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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 computationTue, 09 Dec 2014 14:11:50 +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/09/t14181343197j3a8vmhobv1fwu.htm/, Retrieved Thu, 16 May 2024 18:32:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=264639, Retrieved Thu, 16 May 2024 18:32:11 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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-       [Two-Way ANOVA] [] [2014-12-09 14:11:50] [6d118ae33f5ad8e94ad6fac6c6e53ad2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9 0 1
12.2 1 1
12.8 0 1
7.4 1 1
6.7 1 1
12.6 1 1
14.8 0 1
13.3 1 1
11.1 1 1
8.2 1 1
11.4 1 1
6.4 1 1
10.6 1 1
12 0 1
6.3 0 1
11.3 0 0
11.9 1 1
9.3 0 1
9.6 1 0
10 0 1
6.4 1 1
13.8 1 1
10.8 0 1
13.8 1 1
11.7 1 1
10.9 1 1
16.1 1 0
13.4 0 0
9.9 1 1
11.5 0 1
8.3 0 1
11.7 0 1
9 1 1
9.7 1 1
10.8 1 1
10.3 1 1
10.4 0 1
12.7 1 0
9.3 1 1
11.8 0 1
5.9 1 1
11.4 1 1
13 1 1
10.8 1 1
12.3 1 0
11.3 0 1
11.8 1 1
7.9 1 0
12.7 0 1
12.3 1 0
11.6 1 0
6.7 1 0
10.9 1 1
12.1 1 0
13.3 1 1
10.1 1 1
5.7 0 0
14.3 1 1
8 0 0
13.3 1 0
9.3 1 1
12.5 0 1
7.6 0 1
15.9 1 1
9.2 0 1
9.1 1 0
11.1 0 1
13 1 1
14.5 1 1
12.2 0 0
12.3 0 1
11.4 0 1
8.8 0 0
14.6 1 0
12.6 0 1
13 0 1
12.6 1 0
13.2 0 1
9.9 0 0
7.7 1 1
10.5 0 0
13.4 0 0
10.9 0 0
4.3 1 0
10.3 0 0
11.8 1 0
11.2 1 0
11.4 0 0
8.6 0 0
13.2 0 0
12.6 1 0
5.6 1 0
9.9 1 0
8.8 0 0
7.7 1 0
9 0 0
7.3 1 0
11.4 1 0
13.6 1 0
7.9 1 0
10.7 1 0
10.3 0 0
8.3 1 0
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14.2 1 0
8.5 0 0
13.5 0 0
4.9 0 0
6.4 0 0
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11.6 0 0
11.1 1 0
4.35 1 1
12.7 1 1
18.1 1 1
17.85 1 1
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16.1 1 1
13.35 0 1
18.4 0 1
14.7 1 1
10.6 1 1
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16.2 1 1
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18.9 1 0
14.1 1 1
14.5 1 1
16.15 0 1
14.75 1 1
14.8 1 1
12.45 1 1
12.65 1 1
17.35 1 1
8.6 1 1
18.4 0 1
16.1 1 1
11.6 1 0
17.75 1 1
15.25 1 1
17.65 1 1
16.35 0 1
17.65 0 1
13.6 1 1
14.35 0 1
14.75 0 1
18.25 1 1
9.9 0 1
16 1 1
18.25 1 1
16.85 0 1
14.6 1 0
13.85 1 0
18.95 1 1
15.6 0 1
14.85 0 0
11.75 0 0
18.45 0 0
15.9 1 0
17.1 0 1
16.1 1 1
19.9 0 0
10.95 1 0
18.45 0 0
15.1 1 0
15 0 0
11.35 0 0
15.95 1 0
18.1 0 0
14.6 1 0
15.4 1 1
15.4 1 1
17.6 1 0
13.35 1 1
19.1 0 1
15.35 1 0
7.6 0 1
13.4 0 0
13.9 0 0
19.1 1 1
15.25 0 0
12.9 1 0
16.1 0 0
17.35 0 0
13.15 0 0
12.15 0 0
12.6 1 0
10.35 1 0
15.4 1 0
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18.2 0 0
13.6 0 0
14.85 1 0
14.75 0 1
14.1 0 0
14.9 0 0
16.25 0 0
19.25 1 1
13.6 1 0
13.6 0 1
15.65 0 0
12.75 1 1
14.6 0 0
9.85 1 1
12.65 1 0
19.2 0 0
16.6 1 0
11.2 1 0
15.25 1 1
11.9 0 1
13.2 0 0
16.35 0 1
12.4 1 1
15.85 1 0
18.15 1 1
11.15 1 0
15.65 0 0
17.75 0 1
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19.3 0 1
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17.1 0 1
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19.05 0 1
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19.1 0 1
13.1 1 0
12.85 1 1
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11.85 0 0
13.6 1 1
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13.35 0 1
11.4 0 0
14.9 1 0
19.9 0 0
11.2 1 0
14.6 1 0
17.6 0 1
14.05 1 1
16.1 0 1
13.35 1 1
11.85 1 1
11.95 0 1
14.75 1 0
15.15 0 0
13.2 1 1
16.85 0 0
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15.35 0 0
12.2 1 0
15.1 0 0
17.75 0 0
15.2 1 0
14.6 0 1
16.65 0 0
8.1 1 0

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=264639&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=264639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264639&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
Response ~ Treatment_A * Treatment_B
means13.314-1.1080.3750.317

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 13.314 & -1.108 & 0.375 & 0.317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264639&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]13.314[/C][C]-1.108[/C][C]0.375[/C][C]0.317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264639&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
means13.314-1.1080.3750.317






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A155.09755.0974.8490.028
Treatment_B121.24821.2481.870.173
Treatment_A:Treatment_B11.7031.7030.150.699
Residuals2743113.45611.363 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 55.097 & 55.097 & 4.849 & 0.028 \tabularnewline
Treatment_B & 1 & 21.248 & 21.248 & 1.87 & 0.173 \tabularnewline
Treatment_A:Treatment_B & 1 & 1.703 & 1.703 & 0.15 & 0.699 \tabularnewline
Residuals & 274 & 3113.456 & 11.363 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264639&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]55.097[/C][C]55.097[/C][C]4.849[/C][C]0.028[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]21.248[/C][C]21.248[/C][C]1.87[/C][C]0.173[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]1.703[/C][C]1.703[/C][C]0.15[/C][C]0.699[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]3113.456[/C][C]11.363[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264639&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_A155.09755.0974.8490.028
Treatment_B121.24821.2481.870.173
Treatment_A:Treatment_B11.7031.7030.150.699
Residuals2743113.45611.363






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.899-1.702-0.0950.028
1-00.551-0.2451.3470.174
1:0-0:0-1.108-2.6040.3880.224
0:1-0:00.375-1.2211.9720.93
1:1-0:0-0.416-1.8441.0130.876
0:1-1:01.483-0.0823.0490.07
1:1-1:00.693-0.7012.0860.573
1:1-0:1-0.791-2.2920.710.524

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.899 & -1.702 & -0.095 & 0.028 \tabularnewline
1-0 & 0.551 & -0.245 & 1.347 & 0.174 \tabularnewline
1:0-0:0 & -1.108 & -2.604 & 0.388 & 0.224 \tabularnewline
0:1-0:0 & 0.375 & -1.221 & 1.972 & 0.93 \tabularnewline
1:1-0:0 & -0.416 & -1.844 & 1.013 & 0.876 \tabularnewline
0:1-1:0 & 1.483 & -0.082 & 3.049 & 0.07 \tabularnewline
1:1-1:0 & 0.693 & -0.701 & 2.086 & 0.573 \tabularnewline
1:1-0:1 & -0.791 & -2.292 & 0.71 & 0.524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264639&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]1-0[/C][C]-0.899[/C][C]-1.702[/C][C]-0.095[/C][C]0.028[/C][/ROW]
[ROW][C]1-0[/C][C]0.551[/C][C]-0.245[/C][C]1.347[/C][C]0.174[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-1.108[/C][C]-2.604[/C][C]0.388[/C][C]0.224[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.375[/C][C]-1.221[/C][C]1.972[/C][C]0.93[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-0.416[/C][C]-1.844[/C][C]1.013[/C][C]0.876[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]1.483[/C][C]-0.082[/C][C]3.049[/C][C]0.07[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.693[/C][C]-0.701[/C][C]2.086[/C][C]0.573[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.791[/C][C]-2.292[/C][C]0.71[/C][C]0.524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264639&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
1-0-0.899-1.702-0.0950.028
1-00.551-0.2451.3470.174
1:0-0:0-1.108-2.6040.3880.224
0:1-0:00.375-1.2211.9720.93
1:1-0:0-0.416-1.8441.0130.876
0:1-1:01.483-0.0823.0490.07
1:1-1:00.693-0.7012.0860.573
1:1-0:1-0.791-2.2920.710.524






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.8110.488
274 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.811 & 0.488 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264639&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]0.811[/C][C]0.488[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264639&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264639&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)
Group30.8110.488
274


Figures (Output of Computation)

Input Parameters & R Code

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