FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 18 Jan 2015 15:59:35 +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/2015/Jan/18/t1421597408vjohtiv4qyeo4kh.htm/, Retrieved Tue, 14 May 2024 12:49:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=274241, Retrieved Tue, 14 May 2024 12:49:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84

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 proef...] [2015-01-18 15:59:35] [d71ad52285d92a63edfc83f9fb1da7a1] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21 1 0
26 1 0
22 1 1
22 1 0
18 1 1
23 1 1
12 1 1
20 1 0
22 1 1
21 1 1
19 1 1
22 1 1
15 1 1
20 1 1
19 1 0
18 1 0
15 0 0
20 1 1
21 1 0
21 0 1
15 1 0
16 1 1
23 1 1
21 1 0
18 1 1
25 1 1
9 1 1
30 0 1
20 0 0
23 1 1
16 1 0
16 1 0
19 1 0
25 1 1
25 1 1
18 1 1
23 1 1
21 1 1
10 1 0
14 0 1
22 1 1
26 1 0
23 1 1
23 1 1
24 1 1
24 1 1
18 0 1
23 1 0
15 1 1
19 0 1
16 1 0
25 0 1
23 0 1
17 0 1
19 1 1
21 0 1
18 1 1
27 1 1
21 0 0
13 1 1
8 0 0
29 0 1
28 1 1
23 1 0
21 1 0
19 1 1
19 1 0
20 0 1
18 1 0
19 1 1
17 1 1
19 0 0
25 1 0
19 1 0
22 0 0
23 0 1
26 1 1
14 1 0
28 1 1
16 1 0
24 0 1
20 1 0
12 0 0
24 1 1
22 0 0
12 0 0
22 0 0
20 0 1
10 0 0
23 0 1
17 0 1
22 0 0
24 0 0
18 0 0
21 0 1
20 0 1
20 0 1
22 0 0
19 0 1
20 0 0
26 0 1
23 0 1
24 0 1
21 0 1
21 0 1
19 0 0
8 0 1
17 0 1
20 0 1
11 0 0
8 0 0
15 0 0
18 0 0
18 0 0
19 0 0
19 0 1
23 1 1
22 1 1
21 1 1
25 1 1
30 0 0
17 0 1
27 1 1
23 1 0
23 1 1
18 1 0
18 1 0
23 1 1
19 1 1
15 1 1
20 1 1
16 1 1
24 0 1
25 1 1
25 1 1
19 1 0
19 1 1
16 1 1
19 1 1
19 1 1
23 1 1
21 1 1
22 1 0
19 1 1
20 0 1
20 1 1
3 1 1
23 1 1
14 1 0
23 1 0
20 1 0
15 1 1
13 1 0
16 1 0
7 1 0
24 1 1
17 1 0
24 1 1
24 1 1
19 1 0
25 0 1
20 0 1
28 1 1
23 1 0
27 0 0
18 0 0
28 0 0
21 0 1
19 1 0
23 1 1
27 0 0
22 0 1
28 0 0
25 0 1
21 0 0
22 0 0
28 0 1
20 0 0
29 0 1
25 1 1
25 1 1
20 0 1
20 1 1
16 1 0
20 0 1
20 1 0
23 0 0
18 0 0
25 1 1
18 0 0
19 0 1
25 0 0
25 0 0
25 0 0
24 0 0
19 0 1
26 0 1
10 0 1
17 0 1
13 0 0
17 0 0
30 0 1
25 1 0
4 0 0
16 0 0
21 0 0
23 1 1
22 0 1
17 1 0
20 0 0
20 1 1
22 0 0
16 1 1
23 0 1
16 0 1
0 0 0
18 0 1
25 0 1
23 1 1
12 1 0
18 0 0
24 1 0
11 1 1
18 0 1
14 1 0
23 1 1
24 0 1
29 0 0
18 1 0
15 0 0
29 1 1
16 1 1
19 1 0
22 0 0
16 1 0
23 0 1
23 1 1
19 1 0
4 1 0
20 1 0
24 0 1
20 1 1
4 1 1
24 1 1
22 0 0
16 1 1
3 1 1
15 0 1
24 1 0
17 0 0
20 0 1
27 0 0
23 1 1
26 0 1
23 0 1
17 1 0
20 1 1
22 1 0
19 1 1
24 1 1
19 1 0
23 0 1
15 0 0
27 1 1
26 0 0
22 0 1
22 1 0
18 0 0
15 0 1
22 0 1
27 0 0
10 0 1
20 0 1
17 0 0
23 0 1
19 0 0
13 0 0
27 0 1
23 0 1
16 0 0
25 0 1
2 0 0
26 0 0
20 0 1
23 1 0
22 0 0
24 0 1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274241&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]3 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=274241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274241&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means19.077-0.3312.118-0.292

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 19.077 & -0.331 & 2.118 & -0.292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274241&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]19.077[/C][C]-0.331[/C][C]2.118[/C][C]-0.292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274241&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
means19.077-0.3312.118-0.292






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A18.1058.1050.3150.575
Treatment_B1270.985270.98510.5290.001
Treatment_A:Treatment_B11.4891.4890.0580.81
Residuals2837283.36525.736 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 8.105 & 8.105 & 0.315 & 0.575 \tabularnewline
Treatment_B & 1 & 270.985 & 270.985 & 10.529 & 0.001 \tabularnewline
Treatment_A:Treatment_B & 1 & 1.489 & 1.489 & 0.058 & 0.81 \tabularnewline
Residuals & 283 & 7283.365 & 25.736 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274241&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]8.105[/C][C]8.105[/C][C]0.315[/C][C]0.575[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]270.985[/C][C]270.985[/C][C]10.529[/C][C]0.001[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]1.489[/C][C]1.489[/C][C]0.058[/C][C]0.81[/C][/ROW]
[ROW][C]Residuals[/C][C]283[/C][C]7283.365[/C][C]25.736[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274241&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274241&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_A18.1058.1050.3150.575
Treatment_B1270.985270.98510.5290.001
Treatment_A:Treatment_B11.4891.4890.0580.81
Residuals2837283.36525.736






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.336-1.5170.8440.575
1-01.9550.7653.1450.001
1:0-0:0-0.331-2.6892.0260.984
0:1-0:02.118-0.1264.3610.072
1:1-0:01.495-0.6353.6240.269
0:1-1:02.4490.1464.7510.032
1:1-1:01.826-0.3664.0170.139
1:1-0:1-0.623-2.6911.4450.864

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.336 & -1.517 & 0.844 & 0.575 \tabularnewline
1-0 & 1.955 & 0.765 & 3.145 & 0.001 \tabularnewline
1:0-0:0 & -0.331 & -2.689 & 2.026 & 0.984 \tabularnewline
0:1-0:0 & 2.118 & -0.126 & 4.361 & 0.072 \tabularnewline
1:1-0:0 & 1.495 & -0.635 & 3.624 & 0.269 \tabularnewline
0:1-1:0 & 2.449 & 0.146 & 4.751 & 0.032 \tabularnewline
1:1-1:0 & 1.826 & -0.366 & 4.017 & 0.139 \tabularnewline
1:1-0:1 & -0.623 & -2.691 & 1.445 & 0.864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274241&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]-0.336[/C][C]-1.517[/C][C]0.844[/C][C]0.575[/C][/ROW]
[ROW][C]1-0[/C][C]1.955[/C][C]0.765[/C][C]3.145[/C][C]0.001[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.331[/C][C]-2.689[/C][C]2.026[/C][C]0.984[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]2.118[/C][C]-0.126[/C][C]4.361[/C][C]0.072[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]1.495[/C][C]-0.635[/C][C]3.624[/C][C]0.269[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]2.449[/C][C]0.146[/C][C]4.751[/C][C]0.032[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]1.826[/C][C]-0.366[/C][C]4.017[/C][C]0.139[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.623[/C][C]-2.691[/C][C]1.445[/C][C]0.864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274241&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274241&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
1-0-0.336-1.5170.8440.575
1-01.9550.7653.1450.001
1:0-0:0-0.331-2.6892.0260.984
0:1-0:02.118-0.1264.3610.072
1:1-0:01.495-0.6353.6240.269
0:1-1:02.4490.1464.7510.032
1:1-1:01.826-0.3664.0170.139
1:1-0:1-0.623-2.6911.4450.864






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group32.8080.04
283 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 2.808 & 0.04 \tabularnewline
  & 283 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274241&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]2.808[/C][C]0.04[/C][/ROW]
[ROW][C] [/C][C]283[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274241&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274241&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)
Group32.8080.04
283


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')