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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 computationMon, 15 Dec 2014 14:20:44 +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/15/t1418653344uqabo6h3881rrvh.htm/, Retrieved Thu, 16 May 2024 17:09:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268485, Retrieved Thu, 16 May 2024 17:09:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [ANOVA Fout] [2014-12-15 14:20:44] [093d2a2ec26a339da390c0fc5c0644df] [Current]
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Dataset

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

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268485&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268485&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






ANOVA Model
NUMERACYTOT ~ TOT
means152716.66726102219.52122.66716.66722.33319.3332422.6671922211620.667151821.3332316191921242222.6672813192317.52117.3332022202019.667242520.752320.2519.5818.14320.52018192014.52013152124.1672318.51828.518.6672113.5152114.66718201924.5131820282423.66719202123.52419.52420.6672418.521.521.752520.52313242128424281921023192720232415202123251816.33320262220.51521.66718.52082419121122.52222.5201923.667418.2518161810

\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 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268485&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][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268485&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
means152716.66726102219.52122.66716.66722.33319.3332422.6671922211620.667151821.3332316191921242222.6672813192317.52117.3332022202019.667242520.752320.2519.5818.14320.52018192014.52013152124.1672318.51828.518.6672113.5152114.66718201924.5131820282423.66719202123.52419.52420.6672418.521.521.752520.52313242128424281921023192720232415202123251816.33320262220.51521.66718.52082419121122.52222.5201923.667418.2518161810






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT144118673.143824.11938.1580
Residuals1423066.85721.598 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOT & 144 & 118673.143 & 824.119 & 38.158 & 0 \tabularnewline
Residuals & 142 & 3066.857 & 21.598 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268485&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]144[/C][C]118673.143[/C][C]824.119[/C][C]38.158[/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=268485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268485&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)
TOT144118673.143824.11938.1580
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=268485&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268485&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268485&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)
Group1430.9960.509
142 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 143 & 0.996 & 0.509 \tabularnewline
  & 142 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268485&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]143[/C][C]0.996[/C][C]0.509[/C][/ROW]
[ROW][C] [/C][C]142[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268485&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268485&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)
Group1430.9960.509
142


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = FALSE ;
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')