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, 21 Dec 2016 15:20:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482331883sxm6q3wyhgiaz1x.htm/, Retrieved Mon, 06 May 2024 14:31:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302349, Retrieved Mon, 06 May 2024 14:31:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [] [2016-12-21 14:20:02] [404ac5ee4f7301873f6a96ef36861981] [Current]
Feedback Forum

Post a new message
Dataseries X:
4	1	13
4	2	16
4	2	17
4	2	15
4	1	16
4	2	16
4	2	17
3	2	16
3	1	17
4	1	17
4	1	17
3	1	15
3	1	16
4	1	14
4	1	16
4	2	17
4	1	16
4	2	15
4	2	17
4	2	16
4	1	15
4	2	16
4	2	15
4	1	17
4	1	15
3	1	16
3	1	15
4	1	16
4	1	16
4	1	13
3	2	15
4	1	17
3	1	15
4	2	13
4	1	17
4	1	15
3	2	14
3	1	14
3	1	18
3	2	15
3	2	17
3	2	13
4	2	16
3	2	15
3	2	15
4	2	16
3	2	15
4	2	13
3	2	17
3	1	17
3	2	17
3	2	11
4	1	14
4	2	13
4	1	15
3	1	17
3	2	16
4	1	15
4	2	17
3	2	16
4	2	16
4	2	16
4	1	15
4	2	12
4	1	17
4	2	14
4	1	14
4	2	16
4	2	15
4	2	15
4	1	13
3	2	13
4	1	17
4	2	15
4	1	16
4	2	14
4	1	15
4	2	17
4	2	16
4	1	10
4	1	16
3	1	17
4	2	17
4	2	20
4	2	17
4	2	18
4	2	15
3	1	17
3	2	14
3	1	15
4	1	17
4	1	16
3	1	17
4	2	15
4	2	16
4	2	18
4	1	18
4	2	16
4	1	17
4	1	15
4	2	13
4	2	15
4	2	17
3	2	16
4	1	16
3	1	15
4	1	16
4	2	16
4	2	13
3	2	15
4	1	12
4	1	19
4	2	16
4	1	16
4	1	17
3	2	16
3	1	14
3	1	15
3	1	14
3	2	16
4	2	15
4	2	17
4	2	15
4	2	16
4	1	16
3	1	15
3	2	15
4	2	11
3	2	16
4	1	18
3	2	13
4	1	11
3	1	18
4	2	15
3	1	19
4	1	17
3	1	13
3	1	14
4	2	16
4	1	13
4	2	17
4	2	14
4	2	19
4	2	14
4	1	16
4	1	12
4	1	16
3	1	16
3	2	15
3	2	12
3	2	15
3	2	17
3	1	13
4	2	15
3	1	18
3	2	15
3	1	18
4	1	15
4	1	15
4	1	16
4	1	13
4	2	16
4	2	13
4	1	16




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302349&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302349&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center







ANOVA Model
Response ~ Treatment_A * Treatment_B
means15.852-0.467-0.8521.011

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 15.852 & -0.467 & -0.852 & 1.011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302349&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]15.852[/C][C]-0.467[/C][C]-0.852[/C][C]1.011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302349&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
means15.852-0.467-0.8521.011







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.090.090.0320.859
Treatment_B11.331.330.4650.496
Treatment_A:Treatment_B19.3349.3343.2620.073
Residuals160457.8552.862

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.09 & 0.09 & 0.032 & 0.859 \tabularnewline
Treatment_B & 1 & 1.33 & 1.33 & 0.465 & 0.496 \tabularnewline
Treatment_A:Treatment_B & 1 & 9.334 & 9.334 & 3.262 & 0.073 \tabularnewline
Residuals & 160 & 457.855 & 2.862 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302349&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]0.09[/C][C]0.09[/C][C]0.032[/C][C]0.859[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]1.33[/C][C]1.33[/C][C]0.465[/C][C]0.496[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]9.334[/C][C]9.334[/C][C]3.262[/C][C]0.073[/C][/ROW]
[ROW][C]Residuals[/C][C]160[/C][C]457.855[/C][C]2.862[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302349&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302349&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_A10.090.090.0320.859
Treatment_B11.331.330.4650.496
Treatment_A:Treatment_B19.3349.3343.2620.073
Residuals160457.8552.862







Tukey Honest Significant Difference Comparisons
difflwruprp adj
4-30.05-0.5030.6020.859
2-1-0.18-0.7020.3420.496
4:1-3:1-0.467-1.5090.5750.65
3:2-3:1-0.852-2.0360.3330.246
4:2-3:1-0.308-1.3340.7180.864
3:2-4:1-0.385-1.4140.6450.767
4:2-4:10.159-0.6831.0010.961
4:2-3:20.544-0.471.5570.505

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
4-3 & 0.05 & -0.503 & 0.602 & 0.859 \tabularnewline
2-1 & -0.18 & -0.702 & 0.342 & 0.496 \tabularnewline
4:1-3:1 & -0.467 & -1.509 & 0.575 & 0.65 \tabularnewline
3:2-3:1 & -0.852 & -2.036 & 0.333 & 0.246 \tabularnewline
4:2-3:1 & -0.308 & -1.334 & 0.718 & 0.864 \tabularnewline
3:2-4:1 & -0.385 & -1.414 & 0.645 & 0.767 \tabularnewline
4:2-4:1 & 0.159 & -0.683 & 1.001 & 0.961 \tabularnewline
4:2-3:2 & 0.544 & -0.47 & 1.557 & 0.505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302349&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]4-3[/C][C]0.05[/C][C]-0.503[/C][C]0.602[/C][C]0.859[/C][/ROW]
[ROW][C]2-1[/C][C]-0.18[/C][C]-0.702[/C][C]0.342[/C][C]0.496[/C][/ROW]
[ROW][C]4:1-3:1[/C][C]-0.467[/C][C]-1.509[/C][C]0.575[/C][C]0.65[/C][/ROW]
[ROW][C]3:2-3:1[/C][C]-0.852[/C][C]-2.036[/C][C]0.333[/C][C]0.246[/C][/ROW]
[ROW][C]4:2-3:1[/C][C]-0.308[/C][C]-1.334[/C][C]0.718[/C][C]0.864[/C][/ROW]
[ROW][C]3:2-4:1[/C][C]-0.385[/C][C]-1.414[/C][C]0.645[/C][C]0.767[/C][/ROW]
[ROW][C]4:2-4:1[/C][C]0.159[/C][C]-0.683[/C][C]1.001[/C][C]0.961[/C][/ROW]
[ROW][C]4:2-3:2[/C][C]0.544[/C][C]-0.47[/C][C]1.557[/C][C]0.505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302349&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302349&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
4-30.05-0.5030.6020.859
2-1-0.18-0.7020.3420.496
4:1-3:1-0.467-1.5090.5750.65
3:2-3:1-0.852-2.0360.3330.246
4:2-3:1-0.308-1.3340.7180.864
3:2-4:1-0.385-1.4140.6450.767
4:2-4:10.159-0.6831.0010.961
4:2-3:20.544-0.471.5570.505







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.4080.747
160

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.408 & 0.747 \tabularnewline
  & 160 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302349&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]0.408[/C][C]0.747[/C][/ROW]
[ROW][C] [/C][C]160[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302349&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302349&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)
Group30.4080.747
160



Parameters (Session):
par1 = 3 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;
Parameters (R input):
par1 = 3 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- 'TRUE'
par3 <- '2'
par2 <- '1'
par1 <- '3'
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')