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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 computationSun, 20 Jan 2019 14:56:39 +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/2019/Jan/20/t15479926349bsnkx5q0jotbza.htm/, Retrieved Fri, 03 May 2024 09:05:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316471, Retrieved Fri, 03 May 2024 09:05:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact24

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)] [] [2019-01-20 13:56:39] [f7e6ff93b59ad290328697363b152819] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3	9
5	5
6	6
3	7
2	8
6	5
8	8
5	4
3	3
3	5
4	4
5	9
3	9
5	5
6	6
3	7
2	8
6	5
8	8
5	4
3	3
3	5
4	4
5	9

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316471&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316471&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 time5 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
A ~ B
means31.51.6673021

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
A  ~  B \tabularnewline
means & 3 & 1.5 & 1.667 & 3 & 0 & 2 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316471&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]A  ~  B[/C][/ROW]
[ROW][C]means[/C][C]3[/C][C]1.5[/C][C]1.667[/C][C]3[/C][C]0[/C][C]2[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316471&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
A ~ B
means31.51.6673021






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
B615.52.5830.8730.535
Residuals1750.3332.961 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
B & 6 & 15.5 & 2.583 & 0.873 & 0.535 \tabularnewline
Residuals & 17 & 50.333 & 2.961 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316471&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]B[/C][C]6[/C][C]15.5[/C][C]2.583[/C][C]0.873[/C][C]0.535[/C][/ROW]
[ROW][C]Residuals[/C][C]17[/C][C]50.333[/C][C]2.961[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316471&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)
B615.52.5830.8730.535
Residuals1750.3332.961






Tukey Honest Significant Difference Comparisons
difflwruprp adj
4-31.5-3.4576.4570.946
5-31.667-3.0076.3410.89
6-33-2.7248.7240.599
7-30-5.7245.7241
8-32-2.9576.9570.823
9-31-3.9575.9570.993
5-40.167-3.5283.8621
6-41.5-3.4576.4570.946
7-4-1.5-6.4573.4570.946
8-40.5-3.5484.5481
9-4-0.5-4.5483.5481
6-51.333-3.3416.0070.958
7-5-1.667-6.3413.0070.89
8-50.333-3.3624.0281
9-5-0.667-4.3623.0280.996
7-6-3-8.7242.7240.599
8-6-1-5.9573.9570.993
9-6-2-6.9572.9570.823
8-72-2.9576.9570.823
9-71-3.9575.9570.993
9-8-1-5.0483.0480.979

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
4-3 & 1.5 & -3.457 & 6.457 & 0.946 \tabularnewline
5-3 & 1.667 & -3.007 & 6.341 & 0.89 \tabularnewline
6-3 & 3 & -2.724 & 8.724 & 0.599 \tabularnewline
7-3 & 0 & -5.724 & 5.724 & 1 \tabularnewline
8-3 & 2 & -2.957 & 6.957 & 0.823 \tabularnewline
9-3 & 1 & -3.957 & 5.957 & 0.993 \tabularnewline
5-4 & 0.167 & -3.528 & 3.862 & 1 \tabularnewline
6-4 & 1.5 & -3.457 & 6.457 & 0.946 \tabularnewline
7-4 & -1.5 & -6.457 & 3.457 & 0.946 \tabularnewline
8-4 & 0.5 & -3.548 & 4.548 & 1 \tabularnewline
9-4 & -0.5 & -4.548 & 3.548 & 1 \tabularnewline
6-5 & 1.333 & -3.341 & 6.007 & 0.958 \tabularnewline
7-5 & -1.667 & -6.341 & 3.007 & 0.89 \tabularnewline
8-5 & 0.333 & -3.362 & 4.028 & 1 \tabularnewline
9-5 & -0.667 & -4.362 & 3.028 & 0.996 \tabularnewline
7-6 & -3 & -8.724 & 2.724 & 0.599 \tabularnewline
8-6 & -1 & -5.957 & 3.957 & 0.993 \tabularnewline
9-6 & -2 & -6.957 & 2.957 & 0.823 \tabularnewline
8-7 & 2 & -2.957 & 6.957 & 0.823 \tabularnewline
9-7 & 1 & -3.957 & 5.957 & 0.993 \tabularnewline
9-8 & -1 & -5.048 & 3.048 & 0.979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316471&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]4-3[/C][C]1.5[/C][C]-3.457[/C][C]6.457[/C][C]0.946[/C][/ROW]
[ROW][C]5-3[/C][C]1.667[/C][C]-3.007[/C][C]6.341[/C][C]0.89[/C][/ROW]
[ROW][C]6-3[/C][C]3[/C][C]-2.724[/C][C]8.724[/C][C]0.599[/C][/ROW]
[ROW][C]7-3[/C][C]0[/C][C]-5.724[/C][C]5.724[/C][C]1[/C][/ROW]
[ROW][C]8-3[/C][C]2[/C][C]-2.957[/C][C]6.957[/C][C]0.823[/C][/ROW]
[ROW][C]9-3[/C][C]1[/C][C]-3.957[/C][C]5.957[/C][C]0.993[/C][/ROW]
[ROW][C]5-4[/C][C]0.167[/C][C]-3.528[/C][C]3.862[/C][C]1[/C][/ROW]
[ROW][C]6-4[/C][C]1.5[/C][C]-3.457[/C][C]6.457[/C][C]0.946[/C][/ROW]
[ROW][C]7-4[/C][C]-1.5[/C][C]-6.457[/C][C]3.457[/C][C]0.946[/C][/ROW]
[ROW][C]8-4[/C][C]0.5[/C][C]-3.548[/C][C]4.548[/C][C]1[/C][/ROW]
[ROW][C]9-4[/C][C]-0.5[/C][C]-4.548[/C][C]3.548[/C][C]1[/C][/ROW]
[ROW][C]6-5[/C][C]1.333[/C][C]-3.341[/C][C]6.007[/C][C]0.958[/C][/ROW]
[ROW][C]7-5[/C][C]-1.667[/C][C]-6.341[/C][C]3.007[/C][C]0.89[/C][/ROW]
[ROW][C]8-5[/C][C]0.333[/C][C]-3.362[/C][C]4.028[/C][C]1[/C][/ROW]
[ROW][C]9-5[/C][C]-0.667[/C][C]-4.362[/C][C]3.028[/C][C]0.996[/C][/ROW]
[ROW][C]7-6[/C][C]-3[/C][C]-8.724[/C][C]2.724[/C][C]0.599[/C][/ROW]
[ROW][C]8-6[/C][C]-1[/C][C]-5.957[/C][C]3.957[/C][C]0.993[/C][/ROW]
[ROW][C]9-6[/C][C]-2[/C][C]-6.957[/C][C]2.957[/C][C]0.823[/C][/ROW]
[ROW][C]8-7[/C][C]2[/C][C]-2.957[/C][C]6.957[/C][C]0.823[/C][/ROW]
[ROW][C]9-7[/C][C]1[/C][C]-3.957[/C][C]5.957[/C][C]0.993[/C][/ROW]
[ROW][C]9-8[/C][C]-1[/C][C]-5.048[/C][C]3.048[/C][C]0.979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316471&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316471&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
4-31.5-3.4576.4570.946
5-31.667-3.0076.3410.89
6-33-2.7248.7240.599
7-30-5.7245.7241
8-32-2.9576.9570.823
9-31-3.9575.9570.993
5-40.167-3.5283.8621
6-41.5-3.4576.4570.946
7-4-1.5-6.4573.4570.946
8-40.5-3.5484.5481
9-4-0.5-4.5483.5481
6-51.333-3.3416.0070.958
7-5-1.667-6.3413.0070.89
8-50.333-3.3624.0281
9-5-0.667-4.3623.0280.996
7-6-3-8.7242.7240.599
8-6-1-5.9573.9570.993
9-6-2-6.9572.9570.823
8-72-2.9576.9570.823
9-71-3.9575.9570.993
9-8-1-5.0483.0480.979






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group616.2920
17 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 6 & 16.292 & 0 \tabularnewline
  & 17 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316471&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]6[/C][C]16.292[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]17[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316471&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316471&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)
Group616.2920
17


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par3 = 0,95 ; par4 = two.sided ; par5 = paired ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
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')