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, 29 Jan 2019 18:44:30 +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/2019/Jan/29/t15487839430hm0jfhim7djtg6.htm/, Retrieved Sun, 28 Apr 2024 20:09:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=317018, Retrieved Sun, 28 Apr 2024 20:09:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

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] [] [2019-01-29 17:44:30] [21684ad9fc05505f2c2196f825276d48] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21 0 1
22 1 1
22 0 1
18 1 1
23 1 1
12 1 1
20 0 1
22 1 1
21 1 1
19 1 1
22 1 1
15 1 1
20 1 1
19 0 1
18 0 1
15 0 0
20 1 1
21 0 1
21 1 0
15 0 1
16 1 1
23 1 1
21 0 1
18 1 1
25 1 1
9 1 1
30 1 0
20 0 0
23 1 1
16 0 1
16 0 1
19 0 1
25 1 1
18 1 1
23 1 1
21 1 1
10 0 1
14 1 0
22 1 1
26 0 1
23 1 1
23 1 1
24 1 1
24 1 1
18 1 0
23 0 1
15 1 1
19 1 0
16 0 1
25 1 0
23 1 0
17 1 0
19 1 1
21 1 0
18 1 1
27 1 1
21 0 0
13 1 1
8 0 0
29 1 0
28 1 1
23 0 1
21 0 1
19 1 1
19 0 1
20 1 0
18 0 1
19 1 1
17 1 1
19 0 0
25 0 1
19 0 1
22 0 0
23 1 0
14 0 1
16 0 1
24 1 0
20 0 1
12 0 0
24 1 1
22 0 0
12 0 0
22 0 0
20 1 0
10 0 0
23 1 0
17 1 0
22 0 0
24 0 0
18 0 0
21 1 0
20 1 0
20 1 0
22 0 0
19 1 0
20 0 0
26 1 0
23 1 0
24 1 0
21 1 0
21 1 0
19 0 0
8 1 0
17 1 0
20 1 0
11 0 0
8 0 0
15 0 0
18 0 0
18 0 0
19 0 0
19 1 0
23 1 1
22 1 1
21 1 1
25 1 1
30 0 0
17 1 0
27 1 1
23 0 1
23 1 1
18 0 1
18 0 1
23 1 1
19 1 1
15 1 1
20 1 1
16 1 1
24 1 0
25 1 1
25 1 1
19 0 1
19 1 1
16 1 1
19 1 1
19 1 1
23 1 1
21 1 1
22 0 1
19 1 1
20 1 0
20 1 1
3 1 1
23 1 1
23 0 1
20 0 1
15 1 1
16 0 1
7 0 1
24 1 1
17 0 1
24 1 1
24 1 1
19 0 1
25 1 0
20 1 0
28 1 1
23 0 1
27 0 0
18 0 0
28 0 0
21 1 0
19 0 1
23 1 1
27 0 0
22 1 0
28 0 0
25 1 0
21 0 0
22 0 0
28 1 0
20 0 0
29 1 0
25 1 1
25 1 1
20 1 0
20 1 1
16 0 1
20 1 0
20 0 1
23 0 0
18 0 0
25 1 1
18 0 0
19 1 0
25 0 0
25 0 0
25 0 0
24 0 0
19 1 0
26 1 0
10 1 0
17 1 0
13 0 0
17 0 0
30 1 0
25 0 1
4 0 0
16 0 0
21 0 0
23 1 1
22 1 0
17 0 1
20 0 0
20 1 1
22 0 0
16 1 1
23 1 0
0 0 0
18 1 0
25 1 0
23 1 1
12 0 1
18 0 0
24 0 1
11 1 1
18 1 0
23 1 1
24 1 0
29 0 0
18 0 1
15 0 0
29 1 1
16 1 1
19 0 1
22 0 0
16 0 1
23 1 0
23 1 1
19 0 1
4 0 1
20 0 1
24 1 0
20 1 1
4 1 1
24 1 1
22 0 0
16 1 1
3 1 1
15 1 0
24 0 1
17 0 0
20 1 0
27 0 0
26 1 0
23 1 0
17 0 1
20 1 1
22 0 1
19 1 1
24 1 1
19 0 1
23 1 0
15 0 0
27 1 1
26 0 0
22 1 0
22 0 1
18 0 0
15 1 0
22 1 0
27 0 0
10 1 0
20 1 0
17 0 0
23 1 0
19 0 0
13 0 0
27 1 0
23 1 0
16 0 0
25 1 0
2 0 0
26 0 0
20 1 0
23 0 1
22 0 0
24 1 0

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317018&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]6 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=317018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317018&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 time6 seconds
R ServerBig Analytics Cloud Computing Center






ANOVA Model
Response ~ Treatment_A * Treatment_B
means19.0772.191-0.186-0.737

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 19.077 & 2.191 & -0.186 & -0.737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317018&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]19.077[/C][C]2.191[/C][C]-0.186[/C][C]-0.737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317018&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
means19.0772.191-0.186-0.737






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1213.144213.1448.3320.004
Treatment_B125.14325.1430.9830.322
Treatment_A:Treatment_B19.1789.1780.3590.55
Residuals2747009.53225.582 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 213.144 & 213.144 & 8.332 & 0.004 \tabularnewline
Treatment_B & 1 & 25.143 & 25.143 & 0.983 & 0.322 \tabularnewline
Treatment_A:Treatment_B & 1 & 9.178 & 9.178 & 0.359 & 0.55 \tabularnewline
Residuals & 274 & 7009.532 & 25.582 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317018&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]213.144[/C][C]213.144[/C][C]8.332[/C][C]0.004[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]25.143[/C][C]25.143[/C][C]0.983[/C][C]0.322[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]9.178[/C][C]9.178[/C][C]0.359[/C][C]0.55[/C][/ROW]
[ROW][C]Residuals[/C][C]274[/C][C]7009.532[/C][C]25.582[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317018&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_A1213.144213.1448.3320.004
Treatment_B125.14325.1430.9830.322
Treatment_A:Treatment_B19.1789.1780.3590.55
Residuals2747009.53225.582






Tukey Honest Significant Difference Comparisons
difflwruprp adj
1-01.7680.5622.9740.004
1-0-0.599-1.7940.5960.324
1:0-0:02.191-0.0544.4350.059
0:1-0:0-0.186-2.5812.2090.997
1:1-0:01.268-0.8763.4110.422
0:1-1:0-2.377-4.725-0.0280.046
1:1-1:0-0.923-3.0141.1680.665
1:1-0:11.454-0.7983.7060.342

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & 1.768 & 0.562 & 2.974 & 0.004 \tabularnewline
1-0 & -0.599 & -1.794 & 0.596 & 0.324 \tabularnewline
1:0-0:0 & 2.191 & -0.054 & 4.435 & 0.059 \tabularnewline
0:1-0:0 & -0.186 & -2.581 & 2.209 & 0.997 \tabularnewline
1:1-0:0 & 1.268 & -0.876 & 3.411 & 0.422 \tabularnewline
0:1-1:0 & -2.377 & -4.725 & -0.028 & 0.046 \tabularnewline
1:1-1:0 & -0.923 & -3.014 & 1.168 & 0.665 \tabularnewline
1:1-0:1 & 1.454 & -0.798 & 3.706 & 0.342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317018&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]1.768[/C][C]0.562[/C][C]2.974[/C][C]0.004[/C][/ROW]
[ROW][C]1-0[/C][C]-0.599[/C][C]-1.794[/C][C]0.596[/C][C]0.324[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]2.191[/C][C]-0.054[/C][C]4.435[/C][C]0.059[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]-0.186[/C][C]-2.581[/C][C]2.209[/C][C]0.997[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]1.268[/C][C]-0.876[/C][C]3.411[/C][C]0.422[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]-2.377[/C][C]-4.725[/C][C]-0.028[/C][C]0.046[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]-0.923[/C][C]-3.014[/C][C]1.168[/C][C]0.665[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]1.454[/C][C]-0.798[/C][C]3.706[/C][C]0.342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317018&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317018&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
1-01.7680.5622.9740.004
1-0-0.599-1.7940.5960.324
1:0-0:02.191-0.0544.4350.059
0:1-0:0-0.186-2.5812.2090.997
1:1-0:01.268-0.8763.4110.422
0:1-1:0-2.377-4.725-0.0280.046
1:1-1:0-0.923-3.0141.1680.665
1:1-0:11.454-0.7983.7060.342






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group33.3120.021
274 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 3.312 & 0.021 \tabularnewline
  & 274 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317018&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]3.312[/C][C]0.021[/C][/ROW]
[ROW][C] [/C][C]274[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317018&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317018&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)
Group33.3120.021
274


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):
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')