5[/C][C]8[/C][C]18.143[/C][C]20.5[/C][C]20[/C][C]18[/C][C]19[/C][C]20[/C][C]14.5[/C][C]20[/C][C]13[/C][C]15[/C][C]21[/C][C]24.167[/C][C]23[/C][C]18.5[/C][C]18[/C][C]28.5[/C][C]18.667[/C][C]21[/C][C]13.5[/C][C]15[/C][C]21[/C][C]14.667[/C][C]18[/C][C]20[/C][C]19[/C][C]24.5[/C][C]13[/C][C]18[/C][C]20[/C][C]28[/C][C]24[/C][C]23.667[/C][C]19[/C][C]20[/C][C]21[/C][C]23.5[/C][C]24[/C][C]19.5[/C][C]24[/C][C]20.667[/C][C]24[/C][C]18.5[/C][C]21.5[/C][C]21.75[/C][C]25[/C][C]20.5[/C][C]23[/C][C]13[/C][C]24[/C][C]21[/C][C]28[/C][C]4[/C][C]24[/C][C]28[/C][C]19[/C][C]21[/C][C]0[/C][C]23[/C][C]19[/C][C]27[/C][C]20[/C][C]23[/C][C]24[/C][C]15[/C][C]20[/C][C]21[/C][C]23[/C][C]25[/C][C]18[/C][C]16.333[/C][C]20[/C][C]26[/C][C]22[/C][C]20.5[/C][C]15[/C][C]21.667[/C][C]18.5[/C][C]20[/C][C]8[/C][C]24[/C][C]19[/C][C]12[/C][C]11[/C][C]22.5[/C][C]22[/C][C]22.5[/C][C]20[/C][C]19[/C][C]23.667[/C][C]4[/C][C]18.25[/C][C]18[/C][C]16[/C][C]18[/C][C]10[/C][C]28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265299&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265299&T=1

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


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

ANOVA Model
NUMERACYTOT ~ TOT
means152716.66726102219.52122.66716.66722.33319.3332422.6671922211620.667151821.3332316191921242222.6672813192317.52117.3332022202019.667242520.752320.2519.5818.14320.52018192014.52013152124.1672318.51828.518.6672113.5152114.66718201924.5131820282423.66719202123.52419.52420.6672418.521.521.752520.52313242128424281921023192720232415202123251816.33320262220.51521.66718.52082419121122.52222.5201923.667418.251816181028






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT145119457.143823.84238.1450
Residuals1423066.85721.598 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOT & 145 & 119457.143 & 823.842 & 38.145 & 0 \tabularnewline
Residuals & 142 & 3066.857 & 21.598 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265299&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]TOT[/C][C]145[/C][C]119457.143[/C][C]823.842[/C][C]38.145[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]142[/C][C]3066.857[/C][C]21.598[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265299&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265299&T=2

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


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

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT145119457.143823.84238.1450
Residuals1423066.85721.598






Must Include Intercept to use Tukey Test 

\begin{tabular}{lllllllll}
\hline
Must Include Intercept to use Tukey Test  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265299&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265299&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265299&T=3

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


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

Must Include Intercept to use Tukey Test






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group1440.9930.518
142 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 144 & 0.993 & 0.518 \tabularnewline
  & 142 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265299&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]144[/C][C]0.993[/C][C]0.518[/C][/ROW]
[ROW][C] [/C][C]142[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265299&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265299&T=4

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


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

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group1440.9930.518
142


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = FALSE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
intercept<-as.logical(par3)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
xdf<-data.frame(x1,f1)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
names(xdf)<-c('Response', 'Treatment')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment - 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment, 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$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, paste(V1, ' ~ ', V2), length(lmxdf$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)
a<-table.row.start(a)
a<-table.element(a, V2,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3),,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$Df[2],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], 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, data=xdf, xlab=V2, ylab=V1)
dev.off()
if(intercept==TRUE){
'Tukey Plot'
thsd<-TukeyHSD(aov.xdf)
bitmap(file='TukeyHSDPlot.png')
plot(thsd)
dev.off()
}
if(intercept==TRUE){
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(i in 1:length(rownames(thsd[[1]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[1]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[1]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
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<-leveneTest(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')