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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 computationTue, 23 Jan 2018 15:46:33 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Jan/23/t1516719046bf1uldc0jb6gio6.htm/, Retrieved Wed, 08 May 2024 09:06:00 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 09:06:00 +0200
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
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Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time9 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]9 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B
means19.077-0.1862.191-0.737

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 19.077 & -0.186 & 2.191 & -0.737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]19.077[/C][C]-0.186[/C][C]2.191[/C][C]-0.737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
means19.077-0.1862.191-0.737






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A113.38213.3820.5230.47
Treatment_B1224.905224.9058.7910.003
Treatment_A:Treatment_B19.1789.1780.3590.55
Residuals2747009.53225.582 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 13.382 & 13.382 & 0.523 & 0.47 \tabularnewline
Treatment_B & 1 & 224.905 & 224.905 & 8.791 & 0.003 \tabularnewline
Treatment_A:Treatment_B & 1 & 9.178 & 9.178 & 0.359 & 0.55 \tabularnewline
Residuals & 274 & 7009.532 & 25.582 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]13.382[/C][C]13.382[/C][C]0.523[/C][C]0.47[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]224.905[/C][C]224.905[/C][C]8.791[/C][C]0.003[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]9.178[/C][C]9.178[/C][C]0.359[/C][C]0.55[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]7009.532[/C][C]25.582[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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_A113.38213.3820.5230.47
Treatment_B1224.905224.9058.7910.003
Treatment_A:Treatment_B19.1789.1780.3590.55
Residuals2747009.53225.582






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.439-1.6340.7560.47
1-01.8080.6033.0140.003
1:0-0:0-0.186-2.5812.2090.997
0:1-0:02.191-0.0544.4350.059
1:1-0:01.268-0.8763.4110.422
0:1-1:02.3770.0284.7250.046
1:1-1:01.454-0.7983.7060.342
1:1-0:1-0.923-3.0141.1680.665

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.439 & -1.634 & 0.756 & 0.47 \tabularnewline
1-0 & 1.808 & 0.603 & 3.014 & 0.003 \tabularnewline
1:0-0:0 & -0.186 & -2.581 & 2.209 & 0.997 \tabularnewline
0:1-0:0 & 2.191 & -0.054 & 4.435 & 0.059 \tabularnewline
1:1-0:0 & 1.268 & -0.876 & 3.411 & 0.422 \tabularnewline
0:1-1:0 & 2.377 & 0.028 & 4.725 & 0.046 \tabularnewline
1:1-1:0 & 1.454 & -0.798 & 3.706 & 0.342 \tabularnewline
1:1-0:1 & -0.923 & -3.014 & 1.168 & 0.665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.439[/C][C]-1.634[/C][C]0.756[/C][C]0.47[/C][/ROW]
[ROW][C]1-0[/C][C]1.808[/C][C]0.603[/C][C]3.014[/C][C]0.003[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.186[/C][C]-2.581[/C][C]2.209[/C][C]0.997[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]2.191[/C][C]-0.054[/C][C]4.435[/C][C]0.059[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]1.268[/C][C]-0.876[/C][C]3.411[/C][C]0.422[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]2.377[/C][C]0.028[/C][C]4.725[/C][C]0.046[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]1.454[/C][C]-0.798[/C][C]3.706[/C][C]0.342[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.923[/C][C]-3.014[/C][C]1.168[/C][C]0.665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1-0-0.439-1.6340.7560.47
1-01.8080.6033.0140.003
1:0-0:0-0.186-2.5812.2090.997
0:1-0:02.191-0.0544.4350.059
1:1-0:01.268-0.8763.4110.422
0:1-1:02.3770.0284.7250.046
1:1-1:01.454-0.7983.7060.342
1:1-0:1-0.923-3.0141.1680.665






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group33.3120.021
274 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.312 & 0.021 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3.312[/C][C]0.021[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
Group33.3120.021
274


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1111111111two.sided2211131332222212121212484848481111212FALSEFALSE12two.sidedtwo.sidedtwo.sided1two.sidedtwo.sided3 ; par2 = 22222222220.951122Do not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesInclude Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesTripleTriple11110110.30.30.30.990.990.990,990,990.991 ; par3 = 0.950.950.95Pearson Chi-SquaredExact Pearson Chi-Squared by SimulationExact Pearson Chi-Squared by Simulation0.95TRUE3200.95TRUETRUE3No Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendLinear TrendNo Linear TrendNo Linear TrendNo Linear Trendadditivemultiplicative01110011111520151515152 ; par4 = two.sidedlessgreaterTRUETRUETRUE11112120001121212111TRUE ; par5 = unpairedunpairedunpaired121112121212121212 ; par6 = 0.00.00.012121212121212121212White NoiseWhite NoiseWhite NoiseWhite Noise332 ; par7 = 0.950.950.950.95110 ; par8 = 210 ; par9 = 111 ; par10 = FALSE ;
Parameters (R input):
par1 = 3 ; par2 = 1 ; par3 = 2 ; 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')