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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, 22 Jan 2017 23:32:47 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/22/t1485124409ooyef3ud25dmo2o.htm/, Retrieved Wed, 15 May 2024 13:18:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=303561, Retrieved Wed, 15 May 2024 13:18:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [2 way anova priva...] [2016-12-07 14:17:16] [5d300c3f2919dcb76af3d6c83a609189]
- R PD  [Two-Way ANOVA] [TEST 12] [2017-01-22 22:27:38] [5d300c3f2919dcb76af3d6c83a609189]
- R PD      [Two-Way ANOVA] [df] [2017-01-22 22:32:47] [a5a591d52ec67035c8301aa1739ae761] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22	4	1
24	4	2
21	4	2
21	4	2
24	4	1
20	4	2
22	4	2
20	3	2
19	3	1
23	4	1
21	4	1
19	3	1
19	3	1
21	4	1
21	4	1
22	4	2
22	4	2
19	4	2
21	4	2
21	4	1
21	4	2
20	4	2
22	4	1
22	4	1
24	3	1
21	3	1
19	4	1
19	4	1
23	4	1
21	3	2
21	4	1
19	3	1
21	4	2
19	4	1
21	4	1
21	3	2
23	3	1
19	3	1
19	3	2
19	3	2
18	3	2
22	4	2
18	3	2
22	3	2
18	4	2
22	4	2
22	4	1
19	3	2
22	3	1
25	3	2
19	3	2
19	4	1
19	4	2
19	3	1
21	3	2
21	4	1
20	4	2
19	3	2
19	4	2
22	4	2
26	4	1
19	4	2
21	4	1
21	4	1
20	4	2
23	4	2
22	4	2
22	4	1
22	3	2
21	4	1
21	4	2
22	4	1
23	4	2
18	4	1
24	4	2
22	4	2
21	4	1
21	4	1
21	3	1
23	4	2
21	4	2
23	4	2
21	4	2
19	4	2
21	3	1
21	3	2
21	3	1
23	4	1
23	4	1
20	3	1
20	4	2
19	4	2
23	4	2
22	4	1
19	4	2
23	4	2
22	4	1
22	4	1
21	4	2
21	4	2
21	4	2
21	3	2
22	4	1
25	3	1
21	4	1
23	4	2
19	4	2
22	3	2
20	4	1
21	4	1
25	4	2
21	4	1
19	4	1
23	3	2
22	3	1
21	3	1
24	3	1
21	3	2
19	4	2
18	4	2
19	4	2
20	4	2
19	4	1
22	3	1
21	3	2
22	4	2
24	3	2
28	4	1
19	3	2
18	4	1
23	4	1
19	3	1
23	4	2
19	3	1
22	4	1
21	3	1
19	3	1
22	4	2
21	4	1
23	4	2
22	4	2
19	4	2
19	4	2
21	4	1
22	4	1
21	4	1
20	3	1
23	3	2
22	3	2
23	3	2
22	3	2
21	3	1
20	4	2
18	3	1
18	3	2
20	4	1
19	4	1
21	4	1
24	4	2
19	4	2
20	4	1

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303561&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=303561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303561&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B
means20.6920.5820.16-0.381

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 20.692 & 0.582 & 0.16 & -0.381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303561&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]20.692[/C][C]0.582[/C][C]0.16[/C][C]-0.381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303561&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
means20.6920.5820.16-0.381






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A15.2385.2381.6250.204
Treatment_B10.3710.3710.1150.735
Treatment_A:Treatment_B11.2911.2910.4010.528
Residuals157505.9453.223 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 5.238 & 5.238 & 1.625 & 0.204 \tabularnewline
Treatment_B & 1 & 0.371 & 0.371 & 0.115 & 0.735 \tabularnewline
Treatment_A:Treatment_B & 1 & 1.291 & 1.291 & 0.401 & 0.528 \tabularnewline
Residuals & 157 & 505.945 & 3.223 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303561&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]5.238[/C][C]5.238[/C][C]1.625[/C][C]0.204[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.371[/C][C]0.371[/C][C]0.115[/C][C]0.735[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]1.291[/C][C]1.291[/C][C]0.401[/C][C]0.528[/C][/ROW]
[ROW][C]Residuals[/C][C]157[/C][C]505.945[/C][C]3.223[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303561&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303561&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_A15.2385.2381.6250.204
Treatment_B10.3710.3710.1150.735
Treatment_A:Treatment_B11.2911.2910.4010.528
Residuals157505.9453.223






Tukey Honest Significant Difference Comparisons
difflwruprp adj
4-30.384-0.2110.9780.204
2-1-0.096-0.6550.4630.735
4:1-3:10.582-0.5411.7060.535
3:2-3:10.16-1.1211.440.988
4:2-3:10.36-0.7431.4640.831
3:2-4:1-0.423-1.5320.6870.756
4:2-4:1-0.222-1.120.6770.918
4:2-3:20.201-0.8881.290.964

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
4-3 & 0.384 & -0.211 & 0.978 & 0.204 \tabularnewline
2-1 & -0.096 & -0.655 & 0.463 & 0.735 \tabularnewline
4:1-3:1 & 0.582 & -0.541 & 1.706 & 0.535 \tabularnewline
3:2-3:1 & 0.16 & -1.121 & 1.44 & 0.988 \tabularnewline
4:2-3:1 & 0.36 & -0.743 & 1.464 & 0.831 \tabularnewline
3:2-4:1 & -0.423 & -1.532 & 0.687 & 0.756 \tabularnewline
4:2-4:1 & -0.222 & -1.12 & 0.677 & 0.918 \tabularnewline
4:2-3:2 & 0.201 & -0.888 & 1.29 & 0.964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303561&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]4-3[/C][C]0.384[/C][C]-0.211[/C][C]0.978[/C][C]0.204[/C][/ROW]
[ROW][C]2-1[/C][C]-0.096[/C][C]-0.655[/C][C]0.463[/C][C]0.735[/C][/ROW]
[ROW][C]4:1-3:1[/C][C]0.582[/C][C]-0.541[/C][C]1.706[/C][C]0.535[/C][/ROW]
[ROW][C]3:2-3:1[/C][C]0.16[/C][C]-1.121[/C][C]1.44[/C][C]0.988[/C][/ROW]
[ROW][C]4:2-3:1[/C][C]0.36[/C][C]-0.743[/C][C]1.464[/C][C]0.831[/C][/ROW]
[ROW][C]3:2-4:1[/C][C]-0.423[/C][C]-1.532[/C][C]0.687[/C][C]0.756[/C][/ROW]
[ROW][C]4:2-4:1[/C][C]-0.222[/C][C]-1.12[/C][C]0.677[/C][C]0.918[/C][/ROW]
[ROW][C]4:2-3:2[/C][C]0.201[/C][C]-0.888[/C][C]1.29[/C][C]0.964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303561&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303561&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
4-30.384-0.2110.9780.204
2-1-0.096-0.6550.4630.735
4:1-3:10.582-0.5411.7060.535
3:2-3:10.16-1.1211.440.988
4:2-3:10.36-0.7431.4640.831
3:2-4:1-0.423-1.5320.6870.756
4:2-4:1-0.222-1.120.6770.918
4:2-3:20.201-0.8881.290.964






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group30.640.591
157 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 0.64 & 0.591 \tabularnewline
  & 157 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303561&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]0.64[/C][C]0.591[/C][/ROW]
[ROW][C] [/C][C]157[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303561&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303561&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)
Group30.640.591
157


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; 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')