FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

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, 28 Oct 2012 14:01:15 -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/2012/Oct/28/t1351447307t6kh36synen5mgh.htm/, Retrieved Fri, 03 May 2024 08:16:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=184436, Retrieved Fri, 03 May 2024 08:16:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Paired and Unpaired Two Samples Tests about the Mean] [WS 5 - Q 1] [2012-10-26 16:53:42] [0604709baf8ca89a71bc0fcadc3cdffd]
- R  D  [Paired and Unpaired Two Samples Tests about the Mean] [WS 5 - Q 2] [2012-10-26 17:00:24] [0604709baf8ca89a71bc0fcadc3cdffd]
-   PD    [Paired and Unpaired Two Samples Tests about the Mean] [WS 5 - Q 5.2] [2012-10-26 17:11:56] [0604709baf8ca89a71bc0fcadc3cdffd]
-    D      [Paired and Unpaired Two Samples Tests about the Mean] [WS 5 - Q 7] [2012-10-26 17:18:33] [0604709baf8ca89a71bc0fcadc3cdffd]
- RMPD          [Two-Way ANOVA] [WS 5 - Q8] [2012-10-28 18:01:15] [b650a28572edc4a1d205c228043a3295] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
0	0	'H'	0	1
0	1	'E'	1	1
0	1	'F'	1	1
0	0	'E'	0	1
0	1	'F'	1	0
0	0	'H'	0	0
0	0	'E'	0	0
0	1	'F'	1	1
0	0	'H'	0	0
0	1	'E'	1	0
0	0	'H'	0	0
0	0	'E'	0	1
0	0	'F'	0	1
0	0	'H'	0	0
0	1	'F'	1	0
0	0	'H'	0	0
0	0	'H'	0	1
0	0	'H'	0	0
0	0	'E'	0	0
0	1	'F'	1	0
0	1	'E'	1	0
0	1	'E'	1	0
1	1	'F'	0	1
0	0	'F'	0	0
0	0	'H'	0	0
0	0	'E'	0	1
0	1	'E'	1	1
0	0	'H'	0	1
0	1	'E'	1	1
0	1	'F'	1	1
0	0	'E'	0	1
0	1	'F'	1	0
0	0	'H'	0	0
0	1	'E'	1	0
0	1	'F'	1	0
0	1	'F'	1	0
0	0	'F'	0	0
0	1	'F'	1	0
0	1	'H'	1	1
0	1	'E'	1	0
0	0	'E'	0	0
0	0	'H'	0	0
0	1	'E'	1	1
0	0	'F'	0	1
0	0	'F'	0	0
0	0	'H'	0	0
0	0	'E'	0	1
0	1	'F'	1	1
0	1	'E'	1	1
0	0	'H'	0	1
0	0	'H'	0	1
0	0	'H'	0	1
0	0	'E'	0	1
0	0	'H'	0	0
0	1	'E'	1	0
0	0	'H'	0	1
0	0	'F'	0	1
0	0	'H'	0	1
0	1	'F'	1	0
0	0	'E'	0	1
0	1	'E'	1	1
0	0	'F'	0	0
0	0	'H'	0	1
0	0	'F'	0	0
0	0	'E'	0	1
1	0	'E'	-1	1
0	0	'H'	0	0
0	0	'H'	0	1
0	0	'F'	0	1
0	0	'H'	0	1
0	1	'E'	1	0
0	0	'F'	0	1
0	1	'E'	1	0
0	0	'E'	0	0
0	0	'E'	0	0
0	0	'F'	0	1
0	0	'E'	0	1
0	1	'F'	1	1
0	0	'H'	0	1
1	1	'H'	0	1
0	0	'H'	0	1
0	0	'F'	0	0
0	0	'H'	0	1
0	0	'H'	0	1
0	1	'F'	1	1
0	1	'F'	1	1
0	0	'H'	0	0
0	0	'F'	0	1
0	0	'H'	0	1
0	0	'E'	0	0
0	1	'F'	1	1
0	0	'E'	0	0
0	0	'H'	0	1
0	1	'F'	1	1
1	1	'F'	0	1
0	0	'H'	0	1
0	1	'E'	1	1
0	0	'F'	0	0
0	0	'H'	0	1
0	0	'E'	0	1
0	0	'F'	0	0
0	0	'H'	0	0
0	0	'H'	0	1
0	1	'F'	1	1
0	1	'F'	1	1
0	0	'H'	0	1
0	0	'E'	0	0
0	0	'H'	0	1
0	0	'E'	0	1
0	0	'E'	0	0
0	0	'F'	0	1
0	0	'F'	0	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=184436&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=184436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=184436&T=0

As an alternative you can also use a QR Code:  
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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.5970.403-0.070.07

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.597 & 0.403 & -0.07 & 0.07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=184436&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.597[/C][C]0.403[/C][C]-0.07[/C][C]0.07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=184436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=184436&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means0.5970.403-0.070.07






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.6970.6972.8650.093
Treatment_B10.1150.1150.4740.492
Treatment_A:Treatment_B10.0040.0040.0150.904
Residuals11327.4920.243 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.697 & 0.697 & 2.865 & 0.093 \tabularnewline
Treatment_B & 1 & 0.115 & 0.115 & 0.474 & 0.492 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.004 & 0.004 & 0.015 & 0.904 \tabularnewline
Residuals & 113 & 27.492 & 0.243 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=184436&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]0.697[/C][C]0.697[/C][C]2.865[/C][C]0.093[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.115[/C][C]0.115[/C][C]0.474[/C][C]0.492[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.004[/C][C]0.004[/C][C]0.015[/C][C]0.904[/C][/ROW]
[ROW][C]Residuals[/C][C]113[/C][C]27.492[/C][C]0.243[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=184436&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=184436&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A10.6970.6972.8650.093
Treatment_B10.1150.1150.4740.492
Treatment_A:Treatment_B10.0040.0040.0150.904
Residuals11327.4920.243






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.425-0.0720.9220.093
1-0-0.066-0.2570.1260.498
1:0-0:00.403-0.8921.6970.849
0:1-0:0-0.07-0.3290.190.897
1:1-0:00.403-0.3541.160.51
0:1-1:0-0.472-1.7760.8320.781
1:1-1:00-1.4851.4851
1:1-0:10.472-0.3011.2450.387

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 0.425 & -0.072 & 0.922 & 0.093 \tabularnewline
1-0 & -0.066 & -0.257 & 0.126 & 0.498 \tabularnewline
1:0-0:0 & 0.403 & -0.892 & 1.697 & 0.849 \tabularnewline
0:1-0:0 & -0.07 & -0.329 & 0.19 & 0.897 \tabularnewline
1:1-0:0 & 0.403 & -0.354 & 1.16 & 0.51 \tabularnewline
0:1-1:0 & -0.472 & -1.776 & 0.832 & 0.781 \tabularnewline
1:1-1:0 & 0 & -1.485 & 1.485 & 1 \tabularnewline
1:1-0:1 & 0.472 & -0.301 & 1.245 & 0.387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=184436&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]0.425[/C][C]-0.072[/C][C]0.922[/C][C]0.093[/C][/ROW]
[ROW][C]1-0[/C][C]-0.066[/C][C]-0.257[/C][C]0.126[/C][C]0.498[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]0.403[/C][C]-0.892[/C][C]1.697[/C][C]0.849[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-0.07[/C][C]-0.329[/C][C]0.19[/C][C]0.897[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]0.403[/C][C]-0.354[/C][C]1.16[/C][C]0.51[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-0.472[/C][C]-1.776[/C][C]0.832[/C][C]0.781[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0[/C][C]-1.485[/C][C]1.485[/C][C]1[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]0.472[/C][C]-0.301[/C][C]1.245[/C][C]0.387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=184436&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=184436&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-00.425-0.0720.9220.093
1-0-0.066-0.2570.1260.498
1:0-0:00.403-0.8921.6970.849
0:1-0:0-0.07-0.3290.190.897
1:1-0:00.403-0.3541.160.51
0:1-1:0-0.472-1.7760.8320.781
1:1-1:00-1.4851.4851
1:1-0:10.472-0.3011.2450.387






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.1180.345
113 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.118 & 0.345 \tabularnewline
  & 113 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=184436&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]1.118[/C][C]0.345[/C][/ROW]
[ROW][C] [/C][C]113[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=184436&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=184436&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.1180.345
113


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 5 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;
Parameters (R input):
par1 = 5 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- 'TRUE'
par3 <- '5'
par2 <- '2'
par1 <- '1'
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')