Free Statistics

of Irreproducible Research!

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 computationTue, 25 Nov 2014 14:44:36 +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/2014/Nov/25/t14169266950hgko2doch6h1bp.htm/, Retrieved Sun, 19 May 2024 14:14:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258744, Retrieved Sun, 19 May 2024 14:14:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [Two-Way ANOVA] [2010-11-30 21:42:30] [74be16979710d4c4e7c6647856088456]
- RM    [Two-Way ANOVA] [Two-Way ANOVA - C...] [2011-11-28 17:22:56] [98fd0e87c3eb04e0cc2efde01dbafab6]
- RM D      [Two-Way ANOVA] [part 2- workshop ...] [2014-11-25 14:44:36] [355b666d4c6053a13022141b5cdab7ab] [Current]
Feedback Forum

Post a new message
Dataseries X:
4	'SMK'	'hot'
5	'SMK'	'hot'
3	'SMK'	'hot'
4	'SMK'	'hot'
5	'SMK'	'hot'
3	'SMK'	'hot'
7	'SMK'	'hot'
5	'SMK'	'hot'
6	'SMK'	'hot'
3	'SMK'	'hot'
2	'SMK'	'hot'
4	'SMK'	'hot'
5	'SMK'	'hot'
2	'SMK'	'hot'
3	'SMK'	'hot'
6	'SMK'	'hot'
4	'SMK'	'hot'
4	'SMK'	'hot'
6	'SMK'	'hot'
2	'SMK'	'hot'
3	'SMK'	'mild'
5	'SMK'	'mild'
4	'SMK'	'mild'
2	'SMK'	'mild'
7	'SMK'	'mild'
1	'SMK'	'mild'
4	'SMK'	'mild'
4	'SMK'	'mild'
7	'SMK'	'mild'
4	'SMK'	'mild'
3	'SMK'	'mild'
3	'SMK'	'mild'
3	'SMK'	'mild'
3	'SMK'	'mild'
2	'SMK'	'mild'
5	'SMK'	'mild'
5	'SMK'	'mild'
3	'SMK'	'mild'
6	'SMK'	'mild'
2	'SMK'	'mild'
8	'NS'	'hot'
9	'NS'	'hot'
10	'NS'	'hot'
7	'NS'	'hot'
8	'NS'	'hot'
9	'NS'	'hot'
10	'NS'	'hot'
6	'NS'	'hot'
6	'NS'	'hot'
7	'NS'	'hot'
8	'NS'	'hot'
9	'NS'	'hot'
8	'NS'	'hot'
7	'NS'	'hot'
5	'NS'	'hot'
11	'NS'	'hot'
7	'NS'	'hot'
8	'NS'	'hot'
10	'NS'	'hot'
9	'NS'	'hot'
3	'NS'	'mild'
5	'NS'	'mild'
4	'NS'	'mild'
2	'NS'	'mild'
6	'NS'	'mild'
1	'NS'	'mild'
4	'NS'	'mild'
4	'NS'	'mild'
5	'NS'	'mild'
4	'NS'	'mild'
3	'NS'	'mild'
3	'NS'	'mild'
4	'NS'	'mild'
3	'NS'	'mild'
2	'NS'	'mild'
5	'NS'	'mild'
4	'NS'	'mild'
3	'NS'	'mild'
6	'NS'	'mild'




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=258744&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=258744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258744&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means8.1-3.95-4.3634.013

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 8.1 & -3.95 & -4.363 & 4.013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258744&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]8.1[/C][C]-3.95[/C][C]-4.363[/C][C]4.013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258744&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
means8.1-3.95-4.3634.013







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A178.93778.93734.9830
Treatment_B1107.234107.23447.5230
Treatment_A:Treatment_B179.48179.48135.2240
Residuals75169.2342.256

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 78.937 & 78.937 & 34.983 & 0 \tabularnewline
Treatment_B & 1 & 107.234 & 107.234 & 47.523 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 79.481 & 79.481 & 35.224 & 0 \tabularnewline
Residuals & 75 & 169.234 & 2.256 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258744&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]78.937[/C][C]78.937[/C][C]34.983[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]107.234[/C][C]107.234[/C][C]47.523[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]79.481[/C][C]79.481[/C][C]35.224[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]75[/C][C]169.234[/C][C]2.256[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258744&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258744&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_A178.93778.93734.9830
Treatment_B1107.234107.23447.5230
Treatment_A:Treatment_B179.48179.48135.2240
Residuals75169.2342.256







Tukey Honest Significant Difference Comparisons
difflwruprp adj
SMK-NS-1.999-2.673-1.3260
mild-hot-2.33-3.004-1.6570
SMK:hot-NS:hot-3.95-5.198-2.7020
NS:mild-NS:hot-4.363-5.628-3.0990
SMK:mild-NS:hot-4.3-5.548-3.0520
NS:mild-SMK:hot-0.413-1.6780.8510.826
SMK:mild-SMK:hot-0.35-1.5980.8980.882
SMK:mild-NS:mild0.063-1.2011.3280.999

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
SMK-NS & -1.999 & -2.673 & -1.326 & 0 \tabularnewline
mild-hot & -2.33 & -3.004 & -1.657 & 0 \tabularnewline
SMK:hot-NS:hot & -3.95 & -5.198 & -2.702 & 0 \tabularnewline
NS:mild-NS:hot & -4.363 & -5.628 & -3.099 & 0 \tabularnewline
SMK:mild-NS:hot & -4.3 & -5.548 & -3.052 & 0 \tabularnewline
NS:mild-SMK:hot & -0.413 & -1.678 & 0.851 & 0.826 \tabularnewline
SMK:mild-SMK:hot & -0.35 & -1.598 & 0.898 & 0.882 \tabularnewline
SMK:mild-NS:mild & 0.063 & -1.201 & 1.328 & 0.999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258744&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]SMK-NS[/C][C]-1.999[/C][C]-2.673[/C][C]-1.326[/C][C]0[/C][/ROW]
[ROW][C]mild-hot[/C][C]-2.33[/C][C]-3.004[/C][C]-1.657[/C][C]0[/C][/ROW]
[ROW][C]SMK:hot-NS:hot[/C][C]-3.95[/C][C]-5.198[/C][C]-2.702[/C][C]0[/C][/ROW]
[ROW][C]NS:mild-NS:hot[/C][C]-4.363[/C][C]-5.628[/C][C]-3.099[/C][C]0[/C][/ROW]
[ROW][C]SMK:mild-NS:hot[/C][C]-4.3[/C][C]-5.548[/C][C]-3.052[/C][C]0[/C][/ROW]
[ROW][C]NS:mild-SMK:hot[/C][C]-0.413[/C][C]-1.678[/C][C]0.851[/C][C]0.826[/C][/ROW]
[ROW][C]SMK:mild-SMK:hot[/C][C]-0.35[/C][C]-1.598[/C][C]0.898[/C][C]0.882[/C][/ROW]
[ROW][C]SMK:mild-NS:mild[/C][C]0.063[/C][C]-1.201[/C][C]1.328[/C][C]0.999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258744&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258744&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
SMK-NS-1.999-2.673-1.3260
mild-hot-2.33-3.004-1.6570
SMK:hot-NS:hot-3.95-5.198-2.7020
NS:mild-NS:hot-4.363-5.628-3.0990
SMK:mild-NS:hot-4.3-5.548-3.0520
NS:mild-SMK:hot-0.413-1.6780.8510.826
SMK:mild-SMK:hot-0.35-1.5980.8980.882
SMK:mild-NS:mild0.063-1.2011.3280.999







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.3510.789
75

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.351 & 0.789 \tabularnewline
  & 75 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258744&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]0.351[/C][C]0.789[/C][/ROW]
[ROW][C] [/C][C]75[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258744&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258744&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)
Group30.3510.789
75



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')