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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_bootstrapplot.wasp
Title produced by softwareBlocked Bootstrap Plot - Central Tendency
Date of computationFri, 26 Oct 2007 05:36:24 -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/2007/Oct/26/oon01kzihapools1193401859.htm/, Retrieved Sun, 28 Apr 2024 21:26:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1886, Retrieved Sun, 28 Apr 2024 21:26:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsblocked bootstrap
Estimated Impact469

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Blocked Bootstrap Plot - Central Tendency] [workshop 3] [2007-10-26 12:36:24] [d06427f3e67cec1f6334fc93f511b0b4] [Current]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4: test the hypo...] [2008-10-28 20:43:37] [1e1d8320a8a1170c475bf6e4ce119de6]
F R PD    [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2008-10-29 12:56:37] [b635de6fc42b001d22cbe6e730fec936]
F           [Blocked Bootstrap Plot - Central Tendency] [Taak 1, Q4] [2008-10-29 16:05:43] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
F           [Blocked Bootstrap Plot - Central Tendency] [Q4 Blocked bootstrap] [2008-10-30 09:04:04] [fe7291e888d31b8c4db0b24d6c0f75c6]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Herberekening tas...] [2008-10-29 13:05:50] [819b576fab25b35cfda70f80599828ec]
F   PD    [Blocked Bootstrap Plot - Central Tendency] [Q4 blocked bootstrap] [2008-10-29 14:06:15] [7173087adebe3e3a714c80ea2417b3eb]
F   P       [Blocked Bootstrap Plot - Central Tendency] [q4] [2008-11-03 17:18:23] [e43247bc0ab243a5af99ac7f55ba0b41]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4 BBP] [2008-10-29 14:22:35] [8e4e5f204c24e6d05647858dae308d17]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2008-10-29 14:54:01] [495cd80c1a9baafb03c09cd9ab8d8fb5]
F R  D    [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap] [2008-10-29 16:57:59] [b518240a1c80d4f939bf8b3e34f77cec]
F   PD      [Blocked Bootstrap Plot - Central Tendency] [Q4 1000 trekkingen] [2008-10-30 21:12:40] [aa5573c1db401b164e448aef050955a1]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-10-29 17:41:05] [a57f5cc542637534b8bb5bcb4d37eab1]
-    D      [Blocked Bootstrap Plot - Central Tendency] [Paper - Bootstrap...] [2008-12-14 15:39:02] [a57f5cc542637534b8bb5bcb4d37eab1]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4] [2008-10-29 18:01:33] [87cabf13a90315c7085b765dcebb7412]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4: Bootstrap sim...] [2008-10-30 10:46:41] [12d343c4448a5f9e527bb31caeac580b]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-10-30 13:41:35] [063e4b67ad7d3a8a83eccec794cd5aa7]
F    D    [Blocked Bootstrap Plot - Central Tendency] [] [2008-10-30 13:47:09] [1376d48f59a7212e8dd85a587491a69b]
F    D    [Blocked Bootstrap Plot - Central Tendency] [taak 4 - Q4 boots...] [2008-10-30 13:47:32] [46c5a5fbda57fdfa1d4ef48658f82a0c]
-           [Blocked Bootstrap Plot - Central Tendency] [Task 1, Result 4] [2008-10-31 12:31:20] [70cb582895831af4be81fec73c607e93]
F           [Blocked Bootstrap Plot - Central Tendency] [TAAK 1 Q4] [2008-10-31 12:36:05] [29647dffafb5b58c12a48dbf6cba2b57]
F R  D        [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2008-11-03 08:34:00] [b5373f20234c18c6452d5f98d8abf0fe]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-10-30 13:46:38] [38f43994ada0e6172896e12525dcc585]
F    D      [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-11-02 13:43:40] [d32f94eec6fe2d8c421bd223368a5ced]
-    D    [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap ] [2008-10-30 13:51:28] [e1a46c1dcfccb0cb690f79a1a409b517]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-10-30 14:35:54] [58bf45a666dc5198906262e8815a9722]
F           [Blocked Bootstrap Plot - Central Tendency] [] [2008-11-03 19:14:46] [d2d412c7f4d35ffbf5ee5ee89db327d4]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4: Blocked boots...] [2008-10-30 15:02:36] [1ce0d16c8f4225c977b42c8fa93bc163]
F           [Blocked Bootstrap Plot - Central Tendency] [Q4] [2008-11-03 22:03:10] [76963dc1903f0f612b6153510a3818cf]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4] [2008-10-30 15:06:18] [cb714085b233acee8e8acd879ea442b6]
F    D    [Blocked Bootstrap Plot - Central Tendency] [q4 bootstap] [2008-10-30 15:43:45] [44a98561a4b3e6ab8cd5a857b48b0914]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Q4 Bootstrap] [2008-10-30 17:32:08] [cf9c64468d04c2c4dd548cc66b4e3677]
-    D    [Blocked Bootstrap Plot - Central Tendency] [reproduce Q4 WS 3a] [2008-10-30 17:50:52] [8545382734d98368249ce527c6558129]
F   PD    [Blocked Bootstrap Plot - Central Tendency] [Hypothesen Q4] [2008-10-31 10:26:37] [e5d91604aae608e98a8ea24759233f66]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-10-31 12:03:01] [44ec60eb6065a3f81a5f756bd5af1faf]
F   PD    [Blocked Bootstrap Plot - Central Tendency] [Opdracht 4 Q4 Boo...] [2008-10-31 12:44:33] [1848c1c05ef454c234bcbe26cf08badc]
F    D    [Blocked Bootstrap Plot - Central Tendency] [workshop 3a] [2008-10-31 12:58:34] [28075c6928548bea087cb2be962cfe7e]
- R  D    [Blocked Bootstrap Plot - Central Tendency] [Blocked bootstrap...] [2008-10-31 20:33:17] [e7f730ba3fad917ffc21bb9e72c10880]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Hypothesis Testin...] [2008-11-01 09:50:15] [6743688719638b0cb1c0a6e0bf433315]
F           [Blocked Bootstrap Plot - Central Tendency] [q4] [2008-11-03 19:59:59] [988ab43f527fc78aae41c84649095267]
F             [Blocked Bootstrap Plot - Central Tendency] [Hypothesis testin...] [2008-11-03 20:58:36] [3754dd41128068acfc463ebbabce5a9c]
F    D    [Blocked Bootstrap Plot - Central Tendency] [] [2008-11-01 10:52:10] [a4ee3bef49b119f4bd2e925060c84f5e]
F    D    [Blocked Bootstrap Plot - Central Tendency] [WS 3, Task 1,Q4] [2008-11-01 11:10:08] [fad8a251ac01c156a8ae23a83577546f]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Testing Hypothese...] [2008-11-01 12:09:27] [33f4701c7363e8b81858dafbf0350eed]
F           [Blocked Bootstrap Plot - Central Tendency] [T1 - Q4] [2008-11-03 18:52:56] [b187fac1a1b0cb3920f54366df47fea3]
F             [Blocked Bootstrap Plot - Central Tendency] [q4] [2008-11-03 22:56:26] [b641c14ac36cb6fee377f3b099dcac19]
-             [Blocked Bootstrap Plot - Central Tendency] [] [2008-11-09 18:51:01] [888addc516c3b812dd7be4bd54caa358]
-             [Blocked Bootstrap Plot - Central Tendency] [] [2008-11-09 18:51:01] [888addc516c3b812dd7be4bd54caa358]
F    D    [Blocked Bootstrap Plot - Central Tendency] [Blocked bootstrap...] [2008-11-01 17:10:45] [74be16979710d4c4e7c6647856088456]

[Truncated]
Feedback Forum
2008-11-09 15:19:30 [Vincent Vanden Poel] [reply] 
Q4: Argumentatie?
2008-11-09 19:30:23 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Q4 is ook goed gemaakt.
2008-11-11 10:43:43 [Jeroen Michel] [reply] 
De density plot gaat over 500 random observaties. De median heeft een klein betrouwbaarheidsinterval, maar bij de midrange is het nog kleiner.

Bootstrapping: gem. Dataset ïƒ 500 x opnieuw
Telkens 1 eruit nemen en een andere terugleggen ( er bestaat dan natuurlijk de kans dat je hetzelfde terug neemt)
Simulation of mean: Alle punten zijn alle berekende gemiddelden, door elkaar.
Simulation of median: meer een patroon
Imulation of midrange: duidelijk patroon
Hoe minder variatie, hoe nauwkeuriger
Midrange als gemiddelde nemen omdat daar de variatie het kleinst is
Maar: daar zijn wel heel veel outliers!!! Je hebt een gemiddelde waarvan de getrouwheidsinterval zeer klein is, maar als je er buiten zit, zit je er wel extreem buiten. Je moet maw zelf een overweging doen. Dwz dat de mean ook goed kan zijn. Het heeft een groter getrouwheidsinterval, maar de outliers zijn minder extreem.
De punten op de grafiek zij gemiddelden, dus je kan ze niet vinden in je dataset
Outliers zijn dus WEL relevant! .. ze bepalen de keuze, MAAR het gaat over gemiddelden
2008-11-11 15:00:30 [Loïque Verhasselt] [reply] 
Q4:De student geeft geen conclusie. De midrange is de beste schatter, diegene met de kleinste spreiding die grote zekerheid heeft in normale gevallen. Maar als het mis gaat, gaat het ook extreem mis.
Aangezien de vele outliers moet dit wel in vraag gesteld worden. Als deze outliers relevant zijn, zou de beste benadering het gemiddelde zijn gezien de weinige outliers. Het gemiddelde heeft veel minder nauwkeurigheid maar minder extreme fouten. De hypothese klopt.
2008-11-11 21:48:03 [c233791e22ae82ed03fa45b0d63a2757] [reply] 
q4: De student zegt hier dat het gemiddelde een betere schatter zou zijn. Het woord beter is echt niet helemaal correct. Een veiligere schatter is meer gepast, aangezien er minder 'gevaarlijke' outliers zijn.
2008-11-11 21:48:50 [Steven Vanhooreweghe] [reply] 
De student zegt hier dat het gemiddelde een betere schatter zou zijn. Het woord beter is echt niet helemaal correct. Een veiligere schatter is meer gepast, aangezien er minder 'gevaarlijke' outliers zijn
2008-11-11 22:45:25 [Gaëlle Smeets] [reply] 
Spijtig dat je geen argumentatie geeft.
De bootstrapping methode maakt gebruik van alle gemiddeldes om een algemene uitspraak te doen over het rekenkundig gemiddelde, de mediaan en de midrange. Dus we zijn niet meer met de oorspronkelijke dataset bezig. De zogenaamde outliers zijn hier berekeningen van een bepaald gemiddelde dat buiten de verdeling valt. Hierbij moet men een keuze maken wat men de veiligste schatter vindt. Midrange heeft een kleine spreiding maar ook veel metingen die buiten de verdeling vallen en die dus kunnen zorgen voor een foutieve conclusie. Het rekenkundig gemiddelde wordt hier meer gebruikt. Het heeft wel een grotere spreiding maar het aantal metingen die buiten de verdeling vallen zijn minder.

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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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 7 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=1886&T=0

[TABLE]
[ROW][C]Summary of compuational 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]7 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=1886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1886&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Estimation Results of Blocked Bootstrap
statisticQ1EstimateQ3S.D.IQR
mean85.893442622950886.893442622950888.10942622950821.717691508793392.21598360655736
median86.487.3881.906347113890141.59999999999999
midrange87.8588.188.851.066768930886071

\begin{tabular}{lllllllll}
\hline
Estimation Results of Blocked Bootstrap \tabularnewline
statistic & Q1 & Estimate & Q3 & S.D. & IQR \tabularnewline
mean & 85.8934426229508 & 86.8934426229508 & 88.1094262295082 & 1.71769150879339 & 2.21598360655736 \tabularnewline
median & 86.4 & 87.3 & 88 & 1.90634711389014 & 1.59999999999999 \tabularnewline
midrange & 87.85 & 88.1 & 88.85 & 1.06676893088607 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1886&T=1

[TABLE]
[ROW][C]Estimation Results of Blocked 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]85.8934426229508[/C][C]86.8934426229508[/C][C]88.1094262295082[/C][C]1.71769150879339[/C][C]2.21598360655736[/C][/ROW]
[ROW][C]median[/C][C]86.4[/C][C]87.3[/C][C]88[/C][C]1.90634711389014[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]midrange[/C][C]87.85[/C][C]88.1[/C][C]88.85[/C][C]1.06676893088607[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1886&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 Blocked Bootstrap
statisticQ1EstimateQ3S.D.IQR
mean85.893442622950886.893442622950888.10942622950821.717691508793392.21598360655736
median86.487.3881.906347113890141.59999999999999
midrange87.8588.188.851.066768930886071


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 12 ;
Parameters (R input):
par1 = 500 ; par2 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
if (par1 < 10) par1 = 10
if (par1 > 5000) par1 = 5000
if (par2 < 3) par2 = 3
if (par2 > length(x)) par2 = length(x)
library(lattice)
library(boot)
boot.stat <- function(s)
{
s.mean <- mean(s)
s.median <- median(s)
s.midrange <- (max(s) + min(s)) / 2
c(s.mean, s.median, s.midrange)
}
(r <- tsboot(x, boot.stat, R=par1, l=12, sim='fixed'))
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$t[,3]))
colnames(z) <- list('mean','median','midrange')
bitmap(file='plot7.png')
boxplot(z,notch=TRUE,ylab='simulated values',main='Bootstrap Simulation - Central Tendency')
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimation Results of Blocked Bootstrap',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'statistic',header=TRUE)
a<-table.element(a,'Q1',header=TRUE)
a<-table.element(a,'Estimate',header=TRUE)
a<-table.element(a,'Q3',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'IQR',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'mean',header=TRUE)
q1 <- quantile(r$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')