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, 02 Nov 2010 08:32:14 +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/2010/Nov/02/t1288686657luzpzn3o0llcp86.htm/, Retrieved Sun, 28 Apr 2024 15:06:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=91214, Retrieved Sun, 28 Apr 2024 15:06:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [Golfballs] [2010-10-25 12:43:22] [b98453cac15ba1066b407e146608df68]
F   PD  [Two-Way ANOVA] [Q6_1] [2010-11-01 09:42:41] [3074aa973ede76ac75d398946b01602f]
-           [Two-Way ANOVA] [] [2010-11-02 08:32:14] [9003764b6a75599accb6eea9154ba195] [Current]
Feedback Forum

Post a new message

Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91214&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91214&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91214&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.1250.3550.110.1060.0760.123

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.125 & 0.355 & 0.11 & 0.106 & 0.076 & 0.123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91214&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.125[/C][C]0.355[/C][C]0.11[/C][C]0.106[/C][C]0.076[/C][C]0.123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91214&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91214&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
means0.1250.3550.110.1060.0760.123






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A13.9073.90718.0410
Treatment_B10.7330.3671.6930.189
Treatment_A:Treatment_B10.0530.0270.1230.885
Residuals9921.440.217 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 3.907 & 3.907 & 18.041 & 0 \tabularnewline
Treatment_B & 1 & 0.733 & 0.367 & 1.693 & 0.189 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.053 & 0.027 & 0.123 & 0.885 \tabularnewline
Residuals & 99 & 21.44 & 0.217 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91214&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]3.907[/C][C]3.907[/C][C]18.041[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.733[/C][C]0.367[/C][C]1.693[/C][C]0.189[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.053[/C][C]0.027[/C][C]0.123[/C][C]0.885[/C][/ROW]
[ROW][C]Residuals[/C][C]99[/C][C]21.44[/C][C]0.217[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91214&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91214&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_A13.9073.90718.0410
Treatment_B10.7330.3671.6930.189
Treatment_A:Treatment_B10.0530.0270.1230.885
Residuals9921.440.217






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.4010.2140.5890
S-E0.161-0.1080.430.332
T-E0.19-0.0750.4550.207
T-S0.029-0.2320.2910.961
1:E-0:E0.355-0.1940.9040.422
0:S-0:E0.11-0.470.690.994
1:S-0:E0.542-0.0331.1160.077
0:T-0:E0.106-0.5020.7140.996
1:T-0:E0.5830.0311.1350.032
0:S-1:E-0.245-0.670.180.553
1:S-1:E0.187-0.2310.6050.786
0:T-1:E-0.249-0.7120.2130.623
1:T-1:E0.228-0.1580.6150.524
1:S-0:S0.431-0.0260.8890.076
0:T-0:S-0.005-0.5030.4941
1:T-0:S0.4730.0440.9020.022
0:T-1:S-0.436-0.9280.0560.114
1:T-1:S0.042-0.380.4631
1:T-0:T0.4780.0120.9430.041

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.401 & 0.214 & 0.589 & 0 \tabularnewline
S-E & 0.161 & -0.108 & 0.43 & 0.332 \tabularnewline
T-E & 0.19 & -0.075 & 0.455 & 0.207 \tabularnewline
T-S & 0.029 & -0.232 & 0.291 & 0.961 \tabularnewline
1:E-0:E & 0.355 & -0.194 & 0.904 & 0.422 \tabularnewline
0:S-0:E & 0.11 & -0.47 & 0.69 & 0.994 \tabularnewline
1:S-0:E & 0.542 & -0.033 & 1.116 & 0.077 \tabularnewline
0:T-0:E & 0.106 & -0.502 & 0.714 & 0.996 \tabularnewline
1:T-0:E & 0.583 & 0.031 & 1.135 & 0.032 \tabularnewline
0:S-1:E & -0.245 & -0.67 & 0.18 & 0.553 \tabularnewline
1:S-1:E & 0.187 & -0.231 & 0.605 & 0.786 \tabularnewline
0:T-1:E & -0.249 & -0.712 & 0.213 & 0.623 \tabularnewline
1:T-1:E & 0.228 & -0.158 & 0.615 & 0.524 \tabularnewline
1:S-0:S & 0.431 & -0.026 & 0.889 & 0.076 \tabularnewline
0:T-0:S & -0.005 & -0.503 & 0.494 & 1 \tabularnewline
1:T-0:S & 0.473 & 0.044 & 0.902 & 0.022 \tabularnewline
0:T-1:S & -0.436 & -0.928 & 0.056 & 0.114 \tabularnewline
1:T-1:S & 0.042 & -0.38 & 0.463 & 1 \tabularnewline
1:T-0:T & 0.478 & 0.012 & 0.943 & 0.041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91214&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]0.401[/C][C]0.214[/C][C]0.589[/C][C]0[/C][/ROW]
[ROW][C]S-E[/C][C]0.161[/C][C]-0.108[/C][C]0.43[/C][C]0.332[/C][/ROW]
[ROW][C]T-E[/C][C]0.19[/C][C]-0.075[/C][C]0.455[/C][C]0.207[/C][/ROW]
[ROW][C]T-S[/C][C]0.029[/C][C]-0.232[/C][C]0.291[/C][C]0.961[/C][/ROW]
[ROW][C]1:E-0:E[/C][C]0.355[/C][C]-0.194[/C][C]0.904[/C][C]0.422[/C][/ROW]
[ROW][C]0:S-0:E[/C][C]0.11[/C][C]-0.47[/C][C]0.69[/C][C]0.994[/C][/ROW]
[ROW][C]1:S-0:E[/C][C]0.542[/C][C]-0.033[/C][C]1.116[/C][C]0.077[/C][/ROW]
[ROW][C]0:T-0:E[/C][C]0.106[/C][C]-0.502[/C][C]0.714[/C][C]0.996[/C][/ROW]
[ROW][C]1:T-0:E[/C][C]0.583[/C][C]0.031[/C][C]1.135[/C][C]0.032[/C][/ROW]
[ROW][C]0:S-1:E[/C][C]-0.245[/C][C]-0.67[/C][C]0.18[/C][C]0.553[/C][/ROW]
[ROW][C]1:S-1:E[/C][C]0.187[/C][C]-0.231[/C][C]0.605[/C][C]0.786[/C][/ROW]
[ROW][C]0:T-1:E[/C][C]-0.249[/C][C]-0.712[/C][C]0.213[/C][C]0.623[/C][/ROW]
[ROW][C]1:T-1:E[/C][C]0.228[/C][C]-0.158[/C][C]0.615[/C][C]0.524[/C][/ROW]
[ROW][C]1:S-0:S[/C][C]0.431[/C][C]-0.026[/C][C]0.889[/C][C]0.076[/C][/ROW]
[ROW][C]0:T-0:S[/C][C]-0.005[/C][C]-0.503[/C][C]0.494[/C][C]1[/C][/ROW]
[ROW][C]1:T-0:S[/C][C]0.473[/C][C]0.044[/C][C]0.902[/C][C]0.022[/C][/ROW]
[ROW][C]0:T-1:S[/C][C]-0.436[/C][C]-0.928[/C][C]0.056[/C][C]0.114[/C][/ROW]
[ROW][C]1:T-1:S[/C][C]0.042[/C][C]-0.38[/C][C]0.463[/C][C]1[/C][/ROW]
[ROW][C]1:T-0:T[/C][C]0.478[/C][C]0.012[/C][C]0.943[/C][C]0.041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91214&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91214&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
1-00.4010.2140.5890
S-E0.161-0.1080.430.332
T-E0.19-0.0750.4550.207
T-S0.029-0.2320.2910.961
1:E-0:E0.355-0.1940.9040.422
0:S-0:E0.11-0.470.690.994
1:S-0:E0.542-0.0331.1160.077
0:T-0:E0.106-0.5020.7140.996
1:T-0:E0.5830.0311.1350.032
0:S-1:E-0.245-0.670.180.553
1:S-1:E0.187-0.2310.6050.786
0:T-1:E-0.249-0.7120.2130.623
1:T-1:E0.228-0.1580.6150.524
1:S-0:S0.431-0.0260.8890.076
0:T-0:S-0.005-0.5030.4941
1:T-0:S0.4730.0440.9020.022
0:T-1:S-0.436-0.9280.0560.114
1:T-1:S0.042-0.380.4631
1:T-0:T0.4780.0120.9430.041






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group51.0980.367
99 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 1.098 & 0.367 \tabularnewline
  & 99 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91214&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]1.098[/C][C]0.367[/C][/ROW]
[ROW][C] [/C][C]99[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91214&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91214&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)
Group51.0980.367
99


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 ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')