FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationTue, 08 Nov 2011 12:41:52 -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/Nov/08/t1320774121potawz6btqreo3g.htm/, Retrieved Sun, 10 Nov 2024 19:45:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=140812, Retrieved Sun, 10 Nov 2024 19:45:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [Question 6 - best...] [2011-11-02 13:56:22] [d0cddc92c01af61bef0226b9e5ade9b3]
- RMPD  [Two-Way ANOVA] [] [2011-11-08 11:52:53] [97a82ed57455ec27012f2e899dc4f1a4]
-    D      [Two-Way ANOVA] [] [2011-11-08 17:41:52] [3b32143baae8ca4a077b118800e50af3] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0	1	'H'
0	1	'H'
0	1	'H'
1	1	'E'
1	1	'F'
0	1	'E'
1	0	'F'
0	0	'H'
0	0	'E'
1	1	'F'
0	0	'H'
1	0	'E'
0	0	'H'
0	1	'E'
0	1	'F'
0	0	'H'
1	0	'F'
0	0	'H'
0	1	'H'
0	0	'H'
0	0	'E'
1	0	'F'
1	0	'E'
1	0	'E'
0	1	'F'
0	0	'F'
0	0	'H'
0	1	'E'
1	1	'E'
0	1	'H'
1	1	'E'
1	1	'F'
0	1	'E'
1	0	'F'
0	0	'H'
1	0	'E'
1	0	'F'
1	0	'F'
0	0	'F'
1	0	'F'
1	1	'H'
1	0	'E'
0	0	'E'
0	0	'H'
1	1	'E'
0	1	'F'
0	0	'F'
0	0	'H'
0	1	'E'
1	1	'F'
1	1	'E'
0	1	'H'
0	1	'H'
0	1	'H'
0	1	'E'
0	0	'H'
1	0	'E'
0	1	'H'
0	1	'F'
0	1	'H'
1	0	'F'
0	1	'E'
1	1	'E'
0	0	'F'
0	1	'H'
0	0	'F'
0	1	'E'
-1	1	'E'
0	0	'H'
0	1	'H'
0	1	'F'
0	1	'H'
1	0	'E'
0	1	'F'
1	0	'E'
0	0	'E'
0	0	'E'
0	1	'F'
0	1	'E'
1	1	'F'
0	1	'H'
0	1	'H'
0	1	'H'
0	0	'F'
0	1	'H'
0	1	'H'
1	1	'F'
1	1	'F'
0	0	'H'
0	1	'F'
0	1	'H'
0	0	'E'
1	1	'F'
0	0	'E'
0	1	'H'
1	1	'F'
0	1	'F'
0	1	'H'
1	1	'E'
0	0	'F'
0	1	'H'
0	1	'E'
0	0	'F'
0	0	'H'
0	1	'H'
1	1	'F'
1	1	'F'
0	1	'H'
0	0	'E'
0	1	'H'
0	1	'E'
0	0	'E'
0	1	'F'
0	1	'F'

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140812&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140812&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'Gwilym Jenkins' @ jenkins.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.471-0.1550.029-0.4710.1550.193

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.471 & -0.155 & 0.029 & -0.471 & 0.155 & 0.193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140812&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.471[/C][C]-0.155[/C][C]0.029[/C][C]-0.471[/C][C]0.155[/C][C]0.193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140812&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
means0.471-0.1550.029-0.4710.1550.193






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.1420.1420.7390.392
Treatment_B14.7262.36312.2690
Treatment_A:Treatment_B10.1890.0940.4910.614
Residuals10820.8020.193 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.142 & 0.142 & 0.739 & 0.392 \tabularnewline
Treatment_B & 1 & 4.726 & 2.363 & 12.269 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.189 & 0.094 & 0.491 & 0.614 \tabularnewline
Residuals & 108 & 20.802 & 0.193 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140812&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]0.142[/C][C]0.142[/C][C]0.739[/C][C]0.392[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]4.726[/C][C]2.363[/C][C]12.269[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.189[/C][C]0.094[/C][C]0.491[/C][C]0.614[/C][/ROW]
[ROW][C]Residuals[/C][C]108[/C][C]20.802[/C][C]0.193[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140812&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_A10.1420.1420.7390.392
Treatment_B14.7262.36312.2690
Treatment_A:Treatment_B10.1890.0940.4910.614
Residuals10820.8020.193






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-0-0.072-0.2370.0940.392
F-E0.115-0.1280.3570.501
H-E-0.355-0.595-0.1160.002
H-F-0.47-0.706-0.2340
1:E-0:E-0.155-0.580.270.897
0:F-0:E0.029-0.4140.4731
1:F-0:E0.029-0.3820.4411
0:H-0:E-0.471-0.93-0.0110.041
1:H-0:E-0.432-0.829-0.0350.025
0:F-1:E0.184-0.2480.6160.818
1:F-1:E0.184-0.2150.5830.762
0:H-1:E-0.316-0.7640.1330.325
1:H-1:E-0.277-0.6620.1070.298
1:F-0:F0-0.4180.4181
0:H-0:F-0.5-0.966-0.0340.028
1:H-0:F-0.462-0.866-0.0570.016
0:H-1:F-0.5-0.935-0.0650.015
1:H-1:F-0.462-0.83-0.0930.006
1:H-0:H0.038-0.3840.4611

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.072 & -0.237 & 0.094 & 0.392 \tabularnewline
F-E & 0.115 & -0.128 & 0.357 & 0.501 \tabularnewline
H-E & -0.355 & -0.595 & -0.116 & 0.002 \tabularnewline
H-F & -0.47 & -0.706 & -0.234 & 0 \tabularnewline
1:E-0:E & -0.155 & -0.58 & 0.27 & 0.897 \tabularnewline
0:F-0:E & 0.029 & -0.414 & 0.473 & 1 \tabularnewline
1:F-0:E & 0.029 & -0.382 & 0.441 & 1 \tabularnewline
0:H-0:E & -0.471 & -0.93 & -0.011 & 0.041 \tabularnewline
1:H-0:E & -0.432 & -0.829 & -0.035 & 0.025 \tabularnewline
0:F-1:E & 0.184 & -0.248 & 0.616 & 0.818 \tabularnewline
1:F-1:E & 0.184 & -0.215 & 0.583 & 0.762 \tabularnewline
0:H-1:E & -0.316 & -0.764 & 0.133 & 0.325 \tabularnewline
1:H-1:E & -0.277 & -0.662 & 0.107 & 0.298 \tabularnewline
1:F-0:F & 0 & -0.418 & 0.418 & 1 \tabularnewline
0:H-0:F & -0.5 & -0.966 & -0.034 & 0.028 \tabularnewline
1:H-0:F & -0.462 & -0.866 & -0.057 & 0.016 \tabularnewline
0:H-1:F & -0.5 & -0.935 & -0.065 & 0.015 \tabularnewline
1:H-1:F & -0.462 & -0.83 & -0.093 & 0.006 \tabularnewline
1:H-0:H & 0.038 & -0.384 & 0.461 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140812&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]-0.072[/C][C]-0.237[/C][C]0.094[/C][C]0.392[/C][/ROW]
[ROW][C]F-E[/C][C]0.115[/C][C]-0.128[/C][C]0.357[/C][C]0.501[/C][/ROW]
[ROW][C]H-E[/C][C]-0.355[/C][C]-0.595[/C][C]-0.116[/C][C]0.002[/C][/ROW]
[ROW][C]H-F[/C][C]-0.47[/C][C]-0.706[/C][C]-0.234[/C][C]0[/C][/ROW]
[ROW][C]1:E-0:E[/C][C]-0.155[/C][C]-0.58[/C][C]0.27[/C][C]0.897[/C][/ROW]
[ROW][C]0:F-0:E[/C][C]0.029[/C][C]-0.414[/C][C]0.473[/C][C]1[/C][/ROW]
[ROW][C]1:F-0:E[/C][C]0.029[/C][C]-0.382[/C][C]0.441[/C][C]1[/C][/ROW]
[ROW][C]0:H-0:E[/C][C]-0.471[/C][C]-0.93[/C][C]-0.011[/C][C]0.041[/C][/ROW]
[ROW][C]1:H-0:E[/C][C]-0.432[/C][C]-0.829[/C][C]-0.035[/C][C]0.025[/C][/ROW]
[ROW][C]0:F-1:E[/C][C]0.184[/C][C]-0.248[/C][C]0.616[/C][C]0.818[/C][/ROW]
[ROW][C]1:F-1:E[/C][C]0.184[/C][C]-0.215[/C][C]0.583[/C][C]0.762[/C][/ROW]
[ROW][C]0:H-1:E[/C][C]-0.316[/C][C]-0.764[/C][C]0.133[/C][C]0.325[/C][/ROW]
[ROW][C]1:H-1:E[/C][C]-0.277[/C][C]-0.662[/C][C]0.107[/C][C]0.298[/C][/ROW]
[ROW][C]1:F-0:F[/C][C]0[/C][C]-0.418[/C][C]0.418[/C][C]1[/C][/ROW]
[ROW][C]0:H-0:F[/C][C]-0.5[/C][C]-0.966[/C][C]-0.034[/C][C]0.028[/C][/ROW]
[ROW][C]1:H-0:F[/C][C]-0.462[/C][C]-0.866[/C][C]-0.057[/C][C]0.016[/C][/ROW]
[ROW][C]0:H-1:F[/C][C]-0.5[/C][C]-0.935[/C][C]-0.065[/C][C]0.015[/C][/ROW]
[ROW][C]1:H-1:F[/C][C]-0.462[/C][C]-0.83[/C][C]-0.093[/C][C]0.006[/C][/ROW]
[ROW][C]1:H-0:H[/C][C]0.038[/C][C]-0.384[/C][C]0.461[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140812&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140812&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
1-0-0.072-0.2370.0940.392
F-E0.115-0.1280.3570.501
H-E-0.355-0.595-0.1160.002
H-F-0.47-0.706-0.2340
1:E-0:E-0.155-0.580.270.897
0:F-0:E0.029-0.4140.4731
1:F-0:E0.029-0.3820.4411
0:H-0:E-0.471-0.93-0.0110.041
1:H-0:E-0.432-0.829-0.0350.025
0:F-1:E0.184-0.2480.6160.818
1:F-1:E0.184-0.2150.5830.762
0:H-1:E-0.316-0.7640.1330.325
1:H-1:E-0.277-0.6620.1070.298
1:F-0:F0-0.4180.4181
0:H-0:F-0.5-0.966-0.0340.028
1:H-0:F-0.462-0.866-0.0570.016
0:H-1:F-0.5-0.935-0.0650.015
1:H-1:F-0.462-0.83-0.0930.006
1:H-0:H0.038-0.3840.4611






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group511.6550
108 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 11.655 & 0 \tabularnewline
  & 108 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140812&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]11.655[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]108[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140812&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140812&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)
Group511.6550
108


Figures (Output of Computation)

Input Parameters & R Code

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')