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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 computationFri, 22 Dec 2017 16:39:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/22/t15139574452v0qwxwk5chcopa.htm/, Retrieved Thu, 16 May 2024 00:58:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310803, Retrieved Thu, 16 May 2024 00:58:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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)] [] [2017-12-22 15:39:09] [788a842113f37cddfb79e55621ea2338] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3	5	3
4	5	5
4	4	4
4	5	4
4	5	3
4	5	3
5	4	4
4	2	3
3	4	3
4	4	4
4	4	3
4	3	3
4	4	3
4	4	4
3	4	2
5	5	4
4	4	2
5	4	3
5	5	3
5	3	3
5	4	4
2	3	2
4	5	3
4	5	2
4	4	4
3	2	2
5	4	4
3	3	3
4	4	3
3	3	3
4	4	5
3	3	2
3	2	2
5	5	1
3	3	4
3	3	4
2	3	3
4	5	4
3	3	2
3	4	4
3	5	3
4	3	3
3	2	2
4	2	2
4	3	4
3	2	2
4	3	4
4	2	3
3	3	5
4	4	4
4	4	5
2	2	2
4	3	4
4	3	3
4	4	3
4	4	3
4	4	3
5	5	3
2	2	2
4	5	4
4	4	3
4	4	3
4	4	3
5	4	3
4	1	2
5	4	4
5	4	3
4	4	4
5	2	4
2	2	4
2	2	2
4	5	4
5	5	3
5	5	4
3	2	3
3	3	3
5	4	3
3	3	2
4	3	4
4	4	4
4	3	4
3	4	4
4	5	3
5	5	3
5	5	4
4	3	4
4	4	3
4	3	3
3	2	3
4	4	4
4	4	4
4	3	4
4	4	4
4	2	3
4	3	2
2	2	2
5	5	2
3	3	2
3	4	3
4	4	4
4	4	3
3	3	3
4	4	3
4	4	2
4	4	4
4	5	4
4	3	3
4	2	3
3	3	3
4	4	3
2	1	2
3	2	2
4	4	2
4	4	2
5	4	4
5	5	3
5	5	3
2	2	2
2	2	1
4	4	4
4	4	4
4	3	4
2	2	1
2	3	2
3	2	3
4	5	4
4	5	4
5	5	3
3	2	2
3	4	3
2	2	4
4	3	3
5	4	4
2	3	2
3	3	2
4	5	1
3	5	3
3	4	3
3	3	3
4	3	3
1	2	2
5	5	2
3	3	3
3	2	2
2	1	3
2	3	1
2	1	3
4	5	5
4	4	4
4	5	2
4	3	2
4	4	4
3	3	3
4	4	3
3	5	4
5	5	2
4	3	4
4	4	3
4	5	2
3	3	3
4	3	3
3	3	4
2	2	3
2	3	2
2	1	3
3	2	3
4	4	4
5	5	3
3	3	2
4	4	4
4	4	3
5	4	3
4	3	4
5	4	3
4	5	3
3	4	3
4	5	4
3	3	3
4	4	4
4	3	2
5	4	4
2	3	2
2	4	4
4	3	4
3	3	4
4	4	4
5	4	4
5	4	3
4	4	3
4	5	4
4	3	3
3	5	2
4	4	3
3	3	1
3	2	3
3	3	3
4	3	3
4	3	4
4	5	2
4	4	3
4	3	4
2	3	2
2	3	1
4	4	2
3	2	3
4	4	3
3	2	3
4	4	4
5	2	3
4	4	4
4	4	4
2	3	2
4	4	3
3	2	2
4	4	1
5	4	4
4	4	4
4	4	2
5	2	2
4	4	3
3	3	3
2	1	2
3	3	2
4	2	4
4	4	3
2	1	2
5	3	2
4	4	3
4	3	3
5	5	4
3	4	3
2	2	3
4	4	3
3	3	3
4	4	4
4	4	4
4	4	4
4	4	4
4	4	2
4	3	5
3	3	3
4	4	2
5	4	2
2	2	2
3	4	4
4	2	3
2	3	2
2	3	2
4	4	4
3	3	4
3	3	3
5	3	4
5	5	2
1	2	1
3	3	3
4	4	4
3	3	3
3	3	2
2	2	2
3	3	2
3	2	2
3	3	3
4	4	4
5	5	4
4	3	5
4	4	4
5	5	3
2	3	4
4	2	2
4	4	3
4	3	4
2	2	4
5	5	4
5	4	4
5	4	4
3	3	2
4	5	4
4	4	3
3	4	3
4	3	3
2	3	2
4	4	2
4	4	4
5	5	4
3	2	3
4	3	3
4	3	3
4	4	4
3	3	3
3	4	5
3	4	3
5	5	4
3	5	1
4	4	3
4	3	4
4	4	3
4	3	1
4	4	4
4	5	4
4	4	3
4	4	4
4	4	4
4	3	3
4	4	3
4	4	3
4	4	4
5	5	5
4	4	4
4	4	4
3	3	2
3	3	2
3	2	4
4	3	3
3	4	3
3	2	2
3	2	3
4	4	3
3	2	3
4	5	4
5	5	4
3	3	3
4	4	3
3	4	4
4	4	4
3	3	3
4	4	3
4	4	4
4	5	4
4	4	4
2	3	2
3	4	4
4	3	4
4	4	3
3	4	4
3	3	4
2	3	2
4	3	4
4	5	4
3	3	4
1	1	2
2	2	3
3	3	2
3	4	4
2	2	3
3	2	3
4	4	4
3	4	4
2	3	4
3	5	5
5	5	4
5	5	4
4	3	4
4	4	3
4	3	3
4	2	3
5	4	3
3	3	4
4	2	4
3	3	3
5	5	4
3	3	3
3	4	4
3	4	4
2	1	2
4	4	3
3	3	3
4	3	2
3	5	4
4	2	2
5	4	4
4	3	4
3	4	4
5	3	5
3	4	3
4	4	4
4	4	4
4	4	3
4	4	5
4	4	4
4	4	5
3	3	2
3	4	3
4	3	3
5	3	3
4	3	4
4	4	4
3	4	2
4	4	3
3	2	3
2	3	4
4	4	4
3	3	4
3	3	3
5	5	4
4	5	5
4	4	2
4	4	4
4	4	4
2	2	3
3	2	3
4	3	4
4	4	4
3	4	4
4	4	2
2	2	3
4	5	4
2	2	4
4	4	3
4	4	3
4	4	3
3	3	4
3	2	3
3	3	3
2	4	4
3	3	4
4	3	4
3	3	2
3	3	3
2	2	2
4	4	4
1	2	2
3	4	3
3	5	3
3	3	3
3	4	4
3	3	4
4	4	4
3	3	3
4	3	4
5	5	4
2	3	2
3	2	3
4	3	4
3	3	5
5	4	5
3	4	3
4	2	2
4	4	4
4	4	3
4	4	3
4	4	3
2	3	4
3	4	4
4	4	5
4	4	4
4	4	4

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310803&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310803&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
IQ3 ~ EOU2
means2.3330.3070.7421.1441.061

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
IQ3  ~  EOU2 \tabularnewline
means & 2.333 & 0.307 & 0.742 & 1.144 & 1.061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310803&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]IQ3  ~  EOU2[/C][/ROW]
[ROW][C]means[/C][C]2.333[/C][C]0.307[/C][C]0.742[/C][C]1.144[/C][C]1.061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310803&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
IQ3 ~ EOU2
means2.3330.3070.7421.1441.061






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
EOU2444.6911.17316.3610
Residuals441301.1480.683 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
EOU2 & 4 & 44.69 & 11.173 & 16.361 & 0 \tabularnewline
Residuals & 441 & 301.148 & 0.683 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310803&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]EOU2[/C][C]4[/C][C]44.69[/C][C]11.173[/C][C]16.361[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]441[/C][C]301.148[/C][C]0.683[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310803&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310803&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)
EOU2444.6911.17316.3610
Residuals441301.1480.683






Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-10.307-0.4991.1130.834
3-10.742-0.0381.5210.071
4-11.1440.371.9170.001
5-11.0610.2561.8650.003
3-20.4350.090.7790.005
4-20.8360.5051.1670
5-20.7530.3561.150
4-30.4020.1410.6630
5-30.319-0.0220.660.079
5-4-0.083-0.410.2440.957

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2-1 & 0.307 & -0.499 & 1.113 & 0.834 \tabularnewline
3-1 & 0.742 & -0.038 & 1.521 & 0.071 \tabularnewline
4-1 & 1.144 & 0.37 & 1.917 & 0.001 \tabularnewline
5-1 & 1.061 & 0.256 & 1.865 & 0.003 \tabularnewline
3-2 & 0.435 & 0.09 & 0.779 & 0.005 \tabularnewline
4-2 & 0.836 & 0.505 & 1.167 & 0 \tabularnewline
5-2 & 0.753 & 0.356 & 1.15 & 0 \tabularnewline
4-3 & 0.402 & 0.141 & 0.663 & 0 \tabularnewline
5-3 & 0.319 & -0.022 & 0.66 & 0.079 \tabularnewline
5-4 & -0.083 & -0.41 & 0.244 & 0.957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310803&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]2-1[/C][C]0.307[/C][C]-0.499[/C][C]1.113[/C][C]0.834[/C][/ROW]
[ROW][C]3-1[/C][C]0.742[/C][C]-0.038[/C][C]1.521[/C][C]0.071[/C][/ROW]
[ROW][C]4-1[/C][C]1.144[/C][C]0.37[/C][C]1.917[/C][C]0.001[/C][/ROW]
[ROW][C]5-1[/C][C]1.061[/C][C]0.256[/C][C]1.865[/C][C]0.003[/C][/ROW]
[ROW][C]3-2[/C][C]0.435[/C][C]0.09[/C][C]0.779[/C][C]0.005[/C][/ROW]
[ROW][C]4-2[/C][C]0.836[/C][C]0.505[/C][C]1.167[/C][C]0[/C][/ROW]
[ROW][C]5-2[/C][C]0.753[/C][C]0.356[/C][C]1.15[/C][C]0[/C][/ROW]
[ROW][C]4-3[/C][C]0.402[/C][C]0.141[/C][C]0.663[/C][C]0[/C][/ROW]
[ROW][C]5-3[/C][C]0.319[/C][C]-0.022[/C][C]0.66[/C][C]0.079[/C][/ROW]
[ROW][C]5-4[/C][C]-0.083[/C][C]-0.41[/C][C]0.244[/C][C]0.957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310803&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310803&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:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-10.307-0.4991.1130.834
3-10.742-0.0381.5210.071
4-11.1440.371.9170.001
5-11.0610.2561.8650.003
3-20.4350.090.7790.005
4-20.8360.5051.1670
5-20.7530.3561.150
4-30.4020.1410.6630
5-30.319-0.0220.660.079
5-4-0.083-0.410.2440.957






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group41.3560.248
441 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 4 & 1.356 & 0.248 \tabularnewline
  & 441 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310803&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]4[/C][C]1.356[/C][C]0.248[/C][/ROW]
[ROW][C] [/C][C]441[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310803&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310803&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)
Group41.3560.248
441


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 3 ; par2 = 2 ; par3 = TRUE ;
Parameters (R input):
par1 = 3 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'TRUE'
par2 <- '1'
par1 <- '3'
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')