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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Mon, 01 Nov 2010 17:09:55 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/01/t1288631329fff78s8fndvw10f.htm/, Retrieved Thu, 31 Oct 2024 23:04:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=91003, Retrieved Thu, 31 Oct 2024 23:04:18 +0000

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User-defined keywords

Estimated Impact

198

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] [Dagelijkse omzet ...] [2010-10-25 11:22:12] [b98453cac15ba1066b407e146608df68]
F   PD  [Paired and Unpaired Two Samples Tests about the Mean] [Workshop 5 Q1] [2010-10-30 15:35:03] [c7506ced21a6c0dca45d37c8a93c80e0]
F R  D    [Paired and Unpaired Two Samples Tests about the Mean] [Workshop 5 Q1] [2010-11-01 15:09:12] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
F RM D        [Two-Way ANOVA] [Workshop 5 Q8] [2010-11-01 17:09:55] [4c92126b39409bf78ea2674c8170c829] [Current]

Feedback Forum

2010-11-09 18:10:34 [411b43619fc9db329bbcdbf7261c55fb] [reply] 
Bij deze oefening heeft auteur gebruik gemaakt van de post resultaten (en niet het verschil van de post-pre). De conclusie die hij afleid bij zijn berekening klopt gedeeltelijk. De F treatment (formule) veroorzaakt inderdaad hogere scores bij de mannen en de vrouwen. (bekijk http://www.freestatistics.org/blog/index.php?v=date/2010/Nov/07/t1289139088faehvkdcz05st1u.htm/ om te controleren wat het resultaat normaal was.) Maar de auteur zegt dat er geen significante verschillen zijn, en dit is fout. Er zijn bij zijn (onjuiste) berekening ook significante verschillen op te merken. Hij vergist zich ook duidelijk bij het analyseren van de gegevens. Een hoge p waarde geeft de indicatie dat er geen significant verschil is. Een lage p waarde daarentegen geeft dan weer een indicatie van een significant verschil. Een belangrijke opmerking bij deze analyse is wel dat we soms moeten opletten met het interpreteren van resultaten, aangezien we geen idee hebben van de type 2 fout (zie H:1 – E:1 tegenover H:0 – E:0, wijst op een interactie verschil) Daarom raad ik hem aan om even de feedback van W5 erbij te nemen, om de andere conclusies te overlopen. Bij deze analyse kunnen we causaliteit (oorzakelijke verbanden) afleiden omdat het over een echt experiment gaat. De treatments werden namelijk at random toegewezen. Algemeen kan je concluderen dat als je niet kan differentiëren (M of V), dan moet je de eenvoudige formule (treatment F) gebruiken. 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91003&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91003&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.471	0.059	-0.471	-0.121	0.156	0.198

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.471 & 0.059 & -0.471 & -0.121 & 0.156 & 0.198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91003&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.471[/C][C]0.059[/C][C]-0.471[/C][C]-0.121[/C][C]0.156[/C][C]0.198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91003&T=1

As an alternative you can also use a QR Code:

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

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.471	0.059	-0.471	-0.121	0.156	0.198

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	5.281	2.641	14.284	0
Treatment_B	2	0	0	0.001	0.98
Treatment_A:Treatment_B	2	0.2	0.1	0.541	0.584
Residuals	111	20.519	0.185

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 2 &  &  &  &  \tabularnewline
Treatment_A & 2 & 5.281 & 2.641 & 14.284 & 0 \tabularnewline
Treatment_B & 2 & 0 & 0 & 0.001 & 0.98 \tabularnewline
Treatment_A:Treatment_B & 2 & 0.2 & 0.1 & 0.541 & 0.584 \tabularnewline
Residuals & 111 & 20.519 & 0.185 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91003&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]2[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]2[/C][C]5.281[/C][C]2.641[/C][C]14.284[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]2[/C][C]0[/C][C]0[/C][C]0.001[/C][C]0.98[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]2[/C][C]0.2[/C][C]0.1[/C][C]0.541[/C][C]0.584[/C][/ROW]
[ROW][C]Residuals[/C][C]111[/C][C]20.519[/C][C]0.185[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91003&T=2

As an alternative you can also use a QR Code:

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

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	2
Treatment_A	2	5.281	2.641	14.284	0
Treatment_B	2	0	0	0.001	0.98
Treatment_A:Treatment_B	2	0.2	0.1	0.541	0.584
Residuals	111	20.519	0.185

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
F-E	0.145	-0.088	0.378	0.307
H-E	-0.355	-0.588	-0.122	0.001
H-F	-0.5	-0.728	-0.272	0
1-0	-0.002	-0.162	0.158	0.98
F:0-E:0	0.059	-0.369	0.487	0.999
H:0-E:0	-0.471	-0.921	-0.021	0.035
E:1-E:0	-0.121	-0.532	0.291	0.957
F:1-E:0	0.095	-0.304	0.493	0.983
H:1-E:0	-0.394	-0.783	-0.005	0.045
H:0-F:0	-0.529	-0.979	-0.079	0.011
E:1-F:0	-0.179	-0.591	0.232	0.803
F:1-F:0	0.036	-0.363	0.435	1
H:1-F:0	-0.452	-0.841	-0.064	0.013
E:1-H:0	0.35	-0.085	0.785	0.189
F:1-H:0	0.565	0.143	0.988	0.002
H:1-H:0	0.077	-0.336	0.49	0.994
F:1-E:1	0.215	-0.166	0.596	0.576
H:1-E:1	-0.273	-0.644	0.098	0.277
H:1-F:1	-0.488	-0.845	-0.131	0.002

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
F-E & 0.145 & -0.088 & 0.378 & 0.307 \tabularnewline
H-E & -0.355 & -0.588 & -0.122 & 0.001 \tabularnewline
H-F & -0.5 & -0.728 & -0.272 & 0 \tabularnewline
1-0 & -0.002 & -0.162 & 0.158 & 0.98 \tabularnewline
F:0-E:0 & 0.059 & -0.369 & 0.487 & 0.999 \tabularnewline
H:0-E:0 & -0.471 & -0.921 & -0.021 & 0.035 \tabularnewline
E:1-E:0 & -0.121 & -0.532 & 0.291 & 0.957 \tabularnewline
F:1-E:0 & 0.095 & -0.304 & 0.493 & 0.983 \tabularnewline
H:1-E:0 & -0.394 & -0.783 & -0.005 & 0.045 \tabularnewline
H:0-F:0 & -0.529 & -0.979 & -0.079 & 0.011 \tabularnewline
E:1-F:0 & -0.179 & -0.591 & 0.232 & 0.803 \tabularnewline
F:1-F:0 & 0.036 & -0.363 & 0.435 & 1 \tabularnewline
H:1-F:0 & -0.452 & -0.841 & -0.064 & 0.013 \tabularnewline
E:1-H:0 & 0.35 & -0.085 & 0.785 & 0.189 \tabularnewline
F:1-H:0 & 0.565 & 0.143 & 0.988 & 0.002 \tabularnewline
H:1-H:0 & 0.077 & -0.336 & 0.49 & 0.994 \tabularnewline
F:1-E:1 & 0.215 & -0.166 & 0.596 & 0.576 \tabularnewline
H:1-E:1 & -0.273 & -0.644 & 0.098 & 0.277 \tabularnewline
H:1-F:1 & -0.488 & -0.845 & -0.131 & 0.002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91003&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]F-E[/C][C]0.145[/C][C]-0.088[/C][C]0.378[/C][C]0.307[/C][/ROW]
[ROW][C]H-E[/C][C]-0.355[/C][C]-0.588[/C][C]-0.122[/C][C]0.001[/C][/ROW]
[ROW][C]H-F[/C][C]-0.5[/C][C]-0.728[/C][C]-0.272[/C][C]0[/C][/ROW]
[ROW][C]1-0[/C][C]-0.002[/C][C]-0.162[/C][C]0.158[/C][C]0.98[/C][/ROW]
[ROW][C]F:0-E:0[/C][C]0.059[/C][C]-0.369[/C][C]0.487[/C][C]0.999[/C][/ROW]
[ROW][C]H:0-E:0[/C][C]-0.471[/C][C]-0.921[/C][C]-0.021[/C][C]0.035[/C][/ROW]
[ROW][C]E:1-E:0[/C][C]-0.121[/C][C]-0.532[/C][C]0.291[/C][C]0.957[/C][/ROW]
[ROW][C]F:1-E:0[/C][C]0.095[/C][C]-0.304[/C][C]0.493[/C][C]0.983[/C][/ROW]
[ROW][C]H:1-E:0[/C][C]-0.394[/C][C]-0.783[/C][C]-0.005[/C][C]0.045[/C][/ROW]
[ROW][C]H:0-F:0[/C][C]-0.529[/C][C]-0.979[/C][C]-0.079[/C][C]0.011[/C][/ROW]
[ROW][C]E:1-F:0[/C][C]-0.179[/C][C]-0.591[/C][C]0.232[/C][C]0.803[/C][/ROW]
[ROW][C]F:1-F:0[/C][C]0.036[/C][C]-0.363[/C][C]0.435[/C][C]1[/C][/ROW]
[ROW][C]H:1-F:0[/C][C]-0.452[/C][C]-0.841[/C][C]-0.064[/C][C]0.013[/C][/ROW]
[ROW][C]E:1-H:0[/C][C]0.35[/C][C]-0.085[/C][C]0.785[/C][C]0.189[/C][/ROW]
[ROW][C]F:1-H:0[/C][C]0.565[/C][C]0.143[/C][C]0.988[/C][C]0.002[/C][/ROW]
[ROW][C]H:1-H:0[/C][C]0.077[/C][C]-0.336[/C][C]0.49[/C][C]0.994[/C][/ROW]
[ROW][C]F:1-E:1[/C][C]0.215[/C][C]-0.166[/C][C]0.596[/C][C]0.576[/C][/ROW]
[ROW][C]H:1-E:1[/C][C]-0.273[/C][C]-0.644[/C][C]0.098[/C][C]0.277[/C][/ROW]
[ROW][C]H:1-F:1[/C][C]-0.488[/C][C]-0.845[/C][C]-0.131[/C][C]0.002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91003&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91003&T=3

As an alternative you can also use a QR Code:

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

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
F-E	0.145	-0.088	0.378	0.307
H-E	-0.355	-0.588	-0.122	0.001
H-F	-0.5	-0.728	-0.272	0
1-0	-0.002	-0.162	0.158	0.98
F:0-E:0	0.059	-0.369	0.487	0.999
H:0-E:0	-0.471	-0.921	-0.021	0.035
E:1-E:0	-0.121	-0.532	0.291	0.957
F:1-E:0	0.095	-0.304	0.493	0.983
H:1-E:0	-0.394	-0.783	-0.005	0.045
H:0-F:0	-0.529	-0.979	-0.079	0.011
E:1-F:0	-0.179	-0.591	0.232	0.803
F:1-F:0	0.036	-0.363	0.435	1
H:1-F:0	-0.452	-0.841	-0.064	0.013
E:1-H:0	0.35	-0.085	0.785	0.189
F:1-H:0	0.565	0.143	0.988	0.002
H:1-H:0	0.077	-0.336	0.49	0.994
F:1-E:1	0.215	-0.166	0.596	0.576
H:1-E:1	-0.273	-0.644	0.098	0.277
H:1-F:1	-0.488	-0.845	-0.131	0.002

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	4.34	0.001
	111

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & 4.34 & 0.001 \tabularnewline
  & 111 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=91003&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]5[/C][C]4.34[/C][C]0.001[/C][/ROW]
[ROW][C] [/C][C]111[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=91003&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=91003&T=4

As an alternative you can also use a QR Code:

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

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	4.34	0.001
	111

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 0.0 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code