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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 15:42:21 -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/t1319744597jq95e2tw29kac7u.htm/, Retrieved Thu, 16 May 2024 12:22:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=137509, Retrieved Thu, 16 May 2024 12:22:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

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 19:42:21] [935c692b8d0e827208dbfd6a4efb0528] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1	1	0
1	1	0
0	1	1
0	0	0
1	1	1
1	1	1
1	1	1
0	1	1
0	1	1
1	1	0
0	0	0
0	1	1
0	1	1
0	1	0
0	0	NA
1	1	1
1	1	0
1	1	1
0	1	1
0	0	1
1	1	1
1	1	0
0	0	NA
1	0	NA
1	1	1
1	0	1
1	1	NA
0	0	NA
0	0	0
1	1	1
1	0	0
1	1	0
0	0	1
0	0	NA
0	0	1
1	1	NA
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'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=137509&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=137509&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137509&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
means0.250.6250-0.05-0.3040.175

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.25 & 0.625 & 0 & -0.05 & -0.304 & 0.175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137509&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.25[/C][C]0.625[/C][C]0[/C][C]-0.05[/C][C]-0.304[/C][C]0.175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137509&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137509&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
means0.250.6250-0.05-0.3040.175






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A11.9231.9239.0280.005
Treatment_B10.3990.1990.9360.403
Treatment_A:Treatment_B10.2640.1320.6190.545
Residuals316.6040.213 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 1.923 & 1.923 & 9.028 & 0.005 \tabularnewline
Treatment_B & 1 & 0.399 & 0.199 & 0.936 & 0.403 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.264 & 0.132 & 0.619 & 0.545 \tabularnewline
Residuals & 31 & 6.604 & 0.213 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137509&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]1.923[/C][C]1.923[/C][C]9.028[/C][C]0.005[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.399[/C][C]0.199[/C][C]0.936[/C][C]0.403[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.264[/C][C]0.132[/C][C]0.619[/C][C]0.545[/C][/ROW]
[ROW][C]Residuals[/C][C]31[/C][C]6.604[/C][C]0.213[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137509&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137509&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_A11.9231.9239.0280.005
Treatment_B10.3990.1990.9360.403
Treatment_A:Treatment_B10.2640.1320.6190.545
Residuals316.6040.213






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.4780.1530.8020.005
1-0-0.22-0.6430.2040.418
NA-0-0.056-0.5960.4840.965
NA-10.164-0.3420.670.708
1:0-0:00.625-0.2331.4830.262
0:1-0:00-0.9910.9911
1:1-0:00.321-0.4731.1160.82
0:NA-0:0-0.05-0.990.891
1:NA-0:00.75-0.4631.9630.435
0:1-1:0-0.625-1.4830.2330.262
1:1-1:0-0.304-0.9240.3170.677
0:NA-1:0-0.675-1.4740.1240.137
1:NA-1:00.125-0.9821.2320.999
1:1-0:10.321-0.4731.1160.82
0:NA-0:1-0.05-0.990.891
1:NA-0:10.75-0.4631.9630.435
0:NA-1:1-0.371-1.1010.3580.639
1:NA-1:10.429-0.631.4880.82
1:NA-0:NA0.8-0.3721.9720.328

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.478 & 0.153 & 0.802 & 0.005 \tabularnewline
1-0 & -0.22 & -0.643 & 0.204 & 0.418 \tabularnewline
NA-0 & -0.056 & -0.596 & 0.484 & 0.965 \tabularnewline
NA-1 & 0.164 & -0.342 & 0.67 & 0.708 \tabularnewline
1:0-0:0 & 0.625 & -0.233 & 1.483 & 0.262 \tabularnewline
0:1-0:0 & 0 & -0.991 & 0.991 & 1 \tabularnewline
1:1-0:0 & 0.321 & -0.473 & 1.116 & 0.82 \tabularnewline
0:NA-0:0 & -0.05 & -0.99 & 0.89 & 1 \tabularnewline
1:NA-0:0 & 0.75 & -0.463 & 1.963 & 0.435 \tabularnewline
0:1-1:0 & -0.625 & -1.483 & 0.233 & 0.262 \tabularnewline
1:1-1:0 & -0.304 & -0.924 & 0.317 & 0.677 \tabularnewline
0:NA-1:0 & -0.675 & -1.474 & 0.124 & 0.137 \tabularnewline
1:NA-1:0 & 0.125 & -0.982 & 1.232 & 0.999 \tabularnewline
1:1-0:1 & 0.321 & -0.473 & 1.116 & 0.82 \tabularnewline
0:NA-0:1 & -0.05 & -0.99 & 0.89 & 1 \tabularnewline
1:NA-0:1 & 0.75 & -0.463 & 1.963 & 0.435 \tabularnewline
0:NA-1:1 & -0.371 & -1.101 & 0.358 & 0.639 \tabularnewline
1:NA-1:1 & 0.429 & -0.63 & 1.488 & 0.82 \tabularnewline
1:NA-0:NA & 0.8 & -0.372 & 1.972 & 0.328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137509&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]0.478[/C][C]0.153[/C][C]0.802[/C][C]0.005[/C][/ROW]
[ROW][C]1-0[/C][C]-0.22[/C][C]-0.643[/C][C]0.204[/C][C]0.418[/C][/ROW]
[ROW][C]NA-0[/C][C]-0.056[/C][C]-0.596[/C][C]0.484[/C][C]0.965[/C][/ROW]
[ROW][C]NA-1[/C][C]0.164[/C][C]-0.342[/C][C]0.67[/C][C]0.708[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.625[/C][C]-0.233[/C][C]1.483[/C][C]0.262[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0[/C][C]-0.991[/C][C]0.991[/C][C]1[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.321[/C][C]-0.473[/C][C]1.116[/C][C]0.82[/C][/ROW]
[ROW][C]0:NA-0:0[/C][C]-0.05[/C][C]-0.99[/C][C]0.89[/C][C]1[/C][/ROW]
[ROW][C]1:NA-0:0[/C][C]0.75[/C][C]-0.463[/C][C]1.963[/C][C]0.435[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.625[/C][C]-1.483[/C][C]0.233[/C][C]0.262[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-0.304[/C][C]-0.924[/C][C]0.317[/C][C]0.677[/C][/ROW]
[ROW][C]0:NA-1:0[/C][C]-0.675[/C][C]-1.474[/C][C]0.124[/C][C]0.137[/C][/ROW]
[ROW][C]1:NA-1:0[/C][C]0.125[/C][C]-0.982[/C][C]1.232[/C][C]0.999[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.321[/C][C]-0.473[/C][C]1.116[/C][C]0.82[/C][/ROW]
[ROW][C]0:NA-0:1[/C][C]-0.05[/C][C]-0.99[/C][C]0.89[/C][C]1[/C][/ROW]
[ROW][C]1:NA-0:1[/C][C]0.75[/C][C]-0.463[/C][C]1.963[/C][C]0.435[/C][/ROW]
[ROW][C]0:NA-1:1[/C][C]-0.371[/C][C]-1.101[/C][C]0.358[/C][C]0.639[/C][/ROW]
[ROW][C]1:NA-1:1[/C][C]0.429[/C][C]-0.63[/C][C]1.488[/C][C]0.82[/C][/ROW]
[ROW][C]1:NA-0:NA[/C][C]0.8[/C][C]-0.372[/C][C]1.972[/C][C]0.328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137509&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137509&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
1-00.4780.1530.8020.005
1-0-0.22-0.6430.2040.418
NA-0-0.056-0.5960.4840.965
NA-10.164-0.3420.670.708
1:0-0:00.625-0.2331.4830.262
0:1-0:00-0.9910.9911
1:1-0:00.321-0.4731.1160.82
0:NA-0:0-0.05-0.990.891
1:NA-0:00.75-0.4631.9630.435
0:1-1:0-0.625-1.4830.2330.262
1:1-1:0-0.304-0.9240.3170.677
0:NA-1:0-0.675-1.4740.1240.137
1:NA-1:00.125-0.9821.2320.999
1:1-0:10.321-0.4731.1160.82
0:NA-0:1-0.05-0.990.891
1:NA-0:10.75-0.4631.9630.435
0:NA-1:1-0.371-1.1010.3580.639
1:NA-1:10.429-0.631.4880.82
1:NA-0:NA0.8-0.3721.9720.328






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.6510.663
31 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.651 & 0.663 \tabularnewline
  & 31 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=137509&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]0.651[/C][C]0.663[/C][/ROW]
[ROW][C] [/C][C]31[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=137509&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=137509&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)
Group50.6510.663
31


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')