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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 computationSun, 18 Dec 2016 16:58:36 +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/2016/Dec/18/t1482077392sxohz4w74i7w6jm.htm/, Retrieved Fri, 01 Nov 2024 03:47:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301158, Retrieved Fri, 01 Nov 2024 03:47:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86

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] [Paper Statistiek] [2016-12-18 15:58:36] [1e2703d0f11438bcd65480dae45a3781] [Current]
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Dataset

Dataseries X:
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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 time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301158&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301158&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B - 1
means4.757.5614141314.25108.59116.56.597.258738.51.75NA1.5-5-4-4.25-4.2502.5NANANA2.5NA-4.833-4-5.25-1.833NANANANA0.333NA-7.857-6.818-7.317-2.571-1NANANA3.75-7.583-4.5-5.45-6.056-1.583NANANANANA-10-9-5.333-6NANANANANANA-6-5-4NANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANA

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B - 1 \tabularnewline
means & 4.75 & 7.5 & 6 & 14 & 14 & 13 & 14.25 & 10 & 8.5 & 9 & 11 & 6.5 & 6.5 & 9 & 7.25 & 8 & 7 & 3 & 8.5 & 1.75 & NA & 1.5 & -5 & -4 & -4.25 & -4.25 & 0 & 2.5 & NA & NA & NA & 2.5 & NA & -4.833 & -4 & -5.25 & -1.833 & NA & NA & NA & NA & 0.333 & NA & -7.857 & -6.818 & -7.317 & -2.571 & -1 & NA & NA & NA & 3.75 & -7.583 & -4.5 & -5.45 & -6.056 & -1.583 & NA & NA & NA & NA & NA & -10 & -9 & -5.333 & -6 & NA & NA & NA & NA & NA & NA & -6 & -5 & -4 & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301158&T=1

[TABLE]
[ROW]ANOVA Model[/C][/ROW]
[ROW]Response ~ Treatment_A * Treatment_B - 1[/C][/ROW]
[ROW][C]means[/C][C]4.75[/C][C]7.5[/C][C]6[/C][C]14[/C][C]14[/C][C]13[/C][C]14.25[/C][C]10[/C][C]8.5[/C][C]9[/C][C]11[/C][C]6.5[/C][C]6.5[/C][C]9[/C][C]7.25[/C][C]8[/C][C]7[/C][C]3[/C][C]8.5[/C][C]1.75[/C][C]NA[/C][C]1.5[/C][C]-5[/C][C]-4[/C][C]-4.25[/C][C]-4.25[/C][C]0[/C][C]2.5[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]2.5[/C][C]NA[/C][C]-4.833[/C][C]-4[/C][C]-5.25[/C][C]-1.833[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.333[/C][C]NA[/C][C]-7.857[/C][C]-6.818[/C][C]-7.317[/C][C]-2.571[/C][C]-1[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]3.75[/C][C]-7.583[/C][C]-4.5[/C][C]-5.45[/C][C]-6.056[/C][C]-1.583[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]-10[/C][C]-9[/C][C]-5.333[/C][C]-6[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]-6[/C][C]-5[/C][C]-4[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301158&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 - 1
means4.757.5614141314.25108.59116.56.597.258738.51.75NA1.5-5-4-4.25-4.2502.5NANANA2.5NA-4.833-4-5.25-1.833NANANANA0.333NA-7.857-6.818-7.317-2.571-1NANANA3.75-7.583-4.5-5.45-6.056-1.583NANANANANA-10-9-5.333-6NANANANANANA-6-5-4NANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANA






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
11
Treatment_A1139339.4923576.3172133.2240
Treatment_B1123.9382.661.5870.128
Treatment_A:Treatment_B1186.1572.7791.6580.03
Residuals110184.4131.676 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 11 &  &  &  &  \tabularnewline
Treatment_A & 11 & 39339.492 & 3576.317 & 2133.224 & 0 \tabularnewline
Treatment_B & 11 & 23.938 & 2.66 & 1.587 & 0.128 \tabularnewline
Treatment_A:Treatment_B & 11 & 86.157 & 2.779 & 1.658 & 0.03 \tabularnewline
Residuals & 110 & 184.413 & 1.676 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301158&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]11[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]11[/C][C]39339.492[/C][C]3576.317[/C][C]2133.224[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]11[/C][C]23.938[/C][C]2.66[/C][C]1.587[/C][C]0.128[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]11[/C][C]86.157[/C][C]2.779[/C][C]1.658[/C][C]0.03[/C][/ROW]
[ROW][C]Residuals[/C][C]110[/C][C]184.413[/C][C]1.676[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301158&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301158&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)
11
Treatment_A1139339.4923576.3172133.2240
Treatment_B1123.9382.661.5870.128
Treatment_A:Treatment_B1186.1572.7791.6580.03
Residuals110184.4131.676






Must Include Intercept to use Tukey Test 

\begin{tabular}{lllllllll}
\hline
Must Include Intercept to use Tukey Test  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301158&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301158&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301158&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:

Must Include Intercept to use Tukey Test






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group500.6670.945
110 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 50 & 0.667 & 0.945 \tabularnewline
  & 110 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301158&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]50[/C][C]0.667[/C][C]0.945[/C][/ROW]
[ROW][C] [/C][C]110[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301158&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301158&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)
Group500.6670.945
110


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = FALSE ;
R code (references can be found in the software module):
par4 <- 'FALSE'
par3 <- '3'
par2 <- '2'
par1 <- '1'
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')