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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 computationFri, 23 Dec 2011 09:31:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324650729garour7nl1buk7z.htm/, Retrieved Fri, 01 Nov 2024 01:00:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160453, Retrieved Fri, 01 Nov 2024 01:00:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

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] [Task 8 - 2 way An...] [2011-10-29 11:16:56] [74b1e5a3104ff0b2404b2865a63336ad]
-   P   [Two-Way ANOVA] [WS V - question 8] [2011-11-08 22:31:23] [7c680a04865e75aa8ab422cdbfd97ac3]
- R P     [Two-Way ANOVA] [Paper two way anova] [2011-12-23 14:14:28] [7c680a04865e75aa8ab422cdbfd97ac3]
-    D        [Two-Way ANOVA] [Paper two way anova] [2011-12-23 14:31:36] [3e388c05c22237d436c48535c44f60bb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
'T'	0	1
'T'	0	0
'T'	1	1
'T'	0	1
'T'	0	1
'T'	0	0
'T'	0	0
'T'	1	1
'T'	1	0
'T'	0	0
'T'	0	1
'T'	1	1
'T'	1	0
'T'	1	1
'T'	0	0
'T'	0	1
'T'	0	0
'T'	0	1
'T'	1	0
'T'	0	1
'T'	0	1
'T'	0	1
'T'	0	0
'T'	-1	0
'T'	0	0
'T'	-1	0
'T'	0	1
'T'	0	1
'T'	0	0
'T'	0	1
'T'	-1	0
'T'	0	1
'T'	0	0
'T'	0	1
'T'	0	1
'T'	0	0
'T'	0	0
'E'	1	0
'E'	1	1
'E'	0	1
'E'	0	0
'E'	0	1
'E'	0	0
'E'	0	1
'E'	0	0
'E'	1	0
'E'	1	1
'E'	0	1
'E'	0	1
'E'	0	1
'E'	1	0
'E'	0	0
'E'	1	1
'E'	0	0
'E'	1	1
'E'	1	1
'E'	1	0
'E'	1	0
'E'	0	0
'E'	0	1
'E'	1	1
'E'	0	1
'E'	0	1
'E'	-1	1
'E'	0	0
'E'	1	0
'E'	1	1
'E'	0	1
'E'	0	1
'E'	0	0
'S'	1	1
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'S'	1	0
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'S'	0	1
'S'	0	0
'S'	0	1
'S'	0	0
'S'	0	1
'S'	1	0

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=160453&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=160453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160453&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
means0.429-0.376-0.429-0.1130.1230.323

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.429 & -0.376 & -0.429 & -0.113 & 0.123 & 0.323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160453&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.429[/C][C]-0.376[/C][C]-0.429[/C][C]-0.113[/C][C]0.123[/C][C]0.323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160453&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
means0.429-0.376-0.429-0.1130.1230.323






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
2
Treatment_A21.8250.9123.1610.047
Treatment_B20.0480.0480.1680.683
Treatment_A:Treatment_B20.4650.2320.8050.45
Residuals9928.5770.289 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 1.825 & 0.912 & 3.161 & 0.047 \tabularnewline
Treatment_B & 2 & 0.048 & 0.048 & 0.168 & 0.683 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.465 & 0.232 & 0.805 & 0.45 \tabularnewline
Residuals & 99 & 28.577 & 0.289 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160453&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]2[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]2[/C][C]1.825[/C][C]0.912[/C][C]3.161[/C][C]0.047[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0.048[/C][C]0.048[/C][C]0.168[/C][C]0.683[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.465[/C][C]0.232[/C][C]0.805[/C][C]0.45[/C][/ROW]
[ROW][C]Residuals[/C][C]99[/C][C]28.577[/C][C]0.289[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160453&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)
2
Treatment_A21.8250.9123.1610.047
Treatment_B20.0480.0480.1680.683
Treatment_A:Treatment_B20.4650.2320.8050.45
Residuals9928.5770.289






Tukey Honest Significant Difference Comparisons
difflwruprp adj
S-E-0.306-0.6170.0040.054
T-E-0.256-0.5620.0510.121
T-S0.051-0.250.3520.915
1-00.043-0.1650.2510.684
S:0-E:0-0.376-0.9260.1740.357
T:0-E:0-0.429-0.9850.1280.23
E:1-E:0-0.113-0.6630.4370.991
S:1-E:0-0.366-0.9380.2050.432
T:1-E:0-0.218-0.7680.3320.858
T:0-S:0-0.053-0.5660.4611
E:1-S:00.263-0.2430.770.659
S:1-S:00.01-0.520.541
T:1-S:00.158-0.3490.6640.944
E:1-T:00.316-0.1980.8290.479
S:1-T:00.062-0.4740.5990.999
T:1-T:00.211-0.3030.7240.84
S:1-E:1-0.253-0.7830.2770.733
T:1-E:1-0.105-0.6120.4010.991
T:1-S:10.148-0.3820.6780.965

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
S-E & -0.306 & -0.617 & 0.004 & 0.054 \tabularnewline
T-E & -0.256 & -0.562 & 0.051 & 0.121 \tabularnewline
T-S & 0.051 & -0.25 & 0.352 & 0.915 \tabularnewline
1-0 & 0.043 & -0.165 & 0.251 & 0.684 \tabularnewline
S:0-E:0 & -0.376 & -0.926 & 0.174 & 0.357 \tabularnewline
T:0-E:0 & -0.429 & -0.985 & 0.128 & 0.23 \tabularnewline
E:1-E:0 & -0.113 & -0.663 & 0.437 & 0.991 \tabularnewline
S:1-E:0 & -0.366 & -0.938 & 0.205 & 0.432 \tabularnewline
T:1-E:0 & -0.218 & -0.768 & 0.332 & 0.858 \tabularnewline
T:0-S:0 & -0.053 & -0.566 & 0.461 & 1 \tabularnewline
E:1-S:0 & 0.263 & -0.243 & 0.77 & 0.659 \tabularnewline
S:1-S:0 & 0.01 & -0.52 & 0.54 & 1 \tabularnewline
T:1-S:0 & 0.158 & -0.349 & 0.664 & 0.944 \tabularnewline
E:1-T:0 & 0.316 & -0.198 & 0.829 & 0.479 \tabularnewline
S:1-T:0 & 0.062 & -0.474 & 0.599 & 0.999 \tabularnewline
T:1-T:0 & 0.211 & -0.303 & 0.724 & 0.84 \tabularnewline
S:1-E:1 & -0.253 & -0.783 & 0.277 & 0.733 \tabularnewline
T:1-E:1 & -0.105 & -0.612 & 0.401 & 0.991 \tabularnewline
T:1-S:1 & 0.148 & -0.382 & 0.678 & 0.965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160453&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]S-E[/C][C]-0.306[/C][C]-0.617[/C][C]0.004[/C][C]0.054[/C][/ROW]
[ROW][C]T-E[/C][C]-0.256[/C][C]-0.562[/C][C]0.051[/C][C]0.121[/C][/ROW]
[ROW][C]T-S[/C][C]0.051[/C][C]-0.25[/C][C]0.352[/C][C]0.915[/C][/ROW]
[ROW][C]1-0[/C][C]0.043[/C][C]-0.165[/C][C]0.251[/C][C]0.684[/C][/ROW]
[ROW][C]S:0-E:0[/C][C]-0.376[/C][C]-0.926[/C][C]0.174[/C][C]0.357[/C][/ROW]
[ROW][C]T:0-E:0[/C][C]-0.429[/C][C]-0.985[/C][C]0.128[/C][C]0.23[/C][/ROW]
[ROW][C]E:1-E:0[/C][C]-0.113[/C][C]-0.663[/C][C]0.437[/C][C]0.991[/C][/ROW]
[ROW][C]S:1-E:0[/C][C]-0.366[/C][C]-0.938[/C][C]0.205[/C][C]0.432[/C][/ROW]
[ROW][C]T:1-E:0[/C][C]-0.218[/C][C]-0.768[/C][C]0.332[/C][C]0.858[/C][/ROW]
[ROW][C]T:0-S:0[/C][C]-0.053[/C][C]-0.566[/C][C]0.461[/C][C]1[/C][/ROW]
[ROW][C]E:1-S:0[/C][C]0.263[/C][C]-0.243[/C][C]0.77[/C][C]0.659[/C][/ROW]
[ROW][C]S:1-S:0[/C][C]0.01[/C][C]-0.52[/C][C]0.54[/C][C]1[/C][/ROW]
[ROW][C]T:1-S:0[/C][C]0.158[/C][C]-0.349[/C][C]0.664[/C][C]0.944[/C][/ROW]
[ROW][C]E:1-T:0[/C][C]0.316[/C][C]-0.198[/C][C]0.829[/C][C]0.479[/C][/ROW]
[ROW][C]S:1-T:0[/C][C]0.062[/C][C]-0.474[/C][C]0.599[/C][C]0.999[/C][/ROW]
[ROW][C]T:1-T:0[/C][C]0.211[/C][C]-0.303[/C][C]0.724[/C][C]0.84[/C][/ROW]
[ROW][C]S:1-E:1[/C][C]-0.253[/C][C]-0.783[/C][C]0.277[/C][C]0.733[/C][/ROW]
[ROW][C]T:1-E:1[/C][C]-0.105[/C][C]-0.612[/C][C]0.401[/C][C]0.991[/C][/ROW]
[ROW][C]T:1-S:1[/C][C]0.148[/C][C]-0.382[/C][C]0.678[/C][C]0.965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160453&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160453&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
S-E-0.306-0.6170.0040.054
T-E-0.256-0.5620.0510.121
T-S0.051-0.250.3520.915
1-00.043-0.1650.2510.684
S:0-E:0-0.376-0.9260.1740.357
T:0-E:0-0.429-0.9850.1280.23
E:1-E:0-0.113-0.6630.4370.991
S:1-E:0-0.366-0.9380.2050.432
T:1-E:0-0.218-0.7680.3320.858
T:0-S:0-0.053-0.5660.4611
E:1-S:00.263-0.2430.770.659
S:1-S:00.01-0.520.541
T:1-S:00.158-0.3490.6640.944
E:1-T:00.316-0.1980.8290.479
S:1-T:00.062-0.4740.5990.999
T:1-T:00.211-0.3030.7240.84
S:1-E:1-0.253-0.7830.2770.733
T:1-E:1-0.105-0.6120.4010.991
T:1-S:10.148-0.3820.6780.965






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group50.820.539
99 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 0.82 & 0.539 \tabularnewline
  & 99 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160453&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]5[/C][C]0.82[/C][C]0.539[/C][/ROW]
[ROW][C] [/C][C]99[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160453&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160453&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)
Group50.820.539
99


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = 3 ; par4 = TRUE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; 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')