Free Statistics

of Irreproducible Research!

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 computationWed, 17 Dec 2014 18:08:30 +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/17/t1418839851w7jw0wjiwmsitb7.htm/, Retrieved Sun, 19 May 2024 20:22:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270553, Retrieved Sun, 19 May 2024 20:22:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2014-12-17 18:08:30] [6baf0af87d9d8aa2cb91b54f39a0a5b0] [Current]
Feedback Forum

Post a new message
Dataseries X:
21 "'S'" 0
22 "'S'" 1
22 "'S'" 0
18 "'S'" 1
23 "'S'" 1
12 "'S'" 1
20 "'S'" 0
22 "'S'" 1
21 "'S'" 1
19 "'S'" 1
22 "'S'" 1
15 "'S'" 1
20 "'S'" 1
19 "'S'" 0
18 "'S'" 0
15 "'B'" 0
20 "'S'" 1
21 "'S'" 0
21 "'B'" 1
15 "'S'" 0
16 "'S'" 1
23 "'S'" 1
21 "'S'" 0
18 "'S'" 1
25 "'S'" 1
9 "'S'" 1
30 "'B'" 1
20 "'B'" 0
23 "'S'" 1
16 "'S'" 0
16 "'S'" 0
19 "'S'" 0
25 "'S'" 1
18 "'S'" 1
23 "'S'" 1
21 "'S'" 1
10 "'S'" 0
14 "'B'" 1
22 "'S'" 1
26 "'S'" 0
23 "'S'" 1
23 "'S'" 1
24 "'S'" 1
24 "'S'" 1
18 "'B'" 1
23 "'S'" 0
15 "'S'" 1
19 "'B'" 1
16 "'S'" 0
25 "'B'" 1
23 "'B'" 1
17 "'B'" 1
19 "'S'" 1
21 "'B'" 1
18 "'S'" 1
27 "'S'" 1
21 "'B'" 0
13 "'S'" 1
8 "'B'" 0
29 "'B'" 1
28 "'S'" 1
23 "'S'" 0
21 "'S'" 0
19 "'S'" 1
19 "'S'" 0
20 "'B'" 1
18 "'S'" 0
19 "'S'" 1
17 "'S'" 1
19 "'B'" 0
25 "'S'" 0
19 "'S'" 0
22 "'B'" 0
23 "'B'" 1
14 "'S'" 0
28 "'S'" 1
16 "'S'" 0
24 "'B'" 1
20 "'S'" 0
12 "'B'" 0
24 "'S'" 1
22 "'B'" 0
12 "'B'" 0
22 "'B'" 0
20 "'B'" 1
10 "'B'" 0
23 "'B'" 1
17 "'B'" 1
22 "'B'" 0
24 "'B'" 0
18 "'B'" 0
21 "'B'" 1
20 "'B'" 1
20 "'B'" 1
22 "'B'" 0
19 "'B'" 1
20 "'B'" 0
26 "'B'" 1
23 "'B'" 1
24 "'B'" 1
21 "'B'" 1
21 "'B'" 1
19 "'B'" 0
8 "'B'" 1
17 "'B'" 1
20 "'B'" 1
11 "'B'" 0
8 "'B'" 0
15 "'B'" 0
18 "'B'" 0
18 "'B'" 0
19 "'B'" 0
19 "'B'" 1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270553&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270553&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means17.2611.8223.532-2.129

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 17.261 & 1.822 & 3.532 & -2.129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270553&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]17.261[/C][C]1.822[/C][C]3.532[/C][C]-2.129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270553&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
means17.2611.8223.532-2.129







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A113.89913.8990.7540.387
Treatment_B1157.789157.7898.5640.004
Treatment_A:Treatment_B130.90930.9091.6780.198
Residuals1092008.2718.424

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 13.899 & 13.899 & 0.754 & 0.387 \tabularnewline
Treatment_B & 1 & 157.789 & 157.789 & 8.564 & 0.004 \tabularnewline
Treatment_A:Treatment_B & 1 & 30.909 & 30.909 & 1.678 & 0.198 \tabularnewline
Residuals & 109 & 2008.27 & 18.424 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270553&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]13.899[/C][C]13.899[/C][C]0.754[/C][C]0.387[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]157.789[/C][C]157.789[/C][C]8.564[/C][C]0.004[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]30.909[/C][C]30.909[/C][C]1.678[/C][C]0.198[/C][/ROW]
[ROW][C]Residuals[/C][C]109[/C][C]2008.27[/C][C]18.424[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270553&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270553&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_A113.89913.8990.7540.387
Treatment_B1157.789157.7898.5640.004
Treatment_A:Treatment_B130.90930.9091.6780.198
Residuals1092008.2718.424







Tukey Honest Significant Difference Comparisons
difflwruprp adj
'S'-'B'0.704-0.9022.3090.387
1-02.3950.7714.0180.004
'S':0-'B':01.822-1.4455.090.468
'B':1-'B':03.5320.4056.6590.02
'S':1-'B':03.2260.2526.1990.028
'B':1-'S':01.71-1.3814.80.475
'S':1-'S':01.403-1.5324.3380.598
'S':1-'B':1-0.307-3.0842.4710.992

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
'S'-'B' & 0.704 & -0.902 & 2.309 & 0.387 \tabularnewline
1-0 & 2.395 & 0.771 & 4.018 & 0.004 \tabularnewline
'S':0-'B':0 & 1.822 & -1.445 & 5.09 & 0.468 \tabularnewline
'B':1-'B':0 & 3.532 & 0.405 & 6.659 & 0.02 \tabularnewline
'S':1-'B':0 & 3.226 & 0.252 & 6.199 & 0.028 \tabularnewline
'B':1-'S':0 & 1.71 & -1.381 & 4.8 & 0.475 \tabularnewline
'S':1-'S':0 & 1.403 & -1.532 & 4.338 & 0.598 \tabularnewline
'S':1-'B':1 & -0.307 & -3.084 & 2.471 & 0.992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270553&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]0.704[/C][C]-0.902[/C][C]2.309[/C][C]0.387[/C][/ROW]
[ROW][C]1-0[/C][C]2.395[/C][C]0.771[/C][C]4.018[/C][C]0.004[/C][/ROW]
[ROW][C]'S':0-'B':0[/C][C]1.822[/C][C]-1.445[/C][C]5.09[/C][C]0.468[/C][/ROW]
[ROW][C]'B':1-'B':0[/C][C]3.532[/C][C]0.405[/C][C]6.659[/C][C]0.02[/C][/ROW]
[ROW][C]'S':1-'B':0[/C][C]3.226[/C][C]0.252[/C][C]6.199[/C][C]0.028[/C][/ROW]
[ROW][C]'B':1-'S':0[/C][C]1.71[/C][C]-1.381[/C][C]4.8[/C][C]0.475[/C][/ROW]
[ROW][C]'S':1-'S':0[/C][C]1.403[/C][C]-1.532[/C][C]4.338[/C][C]0.598[/C][/ROW]
[ROW][C]'S':1-'B':1[/C][C]-0.307[/C][C]-3.084[/C][C]2.471[/C][C]0.992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270553&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270553&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'0.704-0.9022.3090.387
1-02.3950.7714.0180.004
'S':0-'B':01.822-1.4455.090.468
'B':1-'B':03.5320.4056.6590.02
'S':1-'B':03.2260.2526.1990.028
'B':1-'S':01.71-1.3814.80.475
'S':1-'S':01.403-1.5324.3380.598
'S':1-'B':1-0.307-3.0842.4710.992







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.6730.571
109

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.673 & 0.571 \tabularnewline
  & 109 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270553&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]0.673[/C][C]0.571[/C][/ROW]
[ROW][C] [/C][C]109[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270553&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270553&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)
Group30.6730.571
109



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')