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Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationThu, 18 Dec 2014 16:25:08 +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/2014/Dec/18/t1418920075z5qlavg5a71vejo.htm/, Retrieved Fri, 17 May 2024 18:40:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271121, Retrieved Fri, 17 May 2024 18:40:55 +0000
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User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Paired and Unpaired Two Samples Tests about the Mean] [] [2014-12-15 16:20:32] [67894a4ff6098ffac356bc81e6028257]
-    D  [Paired and Unpaired Two Samples Tests about the Mean] [] [2014-12-15 16:32:47] [67894a4ff6098ffac356bc81e6028257]
- RMPD      [Two-Way ANOVA] [] [2014-12-18 16:25:08] [9a966322e4d935aee68609d815c1a240] [Current]
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Dataseries X:
26 "'S'" 0
51 "'S'" 0
57 "'S'" 1
37 "'S'" 0
67 "'S'" 1
43 "'S'" 1
52 "'S'" 1
52 "'S'" 0
43 "'S'" 1
84 "'S'" 1
67 "'S'" 1
49 "'S'" 1
70 "'S'" 1
58 "'S'" 0
68 "'S'" 0
62 "'B'" 0
43 "'S'" 1
56 "'S'" 0
74 "'S'" 0
63 "'S'" 1
58 "'S'" 0
63 "'S'" 1
53 "'S'" 1
57 "'B'" 1
64 "'S'" 1
53 "'S'" 0
29 "'S'" 0
54 "'S'" 0
58 "'S'" 1
51 "'S'" 1
54 "'S'" 0
56 "'B'" 1
47 "'S'" 0
50 "'S'" 1
35 "'S'" 1
30 "'B'" 1
68 "'S'" 0
56 "'B'" 1
43 "'S'" 1
67 "'B'" 1
62 "'S'" 1
57 "'S'" 1
54 "'S'" 1
61 "'S'" 1
56 "'S'" 0
41 "'S'" 0
53 "'S'" 0
46 "'S'" 1
51 "'S'" 0
37 "'S'" 0
42 "'S'" 0
38 "'B'" 1
66 "'S'" 0
53 "'S'" 1
49 "'B'" 0
49 "'B'" 0
59 "'B'" 1
40 "'B'" 0
63 "'B'" 0
34 "'B'" 1
32 "'B'" 0
67 "'B'" 0
61 "'B'" 1
60 "'B'" 0
63 "'B'" 0
52 "'S'" 1
16 "'S'" 1
46 "'S'" 1
56 "'S'" 1
52 "'B'" 0
55 "'B'" 1
50 "'S'" 1
59 "'S'" 0
60 "'S'" 1
52 "'S'" 0
44 "'S'" 0
67 "'S'" 1
52 "'S'" 1
55 "'S'" 1
37 "'S'" 1
54 "'S'" 1
72 "'B'" 1
51 "'S'" 1
48 "'S'" 1
60 "'S'" 0
50 "'S'" 1
63 "'S'" 1
33 "'S'" 1
67 "'S'" 1
46 "'S'" 1
54 "'S'" 1
59 "'S'" 0
61 "'S'" 1
33 "'B'" 1
47 "'S'" 1
69 "'S'" 1
52 "'S'" 1
55 "'S'" 0
55 "'S'" 0
41 "'S'" 0
73 "'S'" 1
51 "'S'" 0
52 "'S'" 0
50 "'S'" 0
51 "'S'" 1
60 "'S'" 0
56 "'S'" 1
56 "'S'" 1
29 "'S'" 0
66 "'B'" 1
66 "'B'" 1
73 "'S'" 1
55 "'S'" 0
64 "'B'" 0
40 "'B'" 0
46 "'B'" 0
58 "'B'" 1
43 "'S'" 0
61 "'S'" 1
51 "'B'" 0
50 "'B'" 1
52 "'B'" 0
54 "'B'" 1
66 "'B'" 0
61 "'B'" 0
80 "'B'" 1
51 "'B'" 0
56 "'B'" 1
56 "'S'" 1
56 "'S'" 1
53 "'B'" 1
47 "'S'" 1
25 "'S'" 0
47 "'B'" 1
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50 "'B'" 0
39 "'B'" 0
51 "'S'" 1
58 "'B'" 0
35 "'B'" 1
58 "'B'" 0
60 "'B'" 0
62 "'B'" 0
63 "'B'" 0
53 "'B'" 1
46 "'B'" 1
67 "'B'" 1
59 "'B'" 1
64 "'B'" 0
38 "'B'" 0
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48 "'S'" 0
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47 "'B'" 0
66 "'B'" 0
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63 "'B'" 1
58 "'S'" 0
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51 "'S'" 1
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55 "'S'" 1
38 "'B'" 1
56 "'B'" 1
45 "'B'" 0
50 "'B'" 1
54 "'B'" 1
57 "'S'" 1
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55 "'B'" 0
56 "'S'" 0
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37 "'B'" 1
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52 "'S'" 0
67 "'B'" 1
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56 "'B'" 0
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50 "'B'" 0
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63 "'S'" 0
63 "'S'" 1
56 "'S'" 1
51 "'S'" 0
50 "'B'" 1
22 "'B'" 0
41 "'S'" 1
59 "'B'" 0
56 "'B'" 1
66 "'S'" 0
53 "'B'" 0
42 "'B'" 1
52 "'B'" 1
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62 "'B'" 1
53 "'B'" 0
50 "'B'" 1
36 "'B'" 0
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66 "'B'" 1
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45 "'B'" 1




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=271121&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=271121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271121&T=0

As an alternative you can also use a 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
means53.039-1.1640.6721.297

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 53.039 & -1.164 & 0.672 & 1.297 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271121&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]53.039[/C][C]-1.164[/C][C]0.672[/C][C]1.297[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271121&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means53.039-1.1640.6721.297







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A17.6747.6740.070.792
Treatment_B1113.219113.2191.0330.311
Treatment_A:Treatment_B124.13524.1350.220.639
Residuals23225436.85109.642

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 7.674 & 7.674 & 0.07 & 0.792 \tabularnewline
Treatment_B & 1 & 113.219 & 113.219 & 1.033 & 0.311 \tabularnewline
Treatment_A:Treatment_B & 1 & 24.135 & 24.135 & 0.22 & 0.639 \tabularnewline
Residuals & 232 & 25436.85 & 109.642 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271121&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]7.674[/C][C]7.674[/C][C]0.07[/C][C]0.792[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]113.219[/C][C]113.219[/C][C]1.033[/C][C]0.311[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]24.135[/C][C]24.135[/C][C]0.22[/C][C]0.639[/C][/ROW]
[ROW][C]Residuals[/C][C]232[/C][C]25436.85[/C][C]109.642[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271121&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271121&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A17.6747.6740.070.792
Treatment_B1113.219113.2191.0330.311
Treatment_A:Treatment_B124.13524.1350.220.639
Residuals23225436.85109.642







Tukey Honest Significant Difference Comparisons
difflwruprp adj
'S'-'B'-0.364-3.0712.3440.792
1-01.388-1.314.0850.312
'S':0-'B':0-1.164-6.4094.0810.94
'B':1-'B':00.672-4.6686.0120.988
'S':1-'B':00.805-4.0875.6970.974
'B':1-'S':01.837-3.3827.0550.799
'S':1-'S':01.969-2.796.7280.708
'S':1-'B':10.133-4.7314.9961

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
'S'-'B' & -0.364 & -3.071 & 2.344 & 0.792 \tabularnewline
1-0 & 1.388 & -1.31 & 4.085 & 0.312 \tabularnewline
'S':0-'B':0 & -1.164 & -6.409 & 4.081 & 0.94 \tabularnewline
'B':1-'B':0 & 0.672 & -4.668 & 6.012 & 0.988 \tabularnewline
'S':1-'B':0 & 0.805 & -4.087 & 5.697 & 0.974 \tabularnewline
'B':1-'S':0 & 1.837 & -3.382 & 7.055 & 0.799 \tabularnewline
'S':1-'S':0 & 1.969 & -2.79 & 6.728 & 0.708 \tabularnewline
'S':1-'B':1 & 0.133 & -4.731 & 4.996 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271121&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'-'B'[/C][C]-0.364[/C][C]-3.071[/C][C]2.344[/C][C]0.792[/C][/ROW]
[ROW][C]1-0[/C][C]1.388[/C][C]-1.31[/C][C]4.085[/C][C]0.312[/C][/ROW]
[ROW][C]'S':0-'B':0[/C][C]-1.164[/C][C]-6.409[/C][C]4.081[/C][C]0.94[/C][/ROW]
[ROW][C]'B':1-'B':0[/C][C]0.672[/C][C]-4.668[/C][C]6.012[/C][C]0.988[/C][/ROW]
[ROW][C]'S':1-'B':0[/C][C]0.805[/C][C]-4.087[/C][C]5.697[/C][C]0.974[/C][/ROW]
[ROW][C]'B':1-'S':0[/C][C]1.837[/C][C]-3.382[/C][C]7.055[/C][C]0.799[/C][/ROW]
[ROW][C]'S':1-'S':0[/C][C]1.969[/C][C]-2.79[/C][C]6.728[/C][C]0.708[/C][/ROW]
[ROW][C]'S':1-'B':1[/C][C]0.133[/C][C]-4.731[/C][C]4.996[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271121&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271121&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
'S'-'B'-0.364-3.0712.3440.792
1-01.388-1.314.0850.312
'S':0-'B':0-1.164-6.4094.0810.94
'B':1-'B':00.672-4.6686.0120.988
'S':1-'B':00.805-4.0875.6970.974
'B':1-'S':01.837-3.3827.0550.799
'S':1-'S':01.969-2.796.7280.708
'S':1-'B':10.133-4.7314.9961







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.1380.937
232

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.138 & 0.937 \tabularnewline
  & 232 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271121&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]0.138[/C][C]0.937[/C][/ROW]
[ROW][C] [/C][C]232[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271121&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271121&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.1380.937
232



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')