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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 computationMon, 23 Jan 2017 11:47:19 +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/2017/Jan/23/t1485168506dx7bktfac5hiwm9.htm/, Retrieved Thu, 31 Oct 2024 23:51:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=304883, Retrieved Thu, 31 Oct 2024 23:51:44 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2017-01-23 10:47:19] [8fee619fda962476c4dedef05f7f9476] [Current]
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Dataseries X:
6 1 "'bach'"
7 0 "'bach'"
2 0 "'bach'"
11 0 "'bach'"
13 0 "'bach'"
3 1 "'bach'"
17 0 "'bach'"
10 0 "'bach'"
4 1 "'bach'"
12 0 "'bach'"
7 0 "'scha'"
11 0 "'scha'"
3 0 "'scha'"
5 1 "'scha'"
1 0 "'scha'"
12 0 "'scha'"
18 0 "'scha'"
8 1 "'scha'"
6 1 "'scha'"
1 0 "'scha'"




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=304883&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=304883&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304883&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 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
means10.286-5.952-2.7144.714

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 10.286 & -5.952 & -2.714 & 4.714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304883&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]10.286[/C][C]-5.952[/C][C]-2.714[/C][C]4.714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304883&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304883&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
means10.286-5.952-2.7144.714







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A154.28854.2882.2130.156
Treatment_B18.458.450.3440.565
Treatment_A:Treatment_B123.33623.3360.9510.344
Residuals16392.47624.53

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 54.288 & 54.288 & 2.213 & 0.156 \tabularnewline
Treatment_B & 1 & 8.45 & 8.45 & 0.344 & 0.565 \tabularnewline
Treatment_A:Treatment_B & 1 & 23.336 & 23.336 & 0.951 & 0.344 \tabularnewline
Residuals & 16 & 392.476 & 24.53 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304883&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]54.288[/C][C]54.288[/C][C]2.213[/C][C]0.156[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]8.45[/C][C]8.45[/C][C]0.344[/C][C]0.565[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]23.336[/C][C]23.336[/C][C]0.951[/C][C]0.344[/C][/ROW]
[ROW][C]Residuals[/C][C]16[/C][C]392.476[/C][C]24.53[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304883&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304883&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_A154.28854.2882.2130.156
Treatment_B18.458.450.3440.565
Treatment_A:Treatment_B123.33623.3360.9510.344
Residuals16392.47624.53







Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-3.595-8.7181.5280.156
'scha'-'bach'-1.3-5.9953.3950.565
1:'bach'-0:'bach'-5.952-15.7313.8260.336
0:'scha'-0:'bach'-2.714-10.2884.860.737
1:'scha'-0:'bach'-3.952-13.7315.8260.661
0:'scha'-1:'bach'3.238-6.5413.0160.78
1:'scha'-1:'bach'2-9.5713.570.959
1:'scha'-0:'scha'-1.238-11.0168.540.983

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -3.595 & -8.718 & 1.528 & 0.156 \tabularnewline
'scha'-'bach' & -1.3 & -5.995 & 3.395 & 0.565 \tabularnewline
1:'bach'-0:'bach' & -5.952 & -15.731 & 3.826 & 0.336 \tabularnewline
0:'scha'-0:'bach' & -2.714 & -10.288 & 4.86 & 0.737 \tabularnewline
1:'scha'-0:'bach' & -3.952 & -13.731 & 5.826 & 0.661 \tabularnewline
0:'scha'-1:'bach' & 3.238 & -6.54 & 13.016 & 0.78 \tabularnewline
1:'scha'-1:'bach' & 2 & -9.57 & 13.57 & 0.959 \tabularnewline
1:'scha'-0:'scha' & -1.238 & -11.016 & 8.54 & 0.983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304883&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]-3.595[/C][C]-8.718[/C][C]1.528[/C][C]0.156[/C][/ROW]
[ROW][C]'scha'-'bach'[/C][C]-1.3[/C][C]-5.995[/C][C]3.395[/C][C]0.565[/C][/ROW]
[ROW][C]1:'bach'-0:'bach'[/C][C]-5.952[/C][C]-15.731[/C][C]3.826[/C][C]0.336[/C][/ROW]
[ROW][C]0:'scha'-0:'bach'[/C][C]-2.714[/C][C]-10.288[/C][C]4.86[/C][C]0.737[/C][/ROW]
[ROW][C]1:'scha'-0:'bach'[/C][C]-3.952[/C][C]-13.731[/C][C]5.826[/C][C]0.661[/C][/ROW]
[ROW][C]0:'scha'-1:'bach'[/C][C]3.238[/C][C]-6.54[/C][C]13.016[/C][C]0.78[/C][/ROW]
[ROW][C]1:'scha'-1:'bach'[/C][C]2[/C][C]-9.57[/C][C]13.57[/C][C]0.959[/C][/ROW]
[ROW][C]1:'scha'-0:'scha'[/C][C]-1.238[/C][C]-11.016[/C][C]8.54[/C][C]0.983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304883&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304883&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
1-0-3.595-8.7181.5280.156
'scha'-'bach'-1.3-5.9953.3950.565
1:'bach'-0:'bach'-5.952-15.7313.8260.336
0:'scha'-0:'bach'-2.714-10.2884.860.737
1:'scha'-0:'bach'-3.952-13.7315.8260.661
0:'scha'-1:'bach'3.238-6.5413.0160.78
1:'scha'-1:'bach'2-9.5713.570.959
1:'scha'-0:'scha'-1.238-11.0168.540.983







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group32.2360.123
16

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 2.236 & 0.123 \tabularnewline
  & 16 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304883&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]2.236[/C][C]0.123[/C][/ROW]
[ROW][C] [/C][C]16[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304883&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304883&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)
Group32.2360.123
16



Parameters (Session):
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')