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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, 22 Jan 2017 23:29:06 +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/Jan/22/t1485124168wdvyvq9ek108t9t.htm/, Retrieved Mon, 13 May 2024 22:04:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=303560, Retrieved Mon, 13 May 2024 22:04:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [2 way anova priva...] [2016-12-07 14:17:16] [5d300c3f2919dcb76af3d6c83a609189]
-   PD    [Two-Way ANOVA] [anova] [2017-01-22 22:29:06] [a5a591d52ec67035c8301aa1739ae761] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15	4	1
13	4	2
14	4	2
13	4	2
12	4	1
17	4	2
12	4	2
13	3	2
13	3	1
16	4	1
12	4	1
12	3	1
13	3	1
16	4	1
15	4	1
12	4	2
15	4	2
12	4	2
15	4	2
11	4	1
13	4	2
13	4	2
14	4	1
14	4	1
14	3	1
15	3	1
16	4	1
16	4	1
16	4	1
13	3	2
13	4	1
14	3	1
13	4	2
14	4	1
12	4	1
17	3	2
14	3	1
15	3	1
13	3	2
14	3	2
15	3	2
19	4	2
14	3	2
13	3	2
12	4	2
14	4	2
15	4	1
15	3	2
12	3	1
14	3	2
11	3	2
12	4	1
10	4	2
14	3	1
14	3	2
15	4	1
15	4	2
13	3	2
15	4	2
16	4	2
12	4	1
17	4	2
15	4	1
12	4	1
16	4	2
15	4	2
15	4	2
12	4	1
13	3	2
10	4	1
14	4	2
11	4	1
12	4	2
14	4	1
12	4	2
14	4	2
12	4	1
13	4	1
13	3	1
14	4	2
12	4	2
15	4	2
13	4	2
13	4	2
11	3	1
12	3	2
16	3	1
11	4	1
13	4	1
12	3	1
17	4	2
14	4	2
15	4	2
8	4	1
13	4	2
13	4	2
15	4	1
14	4	1
13	4	2
14	4	2
12	4	2
19	3	2
15	4	1
14	3	1
14	4	1
15	4	2
13	4	2
15	3	2
14	4	1
11	4	1
17	4	2
13	4	1
9	4	1
12	3	2
13	3	1
17	3	1
14	3	1
13	3	2
16	4	2
14	4	2
14	4	2
14	4	2
10	4	1
12	3	1
13	3	2
14	4	2
18	3	2
14	4	1
14	3	2
13	4	1
13	4	1
16	3	1
13	4	2
14	3	1
8	4	1
13	3	1
13	3	1
16	4	2
14	4	1
13	4	2
14	4	2
12	4	2
16	4	2
18	4	1
16	4	1
15	4	1
18	3	1
15	3	2
14	3	2
14	3	2
15	3	2
9	3	1
17	4	2
11	3	1
15	3	2
15	4	1
13	4	1
15	4	1
15	4	2
14	4	2
13	4	1

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=303560&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=303560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303560&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
Response ~ Treatment_A * Treatment_B
means13.538-0.2250.5730.201

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 13.538 & -0.225 & 0.573 & 0.201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303560&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]13.538[/C][C]-0.225[/C][C]0.573[/C][C]0.201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303560&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
Response ~ Treatment_A * Treatment_B
means13.538-0.2250.5730.201






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.4140.4140.1140.736
Treatment_B120.10820.1085.5320.02
Treatment_A:Treatment_B10.360.360.0990.753
Residuals157570.673.635 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.414 & 0.414 & 0.114 & 0.736 \tabularnewline
Treatment_B & 1 & 20.108 & 20.108 & 5.532 & 0.02 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.36 & 0.36 & 0.099 & 0.753 \tabularnewline
Residuals & 157 & 570.67 & 3.635 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303560&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][/C][C]1[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]1[/C][C]0.414[/C][C]0.414[/C][C]0.114[/C][C]0.736[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]20.108[/C][C]20.108[/C][C]5.532[/C][C]0.02[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.36[/C][C]0.36[/C][C]0.099[/C][C]0.753[/C][/ROW]
[ROW][C]Residuals[/C][C]157[/C][C]570.67[/C][C]3.635[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303560&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303560&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)
1
Treatment_A10.4140.4140.1140.736
Treatment_B120.10820.1085.5320.02
Treatment_A:Treatment_B10.360.360.0990.753
Residuals157570.673.635






Tukey Honest Significant Difference Comparisons
difflwruprp adj
4-3-0.108-0.740.5240.736
2-10.7070.1131.3020.02
4:1-3:1-0.225-1.4180.9680.961
3:2-3:10.573-0.7881.9330.694
4:2-3:10.549-0.6221.7210.617
3:2-4:10.797-0.3811.9760.298
4:2-4:10.774-0.181.7280.156
4:2-3:2-0.023-1.181.1331

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
4-3 & -0.108 & -0.74 & 0.524 & 0.736 \tabularnewline
2-1 & 0.707 & 0.113 & 1.302 & 0.02 \tabularnewline
4:1-3:1 & -0.225 & -1.418 & 0.968 & 0.961 \tabularnewline
3:2-3:1 & 0.573 & -0.788 & 1.933 & 0.694 \tabularnewline
4:2-3:1 & 0.549 & -0.622 & 1.721 & 0.617 \tabularnewline
3:2-4:1 & 0.797 & -0.381 & 1.976 & 0.298 \tabularnewline
4:2-4:1 & 0.774 & -0.18 & 1.728 & 0.156 \tabularnewline
4:2-3:2 & -0.023 & -1.18 & 1.133 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303560&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]-0.108[/C][C]-0.74[/C][C]0.524[/C][C]0.736[/C][/ROW]
[ROW][C]2-1[/C][C]0.707[/C][C]0.113[/C][C]1.302[/C][C]0.02[/C][/ROW]
[ROW][C]4:1-3:1[/C][C]-0.225[/C][C]-1.418[/C][C]0.968[/C][C]0.961[/C][/ROW]
[ROW][C]3:2-3:1[/C][C]0.573[/C][C]-0.788[/C][C]1.933[/C][C]0.694[/C][/ROW]
[ROW][C]4:2-3:1[/C][C]0.549[/C][C]-0.622[/C][C]1.721[/C][C]0.617[/C][/ROW]
[ROW][C]3:2-4:1[/C][C]0.797[/C][C]-0.381[/C][C]1.976[/C][C]0.298[/C][/ROW]
[ROW][C]4:2-4:1[/C][C]0.774[/C][C]-0.18[/C][C]1.728[/C][C]0.156[/C][/ROW]
[ROW][C]4:2-3:2[/C][C]-0.023[/C][C]-1.18[/C][C]1.133[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303560&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303560&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
4-3-0.108-0.740.5240.736
2-10.7070.1131.3020.02
4:1-3:1-0.225-1.4180.9680.961
3:2-3:10.573-0.7881.9330.694
4:2-3:10.549-0.6221.7210.617
3:2-4:10.797-0.3811.9760.298
4:2-4:10.774-0.181.7280.156
4:2-3:2-0.023-1.181.1331






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.1960.313
157 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.196 & 0.313 \tabularnewline
  & 157 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303560&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]3[/C][C]1.196[/C][C]0.313[/C][/ROW]
[ROW][C] [/C][C]157[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303560&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303560&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)
Group31.1960.313
157


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;
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')