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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 computationWed, 17 Dec 2014 20:13:02 +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/Dec/17/t14188472685d3p3b81h03oqbq.htm/, Retrieved Thu, 16 May 2024 20:07:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270644, Retrieved Thu, 16 May 2024 20:07:07 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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] [] [2014-12-17 20:13:02] [18673d63f90870b9c004059cd6229007] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270644&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270644&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'Sir Maurice George Kendall' @ kendall.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means94.3332.38538.9582.408

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 94.333 & 2.385 & 38.958 & 2.408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270644&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]94.333[/C][C]2.385[/C][C]38.958[/C][C]2.408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270644&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
means94.3332.38538.9582.408






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A18882.8258882.8257.5640.006
Treatment_B1108770.798108770.79892.6170
Treatment_A:Treatment_B195.08195.0810.0810.776
Residuals274321788.1731174.409 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 8882.825 & 8882.825 & 7.564 & 0.006 \tabularnewline
Treatment_B & 1 & 108770.798 & 108770.798 & 92.617 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 95.081 & 95.081 & 0.081 & 0.776 \tabularnewline
Residuals & 274 & 321788.173 & 1174.409 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270644&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]8882.825[/C][C]8882.825[/C][C]7.564[/C][C]0.006[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]108770.798[/C][C]108770.798[/C][C]92.617[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]95.081[/C][C]95.081[/C][C]0.081[/C][C]0.776[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]321788.173[/C][C]1174.409[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270644&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_A18882.8258882.8257.5640.006
Treatment_B1108770.798108770.79892.6170
Treatment_A:Treatment_B195.08195.0810.0810.776
Residuals274321788.1731174.409






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-011.4123.24319.5820.006
'S'-'B'38.82530.7346.9190
1:'B'-0:'B'2.385-12.83317.6040.977
0:'S'-0:'B'38.95822.45255.4650
1:'S'-0:'B'43.75229.87957.6250
0:'S'-1:'B'36.57319.65953.4870
1:'S'-1:'B'41.36627.01155.7220
1:'S'-0:'S'4.793-10.92120.5080.86

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 11.412 & 3.243 & 19.582 & 0.006 \tabularnewline
'S'-'B' & 38.825 & 30.73 & 46.919 & 0 \tabularnewline
1:'B'-0:'B' & 2.385 & -12.833 & 17.604 & 0.977 \tabularnewline
0:'S'-0:'B' & 38.958 & 22.452 & 55.465 & 0 \tabularnewline
1:'S'-0:'B' & 43.752 & 29.879 & 57.625 & 0 \tabularnewline
0:'S'-1:'B' & 36.573 & 19.659 & 53.487 & 0 \tabularnewline
1:'S'-1:'B' & 41.366 & 27.011 & 55.722 & 0 \tabularnewline
1:'S'-0:'S' & 4.793 & -10.921 & 20.508 & 0.86 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270644&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]11.412[/C][C]3.243[/C][C]19.582[/C][C]0.006[/C][/ROW]
[ROW][C]'S'-'B'[/C][C]38.825[/C][C]30.73[/C][C]46.919[/C][C]0[/C][/ROW]
[ROW][C]1:'B'-0:'B'[/C][C]2.385[/C][C]-12.833[/C][C]17.604[/C][C]0.977[/C][/ROW]
[ROW][C]0:'S'-0:'B'[/C][C]38.958[/C][C]22.452[/C][C]55.465[/C][C]0[/C][/ROW]
[ROW][C]1:'S'-0:'B'[/C][C]43.752[/C][C]29.879[/C][C]57.625[/C][C]0[/C][/ROW]
[ROW][C]0:'S'-1:'B'[/C][C]36.573[/C][C]19.659[/C][C]53.487[/C][C]0[/C][/ROW]
[ROW][C]1:'S'-1:'B'[/C][C]41.366[/C][C]27.011[/C][C]55.722[/C][C]0[/C][/ROW]
[ROW][C]1:'S'-0:'S'[/C][C]4.793[/C][C]-10.921[/C][C]20.508[/C][C]0.86[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270644&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
1-011.4123.24319.5820.006
'S'-'B'38.82530.7346.9190
1:'B'-0:'B'2.385-12.83317.6040.977
0:'S'-0:'B'38.95822.45255.4650
1:'S'-0:'B'43.75229.87957.6250
0:'S'-1:'B'36.57319.65953.4870
1:'S'-1:'B'41.36627.01155.7220
1:'S'-0:'S'4.793-10.92120.5080.86






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group34.0770.007
274 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 4.077 & 0.007 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270644&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]4.077[/C][C]0.007[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270644&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270644&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)
Group34.0770.007
274


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')