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R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationFri, 16 Jan 2015 09:16:16 +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/16/t142139986544djp902uaqr9iy.htm/, Retrieved Thu, 31 Oct 2024 23:30:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=273620, Retrieved Thu, 31 Oct 2024 23:30:47 +0000
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Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [vraag 3] [2015-01-16 09:16:16] [8a5be748fffbe1272db475ee7e612f22] [Current]
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Dataseries X:
4.2 "'VC'" 0.5
11.5 "'VC'" 0.5
7.3 "'VC'" 0.5
5.8 "'VC'" 0.5
6.4 "'VC'" 0.5
10 "'VC'" 0.5
11.2 "'VC'" 0.5
11.2 "'VC'" 0.5
5.2 "'VC'" 0.5
7 "'VC'" 0.5
16.5 "'VC'" 1
16.5 "'VC'" 1
15.2 "'VC'" 1
17.3 "'VC'" 1
22.5 "'VC'" 1
17.3 "'VC'" 1
13.6 "'VC'" 1
14.5 "'VC'" 1
18.8 "'VC'" 1
15.5 "'VC'" 1
23.6 "'VC'" 2
18.5 "'VC'" 2
33.9 "'VC'" 2
25.5 "'VC'" 2
26.4 "'VC'" 2
32.5 "'VC'" 2
26.7 "'VC'" 2
21.5 "'VC'" 2
23.3 "'VC'" 2
29.5 "'VC'" 2
15.2 "'OJ'" 0.5
21.5 "'OJ'" 0.5
17.6 "'OJ'" 0.5
9.7 "'OJ'" 0.5
14.5 "'OJ'" 0.5
10 "'OJ'" 0.5
8.2 "'OJ'" 0.5
9.4 "'OJ'" 0.5
16.5 "'OJ'" 0.5
9.7 "'OJ'" 0.5
19.7 "'OJ'" 1
23.3 "'OJ'" 1
23.6 "'OJ'" 1
26.4 "'OJ'" 1
20 "'OJ'" 1
25.2 "'OJ'" 1
25.8 "'OJ'" 1
21.2 "'OJ'" 1
14.5 "'OJ'" 1
27.3 "'OJ'" 1
25.5 "'OJ'" 2
26.4 "'OJ'" 2
22.4 "'OJ'" 2
24.5 "'OJ'" 2
24.8 "'OJ'" 2
30.9 "'OJ'" 2
26.4 "'OJ'" 2
27.3 "'OJ'" 2
29.4 "'OJ'" 2
23 "'OJ'" 2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273620&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273620&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273620&T=0

As an alternative you can also use a 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'Gwilym Jenkins' @ jenkins.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means13.23-5.259.4712.83-0.685.33

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 13.23 & -5.25 & 9.47 & 12.83 & -0.68 & 5.33 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273620&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]13.23[/C][C]-5.25[/C][C]9.47[/C][C]12.83[/C][C]-0.68[/C][C]5.33[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273620&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273620&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means13.23-5.259.4712.83-0.685.33







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1205.35205.3515.5720
Treatment_B12426.4341213.217920
Treatment_A:Treatment_B1108.31954.164.1070.022
Residuals54712.10613.187

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 205.35 & 205.35 & 15.572 & 0 \tabularnewline
Treatment_B & 1 & 2426.434 & 1213.217 & 92 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 108.319 & 54.16 & 4.107 & 0.022 \tabularnewline
Residuals & 54 & 712.106 & 13.187 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273620&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]205.35[/C][C]205.35[/C][C]15.572[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]2426.434[/C][C]1213.217[/C][C]92[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]108.319[/C][C]54.16[/C][C]4.107[/C][C]0.022[/C][/ROW]
[ROW][C]Residuals[/C][C]54[/C][C]712.106[/C][C]13.187[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273620&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273620&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1205.35205.3515.5720
Treatment_B12426.4341213.217920
Treatment_A:Treatment_B1108.31954.164.1070.022
Residuals54712.10613.187







Tukey Honest Significant Difference Comparisons
difflwruprp adj
'VC'-'OJ'-3.7-5.58-1.820
1-0.59.136.36211.8980
2-0.515.49512.72718.2630
2-16.3653.5979.1330
'VC':0.5-'OJ':0.5-5.25-10.048-0.4520.024
'OJ':1-'OJ':0.59.474.67214.2680
'VC':1-'OJ':0.53.54-1.2588.3380.264
'OJ':2-'OJ':0.512.838.03217.6280
'VC':2-'OJ':0.512.918.11217.7080
'OJ':1-'VC':0.514.729.92219.5180
'VC':1-'VC':0.58.793.99213.5880
'OJ':2-'VC':0.518.0813.28222.8780
'VC':2-'VC':0.518.1613.36222.9580
'VC':1-'OJ':1-5.93-10.728-1.1320.007
'OJ':2-'OJ':13.36-1.4388.1580.319
'VC':2-'OJ':13.44-1.3588.2380.294
'OJ':2-'VC':19.294.49214.0880
'VC':2-'VC':19.374.57214.1680
'VC':2-'OJ':20.08-4.7184.8781

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
'VC'-'OJ' & -3.7 & -5.58 & -1.82 & 0 \tabularnewline
1-0.5 & 9.13 & 6.362 & 11.898 & 0 \tabularnewline
2-0.5 & 15.495 & 12.727 & 18.263 & 0 \tabularnewline
2-1 & 6.365 & 3.597 & 9.133 & 0 \tabularnewline
'VC':0.5-'OJ':0.5 & -5.25 & -10.048 & -0.452 & 0.024 \tabularnewline
'OJ':1-'OJ':0.5 & 9.47 & 4.672 & 14.268 & 0 \tabularnewline
'VC':1-'OJ':0.5 & 3.54 & -1.258 & 8.338 & 0.264 \tabularnewline
'OJ':2-'OJ':0.5 & 12.83 & 8.032 & 17.628 & 0 \tabularnewline
'VC':2-'OJ':0.5 & 12.91 & 8.112 & 17.708 & 0 \tabularnewline
'OJ':1-'VC':0.5 & 14.72 & 9.922 & 19.518 & 0 \tabularnewline
'VC':1-'VC':0.5 & 8.79 & 3.992 & 13.588 & 0 \tabularnewline
'OJ':2-'VC':0.5 & 18.08 & 13.282 & 22.878 & 0 \tabularnewline
'VC':2-'VC':0.5 & 18.16 & 13.362 & 22.958 & 0 \tabularnewline
'VC':1-'OJ':1 & -5.93 & -10.728 & -1.132 & 0.007 \tabularnewline
'OJ':2-'OJ':1 & 3.36 & -1.438 & 8.158 & 0.319 \tabularnewline
'VC':2-'OJ':1 & 3.44 & -1.358 & 8.238 & 0.294 \tabularnewline
'OJ':2-'VC':1 & 9.29 & 4.492 & 14.088 & 0 \tabularnewline
'VC':2-'VC':1 & 9.37 & 4.572 & 14.168 & 0 \tabularnewline
'VC':2-'OJ':2 & 0.08 & -4.718 & 4.878 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273620&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]'VC'-'OJ'[/C][C]-3.7[/C][C]-5.58[/C][C]-1.82[/C][C]0[/C][/ROW]
[ROW][C]1-0.5[/C][C]9.13[/C][C]6.362[/C][C]11.898[/C][C]0[/C][/ROW]
[ROW][C]2-0.5[/C][C]15.495[/C][C]12.727[/C][C]18.263[/C][C]0[/C][/ROW]
[ROW][C]2-1[/C][C]6.365[/C][C]3.597[/C][C]9.133[/C][C]0[/C][/ROW]
[ROW][C]'VC':0.5-'OJ':0.5[/C][C]-5.25[/C][C]-10.048[/C][C]-0.452[/C][C]0.024[/C][/ROW]
[ROW][C]'OJ':1-'OJ':0.5[/C][C]9.47[/C][C]4.672[/C][C]14.268[/C][C]0[/C][/ROW]
[ROW][C]'VC':1-'OJ':0.5[/C][C]3.54[/C][C]-1.258[/C][C]8.338[/C][C]0.264[/C][/ROW]
[ROW][C]'OJ':2-'OJ':0.5[/C][C]12.83[/C][C]8.032[/C][C]17.628[/C][C]0[/C][/ROW]
[ROW][C]'VC':2-'OJ':0.5[/C][C]12.91[/C][C]8.112[/C][C]17.708[/C][C]0[/C][/ROW]
[ROW][C]'OJ':1-'VC':0.5[/C][C]14.72[/C][C]9.922[/C][C]19.518[/C][C]0[/C][/ROW]
[ROW][C]'VC':1-'VC':0.5[/C][C]8.79[/C][C]3.992[/C][C]13.588[/C][C]0[/C][/ROW]
[ROW][C]'OJ':2-'VC':0.5[/C][C]18.08[/C][C]13.282[/C][C]22.878[/C][C]0[/C][/ROW]
[ROW][C]'VC':2-'VC':0.5[/C][C]18.16[/C][C]13.362[/C][C]22.958[/C][C]0[/C][/ROW]
[ROW][C]'VC':1-'OJ':1[/C][C]-5.93[/C][C]-10.728[/C][C]-1.132[/C][C]0.007[/C][/ROW]
[ROW][C]'OJ':2-'OJ':1[/C][C]3.36[/C][C]-1.438[/C][C]8.158[/C][C]0.319[/C][/ROW]
[ROW][C]'VC':2-'OJ':1[/C][C]3.44[/C][C]-1.358[/C][C]8.238[/C][C]0.294[/C][/ROW]
[ROW][C]'OJ':2-'VC':1[/C][C]9.29[/C][C]4.492[/C][C]14.088[/C][C]0[/C][/ROW]
[ROW][C]'VC':2-'VC':1[/C][C]9.37[/C][C]4.572[/C][C]14.168[/C][C]0[/C][/ROW]
[ROW][C]'VC':2-'OJ':2[/C][C]0.08[/C][C]-4.718[/C][C]4.878[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273620&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273620&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
'VC'-'OJ'-3.7-5.58-1.820
1-0.59.136.36211.8980
2-0.515.49512.72718.2630
2-16.3653.5979.1330
'VC':0.5-'OJ':0.5-5.25-10.048-0.4520.024
'OJ':1-'OJ':0.59.474.67214.2680
'VC':1-'OJ':0.53.54-1.2588.3380.264
'OJ':2-'OJ':0.512.838.03217.6280
'VC':2-'OJ':0.512.918.11217.7080
'OJ':1-'VC':0.514.729.92219.5180
'VC':1-'VC':0.58.793.99213.5880
'OJ':2-'VC':0.518.0813.28222.8780
'VC':2-'VC':0.518.1613.36222.9580
'VC':1-'OJ':1-5.93-10.728-1.1320.007
'OJ':2-'OJ':13.36-1.4388.1580.319
'VC':2-'OJ':13.44-1.3588.2380.294
'OJ':2-'VC':19.294.49214.0880
'VC':2-'VC':19.374.57214.1680
'VC':2-'OJ':20.08-4.7184.8781







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group51.7090.148
54

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 1.709 & 0.148 \tabularnewline
  & 54 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273620&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]5[/C][C]1.709[/C][C]0.148[/C][/ROW]
[ROW][C] [/C][C]54[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273620&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273620&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group51.7090.148
54



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')