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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 15:45:19 -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/t1319744772tcrhjc02ei175i9.htm/, Retrieved Thu, 16 May 2024 19:50:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=137512, Retrieved Thu, 16 May 2024 19:50:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58

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 19:45:19] [935c692b8d0e827208dbfd6a4efb0528] [Current]
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Dataset

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

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137512&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137512&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137512&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'Herman Ole Andreas Wold' @ wold.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means00.40.3330-0.207-0.4

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0 & 0.4 & 0.333 & 0 & -0.207 & -0.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137512&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]0.4[/C][C]0.333[/C][C]0[/C][C]-0.207[/C][C]-0.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137512&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137512&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
means00.40.3330-0.207-0.4






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.7640.7643.1230.089
Treatment_B10.4190.210.8570.435
Treatment_A:Treatment_B10.0920.0460.1880.83
Residuals276.6040.245 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.764 & 0.764 & 3.123 & 0.089 \tabularnewline
Treatment_B & 1 & 0.419 & 0.21 & 0.857 & 0.435 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.092 & 0.046 & 0.188 & 0.83 \tabularnewline
Residuals & 27 & 6.604 & 0.245 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137512&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]0.764[/C][C]0.764[/C][C]3.123[/C][C]0.089[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.419[/C][C]0.21[/C][C]0.857[/C][C]0.435[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.092[/C][C]0.046[/C][C]0.188[/C][C]0.83[/C][/ROW]
[ROW][C]Residuals[/C][C]27[/C][C]6.604[/C][C]0.245[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137512&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137512&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_A10.7640.7643.1230.089
Treatment_B10.4190.210.8570.435
Treatment_A:Treatment_B10.0920.0460.1880.83
Residuals276.6040.245






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.355-0.0570.7670.089
1-00.165-0.3410.6720.7
NA-0-0.146-0.9770.6840.9
NA-1-0.312-1.0660.4430.568
1:0-0:00.4-0.7071.5070.874
0:1-0:00.333-0.9041.570.96
1:1-0:00.526-0.4151.4680.535
0:NA-0:00-1.3831.3831
1:NA-0:00-1.751.751
0:1-1:0-0.067-1.1731.041
1:1-1:00.126-0.6350.8880.995
0:NA-1:0-0.4-1.6680.8680.924
1:NA-1:0-0.4-2.061.260.975
1:1-0:10.193-0.7481.1340.988
0:NA-0:1-0.333-1.7171.050.975
1:NA-0:1-0.333-2.0831.4160.991
0:NA-1:1-0.526-1.6530.60.708
1:NA-1:1-0.526-2.0811.0280.901
1:NA-0:NA0-1.8561.8561

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.355 & -0.057 & 0.767 & 0.089 \tabularnewline
1-0 & 0.165 & -0.341 & 0.672 & 0.7 \tabularnewline
NA-0 & -0.146 & -0.977 & 0.684 & 0.9 \tabularnewline
NA-1 & -0.312 & -1.066 & 0.443 & 0.568 \tabularnewline
1:0-0:0 & 0.4 & -0.707 & 1.507 & 0.874 \tabularnewline
0:1-0:0 & 0.333 & -0.904 & 1.57 & 0.96 \tabularnewline
1:1-0:0 & 0.526 & -0.415 & 1.468 & 0.535 \tabularnewline
0:NA-0:0 & 0 & -1.383 & 1.383 & 1 \tabularnewline
1:NA-0:0 & 0 & -1.75 & 1.75 & 1 \tabularnewline
0:1-1:0 & -0.067 & -1.173 & 1.04 & 1 \tabularnewline
1:1-1:0 & 0.126 & -0.635 & 0.888 & 0.995 \tabularnewline
0:NA-1:0 & -0.4 & -1.668 & 0.868 & 0.924 \tabularnewline
1:NA-1:0 & -0.4 & -2.06 & 1.26 & 0.975 \tabularnewline
1:1-0:1 & 0.193 & -0.748 & 1.134 & 0.988 \tabularnewline
0:NA-0:1 & -0.333 & -1.717 & 1.05 & 0.975 \tabularnewline
1:NA-0:1 & -0.333 & -2.083 & 1.416 & 0.991 \tabularnewline
0:NA-1:1 & -0.526 & -1.653 & 0.6 & 0.708 \tabularnewline
1:NA-1:1 & -0.526 & -2.081 & 1.028 & 0.901 \tabularnewline
1:NA-0:NA & 0 & -1.856 & 1.856 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137512&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]0.355[/C][C]-0.057[/C][C]0.767[/C][C]0.089[/C][/ROW]
[ROW][C]1-0[/C][C]0.165[/C][C]-0.341[/C][C]0.672[/C][C]0.7[/C][/ROW]
[ROW][C]NA-0[/C][C]-0.146[/C][C]-0.977[/C][C]0.684[/C][C]0.9[/C][/ROW]
[ROW][C]NA-1[/C][C]-0.312[/C][C]-1.066[/C][C]0.443[/C][C]0.568[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.4[/C][C]-0.707[/C][C]1.507[/C][C]0.874[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.333[/C][C]-0.904[/C][C]1.57[/C][C]0.96[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.526[/C][C]-0.415[/C][C]1.468[/C][C]0.535[/C][/ROW]
[ROW][C]0:NA-0:0[/C][C]0[/C][C]-1.383[/C][C]1.383[/C][C]1[/C][/ROW]
[ROW][C]1:NA-0:0[/C][C]0[/C][C]-1.75[/C][C]1.75[/C][C]1[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.067[/C][C]-1.173[/C][C]1.04[/C][C]1[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0.126[/C][C]-0.635[/C][C]0.888[/C][C]0.995[/C][/ROW]
[ROW][C]0:NA-1:0[/C][C]-0.4[/C][C]-1.668[/C][C]0.868[/C][C]0.924[/C][/ROW]
[ROW][C]1:NA-1:0[/C][C]-0.4[/C][C]-2.06[/C][C]1.26[/C][C]0.975[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.193[/C][C]-0.748[/C][C]1.134[/C][C]0.988[/C][/ROW]
[ROW][C]0:NA-0:1[/C][C]-0.333[/C][C]-1.717[/C][C]1.05[/C][C]0.975[/C][/ROW]
[ROW][C]1:NA-0:1[/C][C]-0.333[/C][C]-2.083[/C][C]1.416[/C][C]0.991[/C][/ROW]
[ROW][C]0:NA-1:1[/C][C]-0.526[/C][C]-1.653[/C][C]0.6[/C][C]0.708[/C][/ROW]
[ROW][C]1:NA-1:1[/C][C]-0.526[/C][C]-2.081[/C][C]1.028[/C][C]0.901[/C][/ROW]
[ROW][C]1:NA-0:NA[/C][C]0[/C][C]-1.856[/C][C]1.856[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137512&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137512&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
1-00.355-0.0570.7670.089
1-00.165-0.3410.6720.7
NA-0-0.146-0.9770.6840.9
NA-1-0.312-1.0660.4430.568
1:0-0:00.4-0.7071.5070.874
0:1-0:00.333-0.9041.570.96
1:1-0:00.526-0.4151.4680.535
0:NA-0:00-1.3831.3831
1:NA-0:00-1.751.751
0:1-1:0-0.067-1.1731.041
1:1-1:00.126-0.6350.8880.995
0:NA-1:0-0.4-1.6680.8680.924
1:NA-1:0-0.4-2.061.260.975
1:1-0:10.193-0.7481.1340.988
0:NA-0:1-0.333-1.7171.050.975
1:NA-0:1-0.333-2.0831.4160.991
0:NA-1:1-0.526-1.6530.60.708
1:NA-1:1-0.526-2.0811.0280.901
1:NA-0:NA0-1.8561.8561






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.8450.53
27 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.845 & 0.53 \tabularnewline
  & 27 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137512&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]0.845[/C][C]0.53[/C][/ROW]
[ROW][C] [/C][C]27[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137512&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137512&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)
Group50.8450.53
27


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')