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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_bootstrapplot1.wasp
Title produced by softwareBootstrap Plot - Central Tendency
Date of computationWed, 05 Nov 2008 11:11:21 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/05/t1225908762vcqkb6whzef58vz.htm/, Retrieved Sun, 19 May 2024 10:46:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21868, Retrieved Sun, 19 May 2024 10:46:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBootstrap Plot
Estimated Impact158

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Bootstrap Plot - Central Tendency] [Bootstrap Plot op...] [2008-11-05 18:11:21] [20dfa2578b2b18ce36fdb36ac12aedd7] [Current]
Feedback Forum
2008-11-09 12:46:39 [Nathalie Daneels] [reply] 
Evaluatie opdracht 1: Task 1:
Q4: De student vermeldde reeds dat de midrange eigenlijk op het eerste zicht de beste schatter is, gezien de kleinste spreiding, maar dat deze maatstaf ook veel outliers bevat. Zijn/haar volgende keuze was het gemiddelde, omdat die minder outliers bevat, maar die is ook minder nauwkeurig o.w.v. de grotere spreiding. Ik volg hierbij de student zijn mening: de midrange heeft inderdaad de kleinste variantie en daardoor geeft deze maatstaf dus de grootste zekerheid in de normale gevallen. Maar er moet ook rekening gehouden worden met de outliers: kunnen deze worden genegeerd of niet? Als deze niet kunnen worden genegeerd (omdat zij bijvoorbeeld als ze zich zouden voordoen, een fataal gevolg kunnen hebben), dan zou ik opteren voor het gemiddelde als beste 'schatter'. Het gemiddelde heeft ook een zeer mooi verloop (bijna een normaalverdeling), dit kan je zien aan de bijna evengrote oppervlakten boven de mediaan (25%) en onder de mediaan (25%), dit in tegenstelling tot de midrange waarbij de oppervlakte boven de mediaan duidelijk groter is dan deze onder de mediaan.
De maastaf mediaan komt hier niet in aanmerking tot beste 'schatter' gezien deze maatstaf vele outliers heeft en een minder mooi verloop heeft (minder gelijkend op de normaalverdeling).

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109,20
88,60
94,30
98,30
86,40
80,60
104,10
108,20
93,40
71,90
94,10
94,90
96,40
91,10
84,40
86,40
88,00
75,10
109,70
103,00
82,10
68,00
96,40
94,30
90,00
88,00
76,10
82,50
81,40
66,50
97,20
94,10
80,70
70,50
87,80
89,50
99,60
84,20
75,10
92,00
80,80
73,10
99,80
90,00
83,10
72,40
78,80
87,30
91,00
80,10
73,60
86,40
74,50
71,20
92,40
81,50
85,30
69,90
84,20
90,70
100,30

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21868&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21868&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Estimation Results of Bootstrap
statisticQ1EstimateQ3S.D.IQR
mean85.99713114754186.893442622950887.8807377049181.333113273549411.88360655737705
median86.487.3881.663589619119351.59999999999999
midrange88.188.188.850.8589862366239770.75

\begin{tabular}{lllllllll}
\hline
Estimation Results of Bootstrap \tabularnewline
statistic & Q1 & Estimate & Q3 & S.D. & IQR \tabularnewline
mean & 85.997131147541 & 86.8934426229508 & 87.880737704918 & 1.33311327354941 & 1.88360655737705 \tabularnewline
median & 86.4 & 87.3 & 88 & 1.66358961911935 & 1.59999999999999 \tabularnewline
midrange & 88.1 & 88.1 & 88.85 & 0.858986236623977 & 0.75 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21868&T=1

[TABLE]
[ROW][C]Estimation Results of Bootstrap[/C][/ROW]
[ROW][C]statistic[/C][C]Q1[/C][C]Estimate[/C][C]Q3[/C][C]S.D.[/C][C]IQR[/C][/ROW]
[ROW][C]mean[/C][C]85.997131147541[/C][C]86.8934426229508[/C][C]87.880737704918[/C][C]1.33311327354941[/C][C]1.88360655737705[/C][/ROW]
[ROW][C]median[/C][C]86.4[/C][C]87.3[/C][C]88[/C][C]1.66358961911935[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]midrange[/C][C]88.1[/C][C]88.1[/C][C]88.85[/C][C]0.858986236623977[/C][C]0.75[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21868&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:

Estimation Results of Bootstrap
statisticQ1EstimateQ3S.D.IQR
mean85.99713114754186.893442622950887.8807377049181.333113273549411.88360655737705
median86.487.3881.663589619119351.59999999999999
midrange88.188.188.850.8589862366239770.75


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ;
Parameters (R input):
par1 = 500 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par1 < 10) par1 = 10
if (par1 > 5000) par1 = 5000
library(lattice)
library(boot)
boot.stat <- function(s,i)
{
s.mean <- mean(s[i])
s.median <- median(s[i])
s.midrange <- (max(s[i]) + min(s[i])) / 2
c(s.mean, s.median, s.midrange)
}
(r <- boot(x,boot.stat, R=par1, stype='i'))
bitmap(file='plot1.png')
plot(r$t[,1],type='p',ylab='simulated values',main='Simulation of Mean')
grid()
dev.off()
bitmap(file='plot2.png')
plot(r$t[,2],type='p',ylab='simulated values',main='Simulation of Median')
grid()
dev.off()
bitmap(file='plot3.png')
plot(r$t[,3],type='p',ylab='simulated values',main='Simulation of Midrange')
grid()
dev.off()
bitmap(file='plot4.png')
densityplot(~r$t[,1],col='black',main='Density Plot',xlab='mean')
dev.off()
bitmap(file='plot5.png')
densityplot(~r$t[,2],col='black',main='Density Plot',xlab='median')
dev.off()
bitmap(file='plot6.png')
densityplot(~r$t[,3],col='black',main='Density Plot',xlab='midrange')
dev.off()
z <- data.frame(cbind(r$t[,1],r$t[,2],r$t[,3]))
colnames(z) <- list('mean','median','midrange')
bitmap(file='plot7.png')
boxplot(z,notch=TRUE,ylab='simulated values',main='Bootstrap Simulation - Central Tendency')
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimation Results of Bootstrap',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'statistic',header=TRUE)
a<-table.element(a,'Q1',header=TRUE)
a<-table.element(a,'Estimate',header=TRUE)
a<-table.element(a,'Q3',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'IQR',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'mean',header=TRUE)
q1 <- quantile(r$t[,1],0.25)[[1]]
q3 <- quantile(r$t[,1],0.75)[[1]]
a<-table.element(a,q1)
a<-table.element(a,r$t0[1])
a<-table.element(a,q3)
a<-table.element(a,sqrt(var(r$t[,1])))
a<-table.element(a,q3-q1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'median',header=TRUE)
q1 <- quantile(r$t[,2],0.25)[[1]]
q3 <- quantile(r$t[,2],0.75)[[1]]
a<-table.element(a,q1)
a<-table.element(a,r$t0[2])
a<-table.element(a,q3)
a<-table.element(a,sqrt(var(r$t[,2])))
a<-table.element(a,q3-q1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'midrange',header=TRUE)
q1 <- quantile(r$t[,3],0.25)[[1]]
q3 <- quantile(r$t[,3],0.75)[[1]]
a<-table.element(a,q1)
a<-table.element(a,r$t0[3])
a<-table.element(a,q3)
a<-table.element(a,sqrt(var(r$t[,3])))
a<-table.element(a,q3-q1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')