## 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 computationSun, 30 Oct 2011 10:00:47 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/30/t1319983293j4jam28wtp9ieg8.htm/, Retrieved Wed, 27 Sep 2023 08:47:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=138041, Retrieved Wed, 27 Sep 2023 08:47:08 +0000
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User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [] [2010-11-02 14:42:14] [b98453cac15ba1066b407e146608df68]
-   PD    [Two-Way ANOVA] [vraag 8] [2011-10-30 14:00:47] [e1aba6efa0fba8dc2a9839c208d0186e] [Current]
- RMPD      [Histogram] [Histogram] [2011-11-11 15:56:27] [c26e829f03d42da3805b9c4b60f90f25]
- RMPD      [Kernel Density Estimation] [] [2011-11-11 15:58:58] [c26e829f03d42da3805b9c4b60f90f25]
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Dataseries X:
0	0	'E'	0	1
0	1	'F'	1	0
0	0	'F'	0	1
0	0	'H'	0	1
0	0	'H'	0	1
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1	0	'E'	-1	1
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 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=138041&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=138041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=138041&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 Output view raw output of R engine Computing time 1 seconds R Server 'Herman Ole Andreas Wold' @ wold.wessa.net

 ANOVA Model Response ~ Treatment_A * Treatment_B means 0.471 0.059 -0.471 -0.171 0.119 0.209

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.471 & 0.059 & -0.471 & -0.171 & 0.119 & 0.209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=138041&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.471[/C][C]0.059[/C][C]-0.471[/C][C]-0.171[/C][C]0.119[/C][C]0.209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=138041&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=138041&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 means 0.471 0.059 -0.471 -0.171 0.119 0.209

 ANOVA Statistics Df Sum Sq Mean Sq F value Pr(>F) 2 Treatment_A 2 4.852 2.426 12.601 0 Treatment_B 2 0.105 0.105 0.546 0.462 Treatment_A:Treatment_B 2 0.201 0.101 0.523 0.594 Residuals 111 21.371 0.193

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
& Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
& 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 4.852 & 2.426 & 12.601 & 0 \tabularnewline
Treatment_B & 2 & 0.105 & 0.105 & 0.546 & 0.462 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.201 & 0.101 & 0.523 & 0.594 \tabularnewline
Residuals & 111 & 21.371 & 0.193 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=138041&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]2[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]2[/C][C]4.852[/C][C]2.426[/C][C]12.601[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0.105[/C][C]0.105[/C][C]0.546[/C][C]0.462[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.201[/C][C]0.101[/C][C]0.523[/C][C]0.594[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]21.371[/C][C]0.193[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=138041&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=138041&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 Df Sum Sq Mean Sq F value Pr(>F) 2 Treatment_A 2 4.852 2.426 12.601 0 Treatment_B 2 0.105 0.105 0.546 0.462 Treatment_A:Treatment_B 2 0.201 0.101 0.523 0.594 Residuals 111 21.371 0.193

 Tukey Honest Significant Difference Comparisons diff lwr upr p adj F-E 0.122 -0.116 0.359 0.447 H-E -0.353 -0.591 -0.116 0.002 H-F -0.475 -0.708 -0.242 0 1-0 -0.061 -0.224 0.103 0.463 F:0-E:0 0.059 -0.378 0.495 0.999 H:0-E:0 -0.471 -0.93 -0.011 0.041 E:1-E:0 -0.171 -0.59 0.249 0.846 F:1-E:0 0.008 -0.399 0.415 1 H:1-E:0 -0.432 -0.829 -0.035 0.024 H:0-F:0 -0.529 -0.989 -0.07 0.014 E:1-F:0 -0.229 -0.649 0.19 0.61 F:1-F:0 -0.051 -0.458 0.356 0.999 H:1-F:0 -0.491 -0.888 -0.094 0.006 E:1-H:0 0.3 -0.143 0.743 0.371 F:1-H:0 0.478 0.047 0.91 0.021 H:1-H:0 0.038 -0.383 0.46 1 F:1-E:1 0.178 -0.211 0.567 0.768 H:1-E:1 -0.262 -0.64 0.117 0.347 H:1-F:1 -0.44 -0.804 -0.076 0.009

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
& diff & lwr & upr & p adj \tabularnewline
F-E & 0.122 & -0.116 & 0.359 & 0.447 \tabularnewline
H-E & -0.353 & -0.591 & -0.116 & 0.002 \tabularnewline
H-F & -0.475 & -0.708 & -0.242 & 0 \tabularnewline
1-0 & -0.061 & -0.224 & 0.103 & 0.463 \tabularnewline
F:0-E:0 & 0.059 & -0.378 & 0.495 & 0.999 \tabularnewline
H:0-E:0 & -0.471 & -0.93 & -0.011 & 0.041 \tabularnewline
E:1-E:0 & -0.171 & -0.59 & 0.249 & 0.846 \tabularnewline
F:1-E:0 & 0.008 & -0.399 & 0.415 & 1 \tabularnewline
H:1-E:0 & -0.432 & -0.829 & -0.035 & 0.024 \tabularnewline
H:0-F:0 & -0.529 & -0.989 & -0.07 & 0.014 \tabularnewline
E:1-F:0 & -0.229 & -0.649 & 0.19 & 0.61 \tabularnewline
F:1-F:0 & -0.051 & -0.458 & 0.356 & 0.999 \tabularnewline
H:1-F:0 & -0.491 & -0.888 & -0.094 & 0.006 \tabularnewline
E:1-H:0 & 0.3 & -0.143 & 0.743 & 0.371 \tabularnewline
F:1-H:0 & 0.478 & 0.047 & 0.91 & 0.021 \tabularnewline
H:1-H:0 & 0.038 & -0.383 & 0.46 & 1 \tabularnewline
F:1-E:1 & 0.178 & -0.211 & 0.567 & 0.768 \tabularnewline
H:1-E:1 & -0.262 & -0.64 & 0.117 & 0.347 \tabularnewline
H:1-F:1 & -0.44 & -0.804 & -0.076 & 0.009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=138041&T=3

[TABLE]
[ROW][C]Tukey Honest Significant Difference Comparisons[/C][/ROW]
[ROW][C]F-E[/C][C]0.122[/C][C]-0.116[/C][C]0.359[/C][C]0.447[/C][/ROW]
[ROW][C]H-E[/C][C]-0.353[/C][C]-0.591[/C][C]-0.116[/C][C]0.002[/C][/ROW]
[ROW][C]H-F[/C][C]-0.475[/C][C]-0.708[/C][C]-0.242[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]-0.061[/C][C]-0.224[/C][C]0.103[/C][C]0.463[/C][/ROW]
[ROW][C]F:0-E:0[/C][C]0.059[/C][C]-0.378[/C][C]0.495[/C][C]0.999[/C][/ROW]
[ROW][C]H:0-E:0[/C][C]-0.471[/C][C]-0.93[/C][C]-0.011[/C][C]0.041[/C][/ROW]
[ROW][C]E:1-E:0[/C][C]-0.171[/C][C]-0.59[/C][C]0.249[/C][C]0.846[/C][/ROW]
[ROW][C]F:1-E:0[/C][C]0.008[/C][C]-0.399[/C][C]0.415[/C][C]1[/C][/ROW]
[ROW][C]H:1-E:0[/C][C]-0.432[/C][C]-0.829[/C][C]-0.035[/C][C]0.024[/C][/ROW]
[ROW][C]H:0-F:0[/C][C]-0.529[/C][C]-0.989[/C][C]-0.07[/C][C]0.014[/C][/ROW]
[ROW][C]E:1-F:0[/C][C]-0.229[/C][C]-0.649[/C][C]0.19[/C][C]0.61[/C][/ROW]
[ROW][C]F:1-F:0[/C][C]-0.051[/C][C]-0.458[/C][C]0.356[/C][C]0.999[/C][/ROW]
[ROW][C]H:1-F:0[/C][C]-0.491[/C][C]-0.888[/C][C]-0.094[/C][C]0.006[/C][/ROW]
[ROW][C]E:1-H:0[/C][C]0.3[/C][C]-0.143[/C][C]0.743[/C][C]0.371[/C][/ROW]
[ROW][C]F:1-H:0[/C][C]0.478[/C][C]0.047[/C][C]0.91[/C][C]0.021[/C][/ROW]
[ROW][C]H:1-H:0[/C][C]0.038[/C][C]-0.383[/C][C]0.46[/C][C]1[/C][/ROW]
[ROW][C]F:1-E:1[/C][C]0.178[/C][C]-0.211[/C][C]0.567[/C][C]0.768[/C][/ROW]
[ROW][C]H:1-E:1[/C][C]-0.262[/C][C]-0.64[/C][C]0.117[/C][C]0.347[/C][/ROW]
[ROW][C]H:1-F:1[/C][C]-0.44[/C][C]-0.804[/C][C]-0.076[/C][C]0.009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=138041&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=138041&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 diff lwr upr p adj F-E 0.122 -0.116 0.359 0.447 H-E -0.353 -0.591 -0.116 0.002 H-F -0.475 -0.708 -0.242 0 1-0 -0.061 -0.224 0.103 0.463 F:0-E:0 0.059 -0.378 0.495 0.999 H:0-E:0 -0.471 -0.93 -0.011 0.041 E:1-E:0 -0.171 -0.59 0.249 0.846 F:1-E:0 0.008 -0.399 0.415 1 H:1-E:0 -0.432 -0.829 -0.035 0.024 H:0-F:0 -0.529 -0.989 -0.07 0.014 E:1-F:0 -0.229 -0.649 0.19 0.61 F:1-F:0 -0.051 -0.458 0.356 0.999 H:1-F:0 -0.491 -0.888 -0.094 0.006 E:1-H:0 0.3 -0.143 0.743 0.371 F:1-H:0 0.478 0.047 0.91 0.021 H:1-H:0 0.038 -0.383 0.46 1 F:1-E:1 0.178 -0.211 0.567 0.768 H:1-E:1 -0.262 -0.64 0.117 0.347 H:1-F:1 -0.44 -0.804 -0.076 0.009

 Levenes Test for Homogeneity of Variance Df F value Pr(>F) Group 5 5.504 0 111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
& Df & F value & Pr(>F) \tabularnewline
Group & 5 & 5.504 & 0 \tabularnewline
& 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=138041&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]5[/C][C]5.504[/C][C]0[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=138041&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=138041&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 Df F value Pr(>F) Group 5 5.504 0 111

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$'Mean Sq'[i+1], digits=3),,FALSE)a<-table.element(a, ' ',,FALSE)a<-table.element(a, ' ',,FALSE)a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable1.tab')bitmap(file='anovaplot.png')boxplot(Response ~ Treatment_A + Treatment_B, data=xdf, xlab=V2, ylab=V1, main='Boxplots of ANOVA Groups')dev.off()bitmap(file='designplot.png')xdf2 <- xdf # to preserve xdf make copy for functionnames(xdf2) <- c(V1, V2, V3)plot.design(xdf2, main='Design Plot of Group Means')dev.off()bitmap(file='interactionplot.png')interaction.plot(xdf$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 nta<-table.end(a)table.save(a,file='hsdtable.tab')}#end if hsd tablesif(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')