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 computationTue, 19 Nov 2013 00:40:51 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/19/t1384839749ylbysaeg6zgwpdk.htm/, Retrieved Fri, 03 May 2024 21:25:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226335, Retrieved Fri, 03 May 2024 21:25:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSmokers, Curry, ANOVA, WS6, Workshop 6
Estimated Impact114

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram, QQplot and Density] [Workshop 1 ] [2010-09-29 15:04:17] [98fd0e87c3eb04e0cc2efde01dbafab6]
- RM    [Histogram, QQplot and Density] [Workshop 1] [2011-10-03 09:04:15] [74be16979710d4c4e7c6647856088456]
- R P     [Histogram, QQplot and Density] [Histogram of WS1 ...] [2013-10-15 01:19:24] [8f1c4a52d8544d995fde3ee47326fd58]
- R PD      [Histogram, QQplot and Density] [Smokers with Korm...] [2013-11-17 23:46:28] [8f1c4a52d8544d995fde3ee47326fd58]
- RMPD          [Two-Way ANOVA] [ANOVA of Curry a...] [2013-11-19 05:40:51] [c0e7c7f61251fedfb27818bf0749c3db] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4	1	1
5	1	1
3	1	1
4	1	1
5	1	1
3	1	1
7	1	1
5	1	1
6	1	1
3	1	1
2	1	1
4	1	1
5	1	1
2	1	1
3	1	1
6	1	1
4	1	1
4	1	1
6	1	1
2	1	1
3	1	2
5	1	2
4	1	2
2	1	2
7	1	2
1	1	2
4	1	2
4	1	2
7	1	2
4	1	2
3	1	2
3	1	2
3	1	2
3	1	2
2	1	2
5	1	2
5	1	2
3	1	2
6	1	2
2	1	2
8	2	1
9	2	1
10	2	1
7	2	1
8	2	1
9	2	1
10	2	1
6	2	1
6	2	1
7	2	1
8	2	1
9	2	1
8	2	1
7	2	1
5	2	1
11	2	1
7	2	1
8	2	1
10	2	1
9	2	1
3	2	2
5	2	2
4	2	2
2	2	2
6	2	2
1	2	2
4	2	2
4	2	2
5	2	2
4	2	2
3	2	2
3	2	2
4	2	2
3	2	2
2	2	2
5	2	2
4	2	2
3	2	2
6	2	2
2	2	2

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'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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226335&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226335&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226335&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'Gwilym Jenkins' @ jenkins.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means4.153.95-0.35-4.1

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 4.15 & 3.95 & -0.35 & -4.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226335&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]4.15[/C][C]3.95[/C][C]-0.35[/C][C]-4.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226335&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226335&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
means4.153.95-0.35-4.1






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A172.272.231.8840
Treatment_B1115.2115.250.8730
Treatment_A:Treatment_B184.0584.0537.1170
Residuals76172.12.264 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 72.2 & 72.2 & 31.884 & 0 \tabularnewline
Treatment_B & 1 & 115.2 & 115.2 & 50.873 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 84.05 & 84.05 & 37.117 & 0 \tabularnewline
Residuals & 76 & 172.1 & 2.264 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226335&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]72.2[/C][C]72.2[/C][C]31.884[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]115.2[/C][C]115.2[/C][C]50.873[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]84.05[/C][C]84.05[/C][C]37.117[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]76[/C][C]172.1[/C][C]2.264[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226335&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226335&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_A172.272.231.8840
Treatment_B1115.2115.250.8730
Treatment_A:Treatment_B184.0584.0537.1170
Residuals76172.12.264






Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-11.91.232.570
2-1-2.4-3.07-1.730
2:1-1:13.952.75.20
1:2-1:1-0.35-1.60.90.882
2:2-1:1-0.5-1.750.750.72
1:2-2:1-4.3-5.55-3.050
2:2-2:1-4.45-5.7-3.20
2:2-1:2-0.15-1.41.10.989

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2-1 & 1.9 & 1.23 & 2.57 & 0 \tabularnewline
2-1 & -2.4 & -3.07 & -1.73 & 0 \tabularnewline
2:1-1:1 & 3.95 & 2.7 & 5.2 & 0 \tabularnewline
1:2-1:1 & -0.35 & -1.6 & 0.9 & 0.882 \tabularnewline
2:2-1:1 & -0.5 & -1.75 & 0.75 & 0.72 \tabularnewline
1:2-2:1 & -4.3 & -5.55 & -3.05 & 0 \tabularnewline
2:2-2:1 & -4.45 & -5.7 & -3.2 & 0 \tabularnewline
2:2-1:2 & -0.15 & -1.4 & 1.1 & 0.989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226335&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]2-1[/C][C]1.9[/C][C]1.23[/C][C]2.57[/C][C]0[/C][/ROW]
[ROW][C]2-1[/C][C]-2.4[/C][C]-3.07[/C][C]-1.73[/C][C]0[/C][/ROW]
[ROW][C]2:1-1:1[/C][C]3.95[/C][C]2.7[/C][C]5.2[/C][C]0[/C][/ROW]
[ROW][C]1:2-1:1[/C][C]-0.35[/C][C]-1.6[/C][C]0.9[/C][C]0.882[/C][/ROW]
[ROW][C]2:2-1:1[/C][C]-0.5[/C][C]-1.75[/C][C]0.75[/C][C]0.72[/C][/ROW]
[ROW][C]1:2-2:1[/C][C]-4.3[/C][C]-5.55[/C][C]-3.05[/C][C]0[/C][/ROW]
[ROW][C]2:2-2:1[/C][C]-4.45[/C][C]-5.7[/C][C]-3.2[/C][C]0[/C][/ROW]
[ROW][C]2:2-1:2[/C][C]-0.15[/C][C]-1.4[/C][C]1.1[/C][C]0.989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226335&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226335&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
2-11.91.232.570
2-1-2.4-3.07-1.730
2:1-1:13.952.75.20
1:2-1:1-0.35-1.60.90.882
2:2-1:1-0.5-1.750.750.72
1:2-2:1-4.3-5.55-3.050
2:2-2:1-4.45-5.7-3.20
2:2-1:2-0.15-1.41.10.989






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.250.861
76 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.25 & 0.861 \tabularnewline
  & 76 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226335&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]0.25[/C][C]0.861[/C][/ROW]
[ROW][C] [/C][C]76[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226335&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226335&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)
Group30.250.861
76


Figures (Output of Computation)

Input Parameters & R Code

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