FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationSat, 04 Jul 2020 19:28:54 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Jul/04/t1593883942ha5z6581h2qfgcp.htm/, Retrieved Fri, 26 Apr 2024 02:13:16 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 26 Apr 2024 02:13:16 +0200
QR Codes:

Original text written by user:
IsPrivate?This computation is private
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-1.56081953319633	'STD'	'VH'
-2.14565644272129	'STD'	'VH'
-1.84455092190476	'STD'	'VH'
-1.82721758695485	'STD'	'VH'
-1.57371456723007	'STD'	'VH'
-1.83056097331282	'STD'	'VH'
-1.9780398162714	'STD'	'VH'
-1.8827287572793	'STD'	'VH'
-1.26077040813751	'STD'	'F'
-1.59801670018547	'STD'	'F'
-1.5097154743611	'STD'	'F'
-1.39577559879453	'STD'	'F'
-1.21065737948472	'STD'	'F'
-1.30562331235357	'STD'	'F'
-1.70275016740384	'STD'	'F'
-1.130407277118	'STD'	'F'
-0.865855334078417	'CAF'	'VH'
-0.879630415422759	'CAF'	'VH'
-1.2009824096476	'CAF'	'VH'
-0.691775333228297	'CAF'	'VH'
-0.962195388639861	'CAF'	'VH'
-1.21623373483694	'CAF'	'VH'
-1.2257740967228	'CAF'	'VH'
-1.32684350395103	'CAF'	'VH'
-0.289495104033093	'CAF'	'F'
-0.915627204280545	'CAF'	'F'
-0.785542548376914	'CAF'	'F'
-1.28424873936245	'CAF'	'F'
-1.07222563761951	'CAF'	'F'
-1.59159254767393	'CAF'	'F'
-0.848904965771165	'CAF'	'F'
-0.828412152653605	'CAF'	'F'

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B
means-0.952-0.437-0.094-0.347

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & -0.952 & -0.437 & -0.094 & -0.347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]-0.952[/C][C]-0.437[/C][C]-0.094[/C][C]-0.347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
means-0.952-0.437-0.094-0.347






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A12.9842.98443.3780
Treatment_B10.5730.5738.3330.007
Treatment_A:Treatment_B10.2410.2413.5020.072
Residuals281.9260.069 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 2.984 & 2.984 & 43.378 & 0 \tabularnewline
Treatment_B & 1 & 0.573 & 0.573 & 8.333 & 0.007 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.241 & 0.241 & 3.502 & 0.072 \tabularnewline
Residuals & 28 & 1.926 & 0.069 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2.984[/C][C]2.984[/C][C]43.378[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.573[/C][C]0.573[/C][C]8.333[/C][C]0.007[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.241[/C][C]0.241[/C][C]3.502[/C][C]0.072[/C][/ROW]
[ROW][C]Residuals[/C][C]28[/C][C]1.926[/C][C]0.069[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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_A12.9842.98443.3780
Treatment_B10.5730.5738.3330.007
Treatment_A:Treatment_B10.2410.2413.5020.072
Residuals281.9260.069






Tukey Honest Significant Difference Comparisons
difflwruprp adj
STD-CAF-0.611-0.801-0.4210
VH-F-0.268-0.458-0.0780.007
STD:F-CAF:F-0.437-0.795-0.0790.012
CAF:VH-CAF:F-0.094-0.4520.2640.889
STD:VH-CAF:F-0.878-1.236-0.520
CAF:VH-STD:F0.343-0.0150.7010.064
STD:VH-STD:F-0.441-0.799-0.0830.011
STD:VH-CAF:VH-0.784-1.142-0.4260

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
STD-CAF & -0.611 & -0.801 & -0.421 & 0 \tabularnewline
VH-F & -0.268 & -0.458 & -0.078 & 0.007 \tabularnewline
STD:F-CAF:F & -0.437 & -0.795 & -0.079 & 0.012 \tabularnewline
CAF:VH-CAF:F & -0.094 & -0.452 & 0.264 & 0.889 \tabularnewline
STD:VH-CAF:F & -0.878 & -1.236 & -0.52 & 0 \tabularnewline
CAF:VH-STD:F & 0.343 & -0.015 & 0.701 & 0.064 \tabularnewline
STD:VH-STD:F & -0.441 & -0.799 & -0.083 & 0.011 \tabularnewline
STD:VH-CAF:VH & -0.784 & -1.142 & -0.426 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]STD-CAF[/C][C]-0.611[/C][C]-0.801[/C][C]-0.421[/C][C]0[/C][/ROW]
[ROW][C]VH-F[/C][C]-0.268[/C][C]-0.458[/C][C]-0.078[/C][C]0.007[/C][/ROW]
[ROW][C]STD:F-CAF:F[/C][C]-0.437[/C][C]-0.795[/C][C]-0.079[/C][C]0.012[/C][/ROW]
[ROW][C]CAF:VH-CAF:F[/C][C]-0.094[/C][C]-0.452[/C][C]0.264[/C][C]0.889[/C][/ROW]
[ROW][C]STD:VH-CAF:F[/C][C]-0.878[/C][C]-1.236[/C][C]-0.52[/C][C]0[/C][/ROW]
[ROW][C]CAF:VH-STD:F[/C][C]0.343[/C][C]-0.015[/C][C]0.701[/C][C]0.064[/C][/ROW]
[ROW][C]STD:VH-STD:F[/C][C]-0.441[/C][C]-0.799[/C][C]-0.083[/C][C]0.011[/C][/ROW]
[ROW][C]STD:VH-CAF:VH[/C][C]-0.784[/C][C]-1.142[/C][C]-0.426[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
STD-CAF-0.611-0.801-0.4210
VH-F-0.268-0.458-0.0780.007
STD:F-CAF:F-0.437-0.795-0.0790.012
CAF:VH-CAF:F-0.094-0.4520.2640.889
STD:VH-CAF:F-0.878-1.236-0.520
CAF:VH-STD:F0.343-0.0150.7010.064
STD:VH-STD:F-0.441-0.799-0.0830.011
STD:VH-CAF:VH-0.784-1.142-0.4260






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.9290.44
28 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.929 & 0.44 \tabularnewline
  & 28 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.929[/C][C]0.44[/C][/ROW]
[ROW][C] [/C][C]28[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
Group30.9290.44
28


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<-leveneTest(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')