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, 09 Dec 2015 16:02:30 +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/2015/Dec/09/t14496769855d3pgsspenl39ns.htm/, Retrieved Thu, 16 May 2024 05:46:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285751, Retrieved Thu, 16 May 2024 05:46:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Two-Way ANOVA] [2-way Anova] [2015-12-09 16:02:30] [d624a477b958b53c469d78e25da15660] [Current]
Feedback Forum

Post a new message
Dataseries X:
2011 0 12.9
2011 1 12.2
2011 0 12.8
2011 1 7.4
2011 1 6.7
2011 1 12.6
2011 0 14.8
2011 1 13.3
2011 1 11.1
2011 1 8.2
2011 1 11.4
2011 1 6.4
2011 1 10.6
2011 0 12
2011 0 6.3
2011 0 11.3
2011 1 11.9
2011 0 9.3
2011 1 9.6
2011 0 10
2011 1 6.4
2011 1 13.8
2011 0 10.8
2011 1 13.8
2011 1 11.7
2011 1 10.9
2011 1 16.1
2011 0 13.4
2011 1 9.9
2011 0 11.5
2011 0 8.3
2011 0 11.7
2011 1 9
2011 1 9.7
2011 1 10.8
2011 1 10.3
2011 0 10.4
2011 1 12.7
2011 1 9.3
2011 0 11.8
2011 1 5.9
2011 1 11.4
2011 1 13
2011 1 10.8
2011 1 12.3
2011 0 11.3
2011 1 11.8
2011 1 7.9
2011 0 12.7
2011 1 12.3
2011 1 11.6
2011 1 6.7
2011 1 10.9
2011 1 12.1
2011 1 13.3
2011 1 10.1
2011 0 5.7
2011 1 14.3
2011 0 8
2011 1 13.3
2011 1 9.3
2011 0 12.5
2011 0 7.6
2011 1 15.9
2011 0 9.2
2011 1 9.1
2011 0 11.1
2011 1 13
2011 1 14.5
2011 0 12.2
2011 0 12.3
2011 0 11.4
2011 0 8.8
2011 1 14.6
2011 0 12.6
2011 0 13
2011 1 12.6
2011 0 13.2
2011 0 9.9
2011 1 7.7
2011 0 10.5
2011 0 13.4
2011 0 10.9
2011 1 4.3
2011 0 10.3
2011 1 11.8
2011 1 11.2
2011 0 11.4
2011 0 8.6
2011 0 13.2
2011 1 12.6
2011 1 5.6
2011 1 9.9
2011 0 8.8
2011 1 7.7
2011 0 9
2011 1 7.3
2011 1 11.4
2011 1 13.6
2011 1 7.9
2011 1 10.7
2011 0 10.3
2011 1 8.3
2011 1 9.6
2011 1 14.2
2011 0 8.5
2011 0 13.5
2011 0 4.9
2011 0 6.4
2011 0 9.6
2011 0 11.6
2011 1 11.1
2012 1 4.35
2012 1 12.7
2012 1 18.1
2012 1 17.85
2012 0 16.6
2012 1 12.6
2012 1 17.1
2012 0 19.1
2012 1 16.1
2012 0 13.35
2012 0 18.4
2012 1 14.7
2012 1 10.6
2012 1 12.6
2012 1 16.2
2012 1 13.6
2012 1 18.9
2012 1 14.1
2012 1 14.5
2012 0 16.15
2012 1 14.75
2012 1 14.8
2012 1 12.45
2012 1 12.65
2012 1 17.35
2012 1 8.6
2012 0 18.4
2012 1 16.1
2012 1 11.6
2012 1 17.75
2012 1 15.25
2012 1 17.65
2012 0 16.35
2012 0 17.65
2012 1 13.6
2012 0 14.35
2012 0 14.75
2012 1 18.25
2012 0 9.9
2012 1 16
2012 1 18.25
2012 0 16.85
2012 1 14.6
2012 1 13.85
2012 1 18.95
2012 0 15.6
2012 0 14.85
2012 0 11.75
2012 0 18.45
2012 1 15.9
2012 0 17.1
2012 1 16.1
2012 0 19.9
2012 1 10.95
2012 0 18.45
2012 1 15.1
2012 0 15
2012 0 11.35
2012 1 15.95
2012 0 18.1
2012 1 14.6
2012 1 15.4
2012 1 15.4
2012 1 17.6
2012 1 13.35
2012 0 19.1
2012 1 15.35
2012 0 7.6
2012 0 13.4
2012 0 13.9
2012 1 19.1
2012 0 15.25
2012 1 12.9
2012 0 16.1
2012 0 17.35
2012 0 13.15
2012 0 12.15
2012 1 12.6
2012 1 10.35
2012 1 15.4
2012 1 9.6
2012 0 18.2
2012 0 13.6
2012 1 14.85
2012 0 14.75
2012 0 14.1
2012 0 14.9
2012 0 16.25
2012 1 19.25
2012 1 13.6
2012 0 13.6
2012 0 15.65
2012 1 12.75
2012 0 14.6
2012 1 9.85
2012 1 12.65
2012 0 19.2
2012 1 16.6
2012 1 11.2
2012 1 15.25
2012 0 11.9
2012 0 13.2
2012 0 16.35
2012 1 12.4
2012 1 15.85
2012 1 18.15
2012 1 11.15
2012 0 15.65
2012 0 17.75
2012 0 7.65
2012 1 12.35
2012 1 15.6
2012 0 19.3
2012 0 15.2
2012 0 17.1
2012 1 15.6
2012 1 18.4
2012 0 19.05
2012 0 18.55
2012 0 19.1
2012 1 13.1
2012 1 12.85
2012 1 9.5
2012 1 4.5
2012 0 11.85
2012 1 13.6
2012 1 11.7
2012 1 12.4
2012 0 13.35
2012 0 11.4
2012 1 14.9
2012 0 19.9
2012 1 11.2
2012 1 14.6
2012 0 17.6
2012 1 14.05
2012 0 16.1
2012 1 13.35
2012 1 11.85
2012 0 11.95
2012 1 14.75
2012 0 15.15
2012 1 13.2
2012 0 16.85
2012 1 7.85
2012 0 7.7
2012 0 12.6
2012 1 7.85
2012 1 10.95
2012 0 12.35
2012 1 9.95
2012 1 14.9
2012 0 16.65
2012 1 13.4
2012 0 13.95
2012 0 15.7
2012 1 16.85
2012 1 10.95
2012 0 15.35
2012 1 12.2
2012 0 15.1
2012 0 17.75
2012 1 15.2
2012 0 14.6
2012 0 16.65
2012 1 8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285751&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285751&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







ANOVA Model
Response ~ Treatment_A * Treatment_B
means10.6324.6910.097-1.535

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 10.632 & 4.691 & 0.097 & -1.535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285751&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]10.632[/C][C]4.691[/C][C]0.097[/C][C]-1.535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285751&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
means10.6324.6910.097-1.535







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1980.704980.704126.3940
Treatment_B146.24446.2445.960.015
Treatment_A:Treatment_B138.56238.5624.970.027
Residuals2742125.9957.759

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 980.704 & 980.704 & 126.394 & 0 \tabularnewline
Treatment_B & 1 & 46.244 & 46.244 & 5.96 & 0.015 \tabularnewline
Treatment_A:Treatment_B & 1 & 38.562 & 38.562 & 4.97 & 0.027 \tabularnewline
Residuals & 274 & 2125.995 & 7.759 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285751&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]980.704[/C][C]980.704[/C][C]126.394[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]46.244[/C][C]46.244[/C][C]5.96[/C][C]0.015[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]38.562[/C][C]38.562[/C][C]4.97[/C][C]0.027[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]2125.995[/C][C]7.759[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285751&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285751&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_A1980.704980.704126.3940
Treatment_B146.24446.2445.960.015
Treatment_A:Treatment_B138.56238.5624.970.027
Residuals2742125.9957.759







Tukey Honest Significant Difference Comparisons
difflwruprp adj
2012-20113.8293.1594.50
1-0-0.823-1.487-0.1590.015
2012:0-2011:04.6913.3456.0380
2011:1-2011:00.097-1.2811.4760.998
2012:1-2011:03.2541.9654.5420
2011:1-2012:0-4.594-5.822-3.3660
2012:1-2012:0-1.438-2.564-0.3120.006
2012:1-2011:13.1561.9924.320

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2012-2011 & 3.829 & 3.159 & 4.5 & 0 \tabularnewline
1-0 & -0.823 & -1.487 & -0.159 & 0.015 \tabularnewline
2012:0-2011:0 & 4.691 & 3.345 & 6.038 & 0 \tabularnewline
2011:1-2011:0 & 0.097 & -1.281 & 1.476 & 0.998 \tabularnewline
2012:1-2011:0 & 3.254 & 1.965 & 4.542 & 0 \tabularnewline
2011:1-2012:0 & -4.594 & -5.822 & -3.366 & 0 \tabularnewline
2012:1-2012:0 & -1.438 & -2.564 & -0.312 & 0.006 \tabularnewline
2012:1-2011:1 & 3.156 & 1.992 & 4.32 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285751&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]2012-2011[/C][C]3.829[/C][C]3.159[/C][C]4.5[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]-0.823[/C][C]-1.487[/C][C]-0.159[/C][C]0.015[/C][/ROW]
[ROW][C]2012:0-2011:0[/C][C]4.691[/C][C]3.345[/C][C]6.038[/C][C]0[/C][/ROW]
[ROW][C]2011:1-2011:0[/C][C]0.097[/C][C]-1.281[/C][C]1.476[/C][C]0.998[/C][/ROW]
[ROW][C]2012:1-2011:0[/C][C]3.254[/C][C]1.965[/C][C]4.542[/C][C]0[/C][/ROW]
[ROW][C]2011:1-2012:0[/C][C]-4.594[/C][C]-5.822[/C][C]-3.366[/C][C]0[/C][/ROW]
[ROW][C]2012:1-2012:0[/C][C]-1.438[/C][C]-2.564[/C][C]-0.312[/C][C]0.006[/C][/ROW]
[ROW][C]2012:1-2011:1[/C][C]3.156[/C][C]1.992[/C][C]4.32[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285751&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285751&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
2012-20113.8293.1594.50
1-0-0.823-1.487-0.1590.015
2012:0-2011:04.6913.3456.0380
2011:1-2011:00.097-1.2811.4760.998
2012:1-2011:03.2541.9654.5420
2011:1-2012:0-4.594-5.822-3.3660
2012:1-2012:0-1.438-2.564-0.3120.006
2012:1-2011:13.1561.9924.320







Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.3160.269
274

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.316 & 0.269 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285751&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]1.316[/C][C]0.269[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285751&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285751&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)
Group31.3160.269
274



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):
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')