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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 computationThu, 18 Dec 2014 12:23:17 +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/18/t1418905423t5xd77jr699rmvn.htm/, Retrieved Fri, 17 May 2024 13:36:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270854, Retrieved Fri, 17 May 2024 13:36:14 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

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] [2014-12-18 12:23:17] [35f348c3c3a72505e6ab9e88b1cb72c0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18 1 0
23 1 1
22 1 0
22 1 1
19 1 1
25 1 1
28 1 0
16 1 1
28 1 1
21 1 1
22 1 1
24 1 1
24 1 1
26 1 0
28 1 0
24 0 0
20 1 1
26 1 0
21 0 1
28 1 0
27 1 1
23 1 1
24 1 0
24 1 1
22 1 1
21 1 1
25 0 1
20 0 0
21 1 1
26 1 0
23 1 0
21 1 0
27 1 1
25 1 1
23 1 1
25 1 1
23 1 0
19 0 1
22 1 1
24 1 0
19 1 1
21 1 1
27 1 1
25 1 1
25 0 1
23 1 0
17 1 1
28 0 1
25 1 0
20 0 1
25 0 1
21 0 1
24 1 1
28 0 1
20 1 1
19 1 1
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21 1 1
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23 0 1
18 1 1
27 1 0
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23 0 1
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27 1 1
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23 1 0
24 1 0
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23 1 1
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26 0 1
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22 0 0
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23 0 0
24 0 0
24 0 0
23 0 1
22 1 1
24 1 1
19 1 1
25 1 1

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270854&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270854&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270854&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'Gertrude Mary Cox' @ cox.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means23.3481.1520.066-2.091

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 23.348 & 1.152 & 0.066 & -2.091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270854&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]23.348[/C][C]1.152[/C][C]0.066[/C][C]-2.091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270854&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270854&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
means23.3481.1520.066-2.091






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.6480.6480.090.765
Treatment_B131.33531.3354.3530.039
Treatment_A:Treatment_B130.2330.234.20.043
Residuals112806.2277.198 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.648 & 0.648 & 0.09 & 0.765 \tabularnewline
Treatment_B & 1 & 31.335 & 31.335 & 4.353 & 0.039 \tabularnewline
Treatment_A:Treatment_B & 1 & 30.23 & 30.23 & 4.2 & 0.043 \tabularnewline
Residuals & 112 & 806.227 & 7.198 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270854&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]0.648[/C][C]0.648[/C][C]0.09[/C][C]0.765[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]31.335[/C][C]31.335[/C][C]4.353[/C][C]0.039[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]30.23[/C][C]30.23[/C][C]4.2[/C][C]0.043[/C][/ROW]
[ROW][C]Residuals[/C][C]112[/C][C]806.227[/C][C]7.198[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270854&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270854&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_A10.6480.6480.090.765
Treatment_B131.33531.3354.3530.039
Treatment_A:Treatment_B130.2330.234.20.043
Residuals112806.2277.198






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.15-1.1430.8420.765
1-0-1.056-2.062-0.0510.04
1:0-0:01.152-0.893.1940.458
0:1-0:00.066-1.8882.021
1:1-0:0-0.873-2.7040.9580.601
0:1-1:0-1.086-3.0170.8450.461
1:1-1:0-2.025-3.832-0.2180.022
1:1-0:1-0.939-2.6450.7680.481

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.15 & -1.143 & 0.842 & 0.765 \tabularnewline
1-0 & -1.056 & -2.062 & -0.051 & 0.04 \tabularnewline
1:0-0:0 & 1.152 & -0.89 & 3.194 & 0.458 \tabularnewline
0:1-0:0 & 0.066 & -1.888 & 2.02 & 1 \tabularnewline
1:1-0:0 & -0.873 & -2.704 & 0.958 & 0.601 \tabularnewline
0:1-1:0 & -1.086 & -3.017 & 0.845 & 0.461 \tabularnewline
1:1-1:0 & -2.025 & -3.832 & -0.218 & 0.022 \tabularnewline
1:1-0:1 & -0.939 & -2.645 & 0.768 & 0.481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270854&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]-0.15[/C][C]-1.143[/C][C]0.842[/C][C]0.765[/C][/ROW]
[ROW][C]1-0[/C][C]-1.056[/C][C]-2.062[/C][C]-0.051[/C][C]0.04[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]1.152[/C][C]-0.89[/C][C]3.194[/C][C]0.458[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.066[/C][C]-1.888[/C][C]2.02[/C][C]1[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-0.873[/C][C]-2.704[/C][C]0.958[/C][C]0.601[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-1.086[/C][C]-3.017[/C][C]0.845[/C][C]0.461[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-2.025[/C][C]-3.832[/C][C]-0.218[/C][C]0.022[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.939[/C][C]-2.645[/C][C]0.768[/C][C]0.481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270854&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270854&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
1-0-0.15-1.1430.8420.765
1-0-1.056-2.062-0.0510.04
1:0-0:01.152-0.893.1940.458
0:1-0:00.066-1.8882.021
1:1-0:0-0.873-2.7040.9580.601
0:1-1:0-1.086-3.0170.8450.461
1:1-1:0-2.025-3.832-0.2180.022
1:1-0:1-0.939-2.6450.7680.481






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.1440.335
112 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.144 & 0.335 \tabularnewline
  & 112 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270854&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]1.144[/C][C]0.335[/C][/ROW]
[ROW][C] [/C][C]112[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270854&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270854&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)
Group31.1440.335
112


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')