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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 computationThu, 27 Oct 2011 15:47:20 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/27/t1319744866y9bekcp597dv0zc.htm/, Retrieved Thu, 16 May 2024 09:55:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=137515, Retrieved Thu, 16 May 2024 09:55:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

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] [question 6 - WS 5] [2011-10-27 19:47:20] [935c692b8d0e827208dbfd6a4efb0528] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0	1	0
0	1	0
0	1	0
0	1	0
1	1	1
1	0	1
0	0	1
1	1	1
1	0	1
1	1	1
0	0	1
0	0	1
0	0	1
1	0	1
0	0	NA
0	0	1
1	0	NA
1	1	1
0	0	1
0	0	NA
1	1	0
1	1	1
1	1	NA
0	1	1
1	1	1
1	1	1
1	1	1
1	1	1
0	0	NA
0	0	0
1	1	0
0	0	1
0	0	0
0	0	1
0	1	0

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137515&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137515&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137515&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'Gertrude Mary Cox' @ cox.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means00.2860.2730.250.3420.464

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0 & 0.286 & 0.273 & 0.25 & 0.342 & 0.464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137515&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0[/C][C]0.286[/C][C]0.273[/C][C]0.25[/C][C]0.342[/C][C]0.464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137515&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137515&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
means00.2860.2730.250.3420.464






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A11.6271.6278.9690.006
Treatment_B11.630.8154.4920.02
Treatment_A:Treatment_B10.1690.0840.4650.633
Residuals295.260.181 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 1.627 & 1.627 & 8.969 & 0.006 \tabularnewline
Treatment_B & 1 & 1.63 & 0.815 & 4.492 & 0.02 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.169 & 0.084 & 0.465 & 0.633 \tabularnewline
Residuals & 29 & 5.26 & 0.181 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137515&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]1.627[/C][C]1.627[/C][C]8.969[/C][C]0.006[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]1.63[/C][C]0.815[/C][C]4.492[/C][C]0.02[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.169[/C][C]0.084[/C][C]0.465[/C][C]0.633[/C][/ROW]
[ROW][C]Residuals[/C][C]29[/C][C]5.26[/C][C]0.181[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137515&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137515&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_A11.6271.6278.9690.006
Treatment_B11.630.8154.4920.02
Treatment_A:Treatment_B10.1690.0840.4650.633
Residuals295.260.181






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.4310.1370.7260.006
1-00.4790.060.8980.022
NA-00.427-0.161.0140.188
NA-1-0.052-0.5760.4710.967
1:0-0:00.286-0.7551.3270.958
0:1-0:00.273-0.7251.2710.959
1:1-0:00.9-0.1061.9060.1
0:NA-0:00.25-0.8741.3740.983
1:NA-0:01-0.592.590.413
0:1-1:0-0.013-0.6410.6151
1:1-1:00.614-0.0261.2540.066
0:NA-1:0-0.036-0.850.7781
1:NA-1:00.714-0.6742.1020.625
1:1-0:10.6270.061.1950.024
0:NA-0:1-0.023-0.7810.7351
1:NA-0:10.727-0.6292.0830.583
0:NA-1:1-0.65-1.4180.1180.135
1:NA-1:10.1-1.2621.4621
1:NA-0:NA0.75-0.7022.2020.621

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.431 & 0.137 & 0.726 & 0.006 \tabularnewline
1-0 & 0.479 & 0.06 & 0.898 & 0.022 \tabularnewline
NA-0 & 0.427 & -0.16 & 1.014 & 0.188 \tabularnewline
NA-1 & -0.052 & -0.576 & 0.471 & 0.967 \tabularnewline
1:0-0:0 & 0.286 & -0.755 & 1.327 & 0.958 \tabularnewline
0:1-0:0 & 0.273 & -0.725 & 1.271 & 0.959 \tabularnewline
1:1-0:0 & 0.9 & -0.106 & 1.906 & 0.1 \tabularnewline
0:NA-0:0 & 0.25 & -0.874 & 1.374 & 0.983 \tabularnewline
1:NA-0:0 & 1 & -0.59 & 2.59 & 0.413 \tabularnewline
0:1-1:0 & -0.013 & -0.641 & 0.615 & 1 \tabularnewline
1:1-1:0 & 0.614 & -0.026 & 1.254 & 0.066 \tabularnewline
0:NA-1:0 & -0.036 & -0.85 & 0.778 & 1 \tabularnewline
1:NA-1:0 & 0.714 & -0.674 & 2.102 & 0.625 \tabularnewline
1:1-0:1 & 0.627 & 0.06 & 1.195 & 0.024 \tabularnewline
0:NA-0:1 & -0.023 & -0.781 & 0.735 & 1 \tabularnewline
1:NA-0:1 & 0.727 & -0.629 & 2.083 & 0.583 \tabularnewline
0:NA-1:1 & -0.65 & -1.418 & 0.118 & 0.135 \tabularnewline
1:NA-1:1 & 0.1 & -1.262 & 1.462 & 1 \tabularnewline
1:NA-0:NA & 0.75 & -0.702 & 2.202 & 0.621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137515&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]0.431[/C][C]0.137[/C][C]0.726[/C][C]0.006[/C][/ROW]
[ROW][C]1-0[/C][C]0.479[/C][C]0.06[/C][C]0.898[/C][C]0.022[/C][/ROW]
[ROW][C]NA-0[/C][C]0.427[/C][C]-0.16[/C][C]1.014[/C][C]0.188[/C][/ROW]
[ROW][C]NA-1[/C][C]-0.052[/C][C]-0.576[/C][C]0.471[/C][C]0.967[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.286[/C][C]-0.755[/C][C]1.327[/C][C]0.958[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.273[/C][C]-0.725[/C][C]1.271[/C][C]0.959[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.9[/C][C]-0.106[/C][C]1.906[/C][C]0.1[/C][/ROW]
[ROW][C]0:NA-0:0[/C][C]0.25[/C][C]-0.874[/C][C]1.374[/C][C]0.983[/C][/ROW]
[ROW][C]1:NA-0:0[/C][C]1[/C][C]-0.59[/C][C]2.59[/C][C]0.413[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.013[/C][C]-0.641[/C][C]0.615[/C][C]1[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.614[/C][C]-0.026[/C][C]1.254[/C][C]0.066[/C][/ROW]
[ROW][C]0:NA-1:0[/C][C]-0.036[/C][C]-0.85[/C][C]0.778[/C][C]1[/C][/ROW]
[ROW][C]1:NA-1:0[/C][C]0.714[/C][C]-0.674[/C][C]2.102[/C][C]0.625[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.627[/C][C]0.06[/C][C]1.195[/C][C]0.024[/C][/ROW]
[ROW][C]0:NA-0:1[/C][C]-0.023[/C][C]-0.781[/C][C]0.735[/C][C]1[/C][/ROW]
[ROW][C]1:NA-0:1[/C][C]0.727[/C][C]-0.629[/C][C]2.083[/C][C]0.583[/C][/ROW]
[ROW][C]0:NA-1:1[/C][C]-0.65[/C][C]-1.418[/C][C]0.118[/C][C]0.135[/C][/ROW]
[ROW][C]1:NA-1:1[/C][C]0.1[/C][C]-1.262[/C][C]1.462[/C][C]1[/C][/ROW]
[ROW][C]1:NA-0:NA[/C][C]0.75[/C][C]-0.702[/C][C]2.202[/C][C]0.621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137515&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137515&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
1-00.4310.1370.7260.006
1-00.4790.060.8980.022
NA-00.427-0.161.0140.188
NA-1-0.052-0.5760.4710.967
1:0-0:00.286-0.7551.3270.958
0:1-0:00.273-0.7251.2710.959
1:1-0:00.9-0.1061.9060.1
0:NA-0:00.25-0.8741.3740.983
1:NA-0:01-0.592.590.413
0:1-1:0-0.013-0.6410.6151
1:1-1:00.614-0.0261.2540.066
0:NA-1:0-0.036-0.850.7781
1:NA-1:00.714-0.6742.1020.625
1:1-0:10.6270.061.1950.024
0:NA-0:1-0.023-0.7810.7351
1:NA-0:10.727-0.6292.0830.583
0:NA-1:1-0.65-1.4180.1180.135
1:NA-1:10.1-1.2621.4621
1:NA-0:NA0.75-0.7022.2020.621






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.3740.862
29 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.374 & 0.862 \tabularnewline
  & 29 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137515&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]0.374[/C][C]0.862[/C][/ROW]
[ROW][C] [/C][C]29[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137515&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137515&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)
Group50.3740.862
29


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')