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, 18 Dec 2016 17:10:59 +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/2016/Dec/18/t1482077474600cnd8zgcw0fe3.htm/, Retrieved Wed, 08 May 2024 23:04:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301159, Retrieved Wed, 08 May 2024 23:04:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79

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] [Paper Statistiek] [2016-12-18 16:10:59] [1e2703d0f11438bcd65480dae45a3781] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12	22	23
12	23	23
12	19	22
12	25	18
13	22	22
13	24	21
13	23	21
13	22	18
13	25	22
13	25	21
13	24	18
13	26	25
13	21	19
13	24	19
13	22	22
13	21	24
14	24	21
14	23	21
14	24	19
14	22	19
14	23	21
14	24	22
14	25	22
14	23	23
14	25	21
14	20	20
14	24	21
14	23	18
14	23	20
14	25	19
14	26	20
14	24	22
14	24	21
14	25	21
15	21	21
15	25	19
15	25	21
15	26	20
15	25	22
15	24	19
15	28	19
15	25	19
15	24	23
15	25	18
15	25	18
15	24	22
15	23	19
15	21	20
15	25	22
15	27	20
15	23	21
15	28	22
15	22	22
15	24	21
15	25	23
15	24	19
15	24	23
15	26	22
15	21	21
15	25	20
15	24	19
15	24	19
15	25	22
15	23	22
15	21	19
15	22	18
15	26	21
15	25	18
15	26	20
15	22	24
15	24	20
15	27	23
15	24	22
16	24	24
16	26	24
16	25	20
16	24	20
16	24	19
16	24	21
16	25	22
16	24	21
16	26	22
16	24	19
16	25	23
16	25	21
16	28	22
16	24	22
16	24	19
16	24	19
16	26	21
16	21	21
16	24	21
16	25	21
16	26	21
16	25	21
16	25	22
16	26	22
16	27	21
16	26	19
16	21	22
16	25	21
16	24	25
16	24	21
16	24	24
16	28	19
16	24	19
16	23	24
16	25	28
16	24	19
16	23	21
16	25	21
16	25	23
16	25	21
16	23	20
16	24	21
16	25	21
16	23	22
17	26	21
17	27	19
17	28	23
17	23	21
17	25	22
17	25	21
17	26	24
17	27	21
17	23	21
17	28	22
17	26	19
17	22	19
17	27	26
17	23	22
17	24	23
17	25	19
17	26	21
17	26	21
17	23	20
17	26	23
17	25	19
17	26	21
17	28	23
17	25	21
17	24	21
17	28	22
17	25	21
17	27	19
18	21	22
18	25	19
18	25	19
18	27	19
18	26	24
18	27	23
18	25	22
18	28	21
18	25	23
18	27	19
18	25	19
18	23	19
19	23	22
19	29	23
19	26	23
20	25	21

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301159&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301159&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B - 1
means4.757.5614141314.25108.59116.56.597.258738.51.75NA1.5-5-4-4.25-4.2502.5NANANA2.5NA-4.833-4-5.25-1.833NANANANA0.333NA-7.857-6.818-7.317-2.571-1NANANA3.75-7.583-4.5-5.45-6.056-1.583NANANANANA-10-9-5.333-6NANANANANANA-6-5-4NANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANA

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B - 1 \tabularnewline
means & 4.75 & 7.5 & 6 & 14 & 14 & 13 & 14.25 & 10 & 8.5 & 9 & 11 & 6.5 & 6.5 & 9 & 7.25 & 8 & 7 & 3 & 8.5 & 1.75 & NA & 1.5 & -5 & -4 & -4.25 & -4.25 & 0 & 2.5 & NA & NA & NA & 2.5 & NA & -4.833 & -4 & -5.25 & -1.833 & NA & NA & NA & NA & 0.333 & NA & -7.857 & -6.818 & -7.317 & -2.571 & -1 & NA & NA & NA & 3.75 & -7.583 & -4.5 & -5.45 & -6.056 & -1.583 & NA & NA & NA & NA & NA & -10 & -9 & -5.333 & -6 & NA & NA & NA & NA & NA & NA & -6 & -5 & -4 & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301159&T=1

[TABLE]
[ROW]ANOVA Model[/C][/ROW]
[ROW]Response ~ Treatment_A * Treatment_B - 1[/C][/ROW]
[ROW][C]means[/C][C]4.75[/C][C]7.5[/C][C]6[/C][C]14[/C][C]14[/C][C]13[/C][C]14.25[/C][C]10[/C][C]8.5[/C][C]9[/C][C]11[/C][C]6.5[/C][C]6.5[/C][C]9[/C][C]7.25[/C][C]8[/C][C]7[/C][C]3[/C][C]8.5[/C][C]1.75[/C][C]NA[/C][C]1.5[/C][C]-5[/C][C]-4[/C][C]-4.25[/C][C]-4.25[/C][C]0[/C][C]2.5[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]2.5[/C][C]NA[/C][C]-4.833[/C][C]-4[/C][C]-5.25[/C][C]-1.833[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.333[/C][C]NA[/C][C]-7.857[/C][C]-6.818[/C][C]-7.317[/C][C]-2.571[/C][C]-1[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]3.75[/C][C]-7.583[/C][C]-4.5[/C][C]-5.45[/C][C]-6.056[/C][C]-1.583[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]-10[/C][C]-9[/C][C]-5.333[/C][C]-6[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]-6[/C][C]-5[/C][C]-4[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301159&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 - 1
means4.757.5614141314.25108.59116.56.597.258738.51.75NA1.5-5-4-4.25-4.2502.5NANANA2.5NA-4.833-4-5.25-1.833NANANANA0.333NA-7.857-6.818-7.317-2.571-1NANANA3.75-7.583-4.5-5.45-6.056-1.583NANANANANA-10-9-5.333-6NANANANANANA-6-5-4NANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANANA






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
11
Treatment_A1139339.4923576.3172133.2240
Treatment_B1123.9382.661.5870.128
Treatment_A:Treatment_B1186.1572.7791.6580.03
Residuals110184.4131.676 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 11 &  &  &  &  \tabularnewline
Treatment_A & 11 & 39339.492 & 3576.317 & 2133.224 & 0 \tabularnewline
Treatment_B & 11 & 23.938 & 2.66 & 1.587 & 0.128 \tabularnewline
Treatment_A:Treatment_B & 11 & 86.157 & 2.779 & 1.658 & 0.03 \tabularnewline
Residuals & 110 & 184.413 & 1.676 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301159&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]11[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]11[/C][C]39339.492[/C][C]3576.317[/C][C]2133.224[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]11[/C][C]23.938[/C][C]2.66[/C][C]1.587[/C][C]0.128[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]11[/C][C]86.157[/C][C]2.779[/C][C]1.658[/C][C]0.03[/C][/ROW]
[ROW][C]Residuals[/C][C]110[/C][C]184.413[/C][C]1.676[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301159&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)
11
Treatment_A1139339.4923576.3172133.2240
Treatment_B1123.9382.661.5870.128
Treatment_A:Treatment_B1186.1572.7791.6580.03
Residuals110184.4131.676






Must Include Intercept to use Tukey Test 

\begin{tabular}{lllllllll}
\hline
Must Include Intercept to use Tukey Test  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301159&T=3

[TABLE]
[ROW][C]Must Include Intercept to use Tukey Test [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301159&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301159&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:

Must Include Intercept to use Tukey Test






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group500.6670.945
110 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 50 & 0.667 & 0.945 \tabularnewline
  & 110 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301159&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]50[/C][C]0.667[/C][C]0.945[/C][/ROW]
[ROW][C] [/C][C]110[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301159&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301159&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)
Group500.6670.945
110


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = FALSE ;
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')