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Author

*The author of this computation has been verified*

R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Tue, 19 Feb 2013 09:11:05 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Feb/19/t1361283083zyuego66t39iub1.htm/, Retrieved Sat, 04 May 2024 01:49:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206580, Retrieved Sat, 04 May 2024 01:49:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

140

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Variability] [Two-Way ANOVA] [2010-11-30 21:42:30] [74be16979710d4c4e7c6647856088456]
- RM    [Two-Way ANOVA] [Two-Way ANOVA - C...] [2011-11-28 17:22:56] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R PD    [Two-Way ANOVA] [Recognising faces] [2013-02-19 14:05:23] [f3df66176306f4bc7dbd536cdf32fa04]
-   P         [Two-Way ANOVA] [Reaction time] [2013-02-19 14:11:05] [4e2c5629241a1e636d9839a5af4aa431] [Current]

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Dataseries X:

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Histogram

Boxplots

1.00	1259.00	1.00	.00
1.00	881.00	1.00	1.00
1.00	944.00	1.00	.00
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1.00	947.00	1.00	1.00
1.00	986.00	1.00	1.00
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1.00	666.00	1.00	1.00
1.00	1025.00	1.00	.00
1.00	758.00	1.00	1.00
1.00	909.00	1.00	.00
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1.00	667.00	1.00	.00
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1.00	1422.00	1.00	1.00
1.00	1469.00	1.00	1.00
1.00	1247.00	1.00	.00
1.00	678.00	1.00	1.00
1.00	1261.00	1.00	1.00
1.00	933.00	1.00	.00
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1.00	673.00	1.00	1.00
1.00	660.00	1.00	1.00
1.00	768.00	1.00	1.00
1.00	591.00	1.00	.00
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1.00	1078.00	1.00	1.00
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1.00	1271.00	1.00	.00
1.00	745.00	1.00	1.00
1.00	738.00	1.00	.00
1.00	792.00	1.00	.00
1.00	1155.00	1.00	.00
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1.00	806.00	1.00	1.00
1.00	755.00	1.00	1.00
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1.00	782.00	1.00	.00
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1.00	861.00	1.00	1.00
1.00	574.00	1.00	1.00
1.00	900.00	1.00	.00
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1.00	651.00	1.00	.00
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1.00	667.00	1.00	1.00
1.00	1185.00	1.00	.00
1.00	619.00	1.00	1.00
1.00	1479.00	1.00	.00
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1.00	1100.00	1.00	.00
1.00	910.00	1.00	.00
1.00	685.00	1.00	1.00
1.00	788.00	1.00	.00
1.00	750.00	1.00	1.00
1.00	711.00	1.00	1.00
1.00	1175.00	1.00	.00
1.00	747.00	1.00	.00
1.00	712.00	1.00	1.00
1.00	845.00	1.00	1.00
1.00	1177.00	1.00	1.00
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1.00	1866.00	.00	1.00
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1.00	949.00	.00	1.00
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1.00	852.00	.00	.00
1.00	849.00	.00	1.00
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1.00	1228.00	.00	.00
1.00	651.00	.00	1.00
1.00	621.00	.00	1.00
1.00	884.00	.00	.00
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1.00	634.00	.00	1.00
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1.00	527.00	.00	.00
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1.00	1335.00	.00	1.00
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1.00	719.00	.00	.00
1.00	1922.00	.00	1.00
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1.00	877.00	.00	1.00
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1.00	792.00	.00	.00
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1.00	792.00	.00	.00
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1.00	711.00	.00	.00
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1.00	585.00	.00	.00
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1.00	763.00	.00	.00
1.00	597.00	.00	1.00
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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	3 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=206580&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=206580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206580&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	889.389	36.861	-36.417	66.71

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 889.389 & 36.861 & -36.417 & 66.71 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206580&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]889.389[/C][C]36.861[/C][C]-36.417[/C][C]66.71[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206580&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	889.389	36.861	-36.417	66.71

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	175179.161	175179.161	1.363	0.245
Treatment_B	1	388.917	388.917	0.003	0.956
Treatment_A:Treatment_B	1	39767.392	39767.392	0.31	0.579
Residuals	139	17859610.963	128486.41

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 175179.161 & 175179.161 & 1.363 & 0.245 \tabularnewline
Treatment_B & 1 & 388.917 & 388.917 & 0.003 & 0.956 \tabularnewline
Treatment_A:Treatment_B & 1 & 39767.392 & 39767.392 & 0.31 & 0.579 \tabularnewline
Residuals & 139 & 17859610.963 & 128486.41 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206580&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]175179.161[/C][C]175179.161[/C][C]1.363[/C][C]0.245[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]388.917[/C][C]388.917[/C][C]0.003[/C][C]0.956[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]39767.392[/C][C]39767.392[/C][C]0.31[/C][C]0.579[/C][/ROW]
[ROW][C]Residuals[/C][C]139[/C][C]17859610.963[/C][C]128486.41[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206580&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206580&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)
	1
Treatment_A	1	175179.161	175179.161	1.363	0.245
Treatment_B	1	388.917	388.917	0.003	0.956
Treatment_A:Treatment_B	1	39767.392	39767.392	0.31	0.579
Residuals	139	17859610.963	128486.41

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	70.003	-48.533	188.538	0.245
1-0	-3.298	-121.833	115.237	0.956
1:0-0:0	36.861	-182.839	256.561	0.972
0:1-0:0	-36.417	-256.116	183.283	0.973
1:1-0:0	67.154	-154.109	288.417	0.859
0:1-1:0	-73.278	-292.978	146.422	0.822
1:1-1:0	30.293	-190.971	251.556	0.984
1:1-0:1	103.571	-117.693	324.834	0.617

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 70.003 & -48.533 & 188.538 & 0.245 \tabularnewline
1-0 & -3.298 & -121.833 & 115.237 & 0.956 \tabularnewline
1:0-0:0 & 36.861 & -182.839 & 256.561 & 0.972 \tabularnewline
0:1-0:0 & -36.417 & -256.116 & 183.283 & 0.973 \tabularnewline
1:1-0:0 & 67.154 & -154.109 & 288.417 & 0.859 \tabularnewline
0:1-1:0 & -73.278 & -292.978 & 146.422 & 0.822 \tabularnewline
1:1-1:0 & 30.293 & -190.971 & 251.556 & 0.984 \tabularnewline
1:1-0:1 & 103.571 & -117.693 & 324.834 & 0.617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206580&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]1-0[/C][C]70.003[/C][C]-48.533[/C][C]188.538[/C][C]0.245[/C][/ROW]
[ROW][C]1-0[/C][C]-3.298[/C][C]-121.833[/C][C]115.237[/C][C]0.956[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]36.861[/C][C]-182.839[/C][C]256.561[/C][C]0.972[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-36.417[/C][C]-256.116[/C][C]183.283[/C][C]0.973[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]67.154[/C][C]-154.109[/C][C]288.417[/C][C]0.859[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-73.278[/C][C]-292.978[/C][C]146.422[/C][C]0.822[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]30.293[/C][C]-190.971[/C][C]251.556[/C][C]0.984[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]103.571[/C][C]-117.693[/C][C]324.834[/C][C]0.617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206580&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206580&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
1-0	70.003	-48.533	188.538	0.245
1-0	-3.298	-121.833	115.237	0.956
1:0-0:0	36.861	-182.839	256.561	0.972
0:1-0:0	-36.417	-256.116	183.283	0.973
1:1-0:0	67.154	-154.109	288.417	0.859
0:1-1:0	-73.278	-292.978	146.422	0.822
1:1-1:0	30.293	-190.971	251.556	0.984
1:1-0:1	103.571	-117.693	324.834	0.617

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	0.422	0.737
	139

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.422 & 0.737 \tabularnewline
  & 139 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206580&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]0.422[/C][C]0.737[/C][/ROW]
[ROW][C] [/C][C]139[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206580&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206580&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	3	0.422	0.737
	139

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; par2 = 3 ; par3 = 4 ; par4 = TRUE ;

Parameters (R input):

par1 = 2 ; par2 = 3 ; par3 = 4 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code