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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 computationMon, 16 Nov 2015 17:14:42 +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/2015/Nov/16/t1447694120bpe5l0hzi4yrxp8.htm/, Retrieved Thu, 31 Oct 2024 23:07:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283384, Retrieved Thu, 31 Oct 2024 23:07:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact258

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] [] [2015-11-16 17:14:42] [63a9f0ea7bb98050796b649e85481845] [Current]
- R PD    [Two-Way ANOVA] [] [2015-12-11 19:15:49] [0e2e3dbefef1c665f3752d42409bac25]
- RMPD    [Paired and Unpaired Two Samples Tests about the Mean] [] [2015-12-11 19:29:01] [0e2e3dbefef1c665f3752d42409bac25]
- RMPD    [Multiple Regression] [] [2015-12-11 21:00:35] [0e2e3dbefef1c665f3752d42409bac25]
- RMPD    [Exponential Smoothing] [] [2015-12-11 21:11:55] [0e2e3dbefef1c665f3752d42409bac25]
- R         [Exponential Smoothing] [] [2015-12-11 21:14:18] [0e2e3dbefef1c665f3752d42409bac25]
- RM D      [(Partial) Autocorrelation Function] [] [2015-12-11 21:47:51] [0e2e3dbefef1c665f3752d42409bac25]
- RM D        [Box-Cox Linearity Plot] [] [2015-12-11 21:55:28] [0e2e3dbefef1c665f3752d42409bac25]
- RM D        [Box-Cox Normality Plot] [] [2015-12-11 21:57:36] [0e2e3dbefef1c665f3752d42409bac25]
- R           [(Partial) Autocorrelation Function] [] [2015-12-11 22:01:00] [0e2e3dbefef1c665f3752d42409bac25]
- RM D        [ARIMA Backward Selection] [] [2015-12-11 22:02:14] [0e2e3dbefef1c665f3752d42409bac25]
- RM D        [Kendall tau Correlation Matrix] [] [2015-12-11 22:11:18] [0e2e3dbefef1c665f3752d42409bac25]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.28	'A'	'M'
0.95	'A'	'M'
0.96	'A'	'M'
0.97	'A'	'M'
0.40	'A'	'M'
0.18	'A'	'M'
0.12	'A'	'M'
0.62	'A'	'M'
1.81	'A'	'F'
1.51	'A'	'F'
1.41	'A'	'F'
1.39	'A'	'F'
1.20	'A'	'F'
1.55	'A'	'F'
1.48	'A'	'F'
1.25	'A'	'F'
0.95	'B'	'M'
1.33	'B'	'M'
0.92	'B'	'M'
0.85	'B'	'M'
1.06	'B'	'M'
0.69	'B'	'M'
0.70	'B'	'M'
0.79	'B'	'M'
2.93	'B'	'F'
3.24	'B'	'F'
3.42	'B'	'F'
2.79	'B'	'F'
2.54	'B'	'F'
3.28	'B'	'F'
2.80	'B'	'F'
3.40	'B'	'F'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ yule.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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283384&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283384&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 time6 seconds
R Server'George Udny Yule' @ yule.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means1.451.6-0.89-1.249

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 1.45 & 1.6 & -0.89 & -1.249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283384&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]1.45[/C][C]1.6[/C][C]-0.89[/C][C]-1.249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283384&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
means1.451.6-0.89-1.249






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A17.6157.61595.1130
Treatment_B118.34718.347229.1610
Treatment_A:Treatment_B13.1193.11938.9550
Residuals282.2420.08 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 7.615 & 7.615 & 95.113 & 0 \tabularnewline
Treatment_B & 1 & 18.347 & 18.347 & 229.161 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 3.119 & 3.119 & 38.955 & 0 \tabularnewline
Residuals & 28 & 2.242 & 0.08 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283384&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]7.615[/C][C]7.615[/C][C]95.113[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]18.347[/C][C]18.347[/C][C]229.161[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]3.119[/C][C]3.119[/C][C]38.955[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]28[/C][C]2.242[/C][C]0.08[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283384&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283384&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_A17.6157.61595.1130
Treatment_B118.34718.347229.1610
Treatment_A:Treatment_B13.1193.11938.9550
Residuals282.2420.08






Tukey Honest Significant Difference Comparisons
difflwruprp adj
B-A0.9760.7711.1810
M-F-1.514-1.719-1.3090
B:F-A:F1.61.2141.9860
A:M-A:F-0.89-1.276-0.5040
B:M-A:F-0.539-0.925-0.1520.004
A:M-B:F-2.49-2.876-2.1040
B:M-B:F-2.139-2.525-1.7520
B:M-A:M0.351-0.0350.7380.085

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
B-A & 0.976 & 0.771 & 1.181 & 0 \tabularnewline
M-F & -1.514 & -1.719 & -1.309 & 0 \tabularnewline
B:F-A:F & 1.6 & 1.214 & 1.986 & 0 \tabularnewline
A:M-A:F & -0.89 & -1.276 & -0.504 & 0 \tabularnewline
B:M-A:F & -0.539 & -0.925 & -0.152 & 0.004 \tabularnewline
A:M-B:F & -2.49 & -2.876 & -2.104 & 0 \tabularnewline
B:M-B:F & -2.139 & -2.525 & -1.752 & 0 \tabularnewline
B:M-A:M & 0.351 & -0.035 & 0.738 & 0.085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283384&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]B-A[/C][C]0.976[/C][C]0.771[/C][C]1.181[/C][C]0[/C][/ROW]
[ROW][C]M-F[/C][C]-1.514[/C][C]-1.719[/C][C]-1.309[/C][C]0[/C][/ROW]
[ROW][C]B:F-A:F[/C][C]1.6[/C][C]1.214[/C][C]1.986[/C][C]0[/C][/ROW]
[ROW][C]A:M-A:F[/C][C]-0.89[/C][C]-1.276[/C][C]-0.504[/C][C]0[/C][/ROW]
[ROW][C]B:M-A:F[/C][C]-0.539[/C][C]-0.925[/C][C]-0.152[/C][C]0.004[/C][/ROW]
[ROW][C]A:M-B:F[/C][C]-2.49[/C][C]-2.876[/C][C]-2.104[/C][C]0[/C][/ROW]
[ROW][C]B:M-B:F[/C][C]-2.139[/C][C]-2.525[/C][C]-1.752[/C][C]0[/C][/ROW]
[ROW][C]B:M-A:M[/C][C]0.351[/C][C]-0.035[/C][C]0.738[/C][C]0.085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283384&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283384&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
B-A0.9760.7711.1810
M-F-1.514-1.719-1.3090
B:F-A:F1.61.2141.9860
A:M-A:F-0.89-1.276-0.5040
B:M-A:F-0.539-0.925-0.1520.004
A:M-B:F-2.49-2.876-2.1040
B:M-B:F-2.139-2.525-1.7520
B:M-A:M0.351-0.0350.7380.085






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group33.6960.023
28 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.696 & 0.023 \tabularnewline
  & 28 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283384&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]3.696[/C][C]0.023[/C][/ROW]
[ROW][C] [/C][C]28[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283384&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283384&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)
Group33.6960.023
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<-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')