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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_babies.wasp
Title produced by softwareExercise 1.13
Date of computationSun, 10 Oct 2010 11:16:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/10/t1286709323mx9wtnqedwn79pc.htm/, Retrieved Thu, 02 May 2024 21:46:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=82232, Retrieved Thu, 02 May 2024 21:46:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Exercise 1.13] [Babies 60% boys 3...] [2010-10-10 11:16:26] [66b4703b90a9701067ac75b10c82aca9] [Current]
Feedback Forum
2010-10-18 09:06:05 [Michael Van Goethem] [reply] 
De grafieken zijn juist, maar je had ook nog het verschil kunnen aangeven tussen de 2 grafieken. Zo kon je aangeven dat de kans dat er een jongen geboren wordt waarschijnlijker is in het kleine ziekenhuis (15%) dan in het grote ziekenhuis (7%).

Voor de oplossing met de binomiale verdeling had je de formule van de binomiale verdeling nodig (zie pdf). De berekening gaat als volgt:

Groot ziekenhuis:
x= de stochastische variabele (27= 60% van 45)
n= aantal experimenten (45)
p= de waarschijnlijkheid op de geboorte van een jongen (50%)
q= de waarschijnlijkheid op de geboorte van een meisje (50%)
Je kan dit in excel berekenen via de formule BINOM.VERD waarbij aantal-gunstig = 27 (60% van 45), experimenten = 45 en kans-gunstig = 0,5. De uitkomst van deze formule = 0.9324. Daarna wordt de waarschijnlijkheid van 1 afgetrokken: 1-0.9324 = 0.0676. De waarschijnlijkheid dat in het groot ziekenhuis meer dan 60% van de geboortes per dag jongens zijn, is 7%.

Klein ziekenhuis:
x= de stochastische variabele (9= 60% van 15)
n= aantal experimenten (15)
p= de waarschijnlijkheid op een geboorte van een jongen (50%)
q= de waarschijnlijkheid op een geboorte van een meisje (50%)
Je kan dit in excel berekenen via de formule BINOM.VERD waarbij aantal-gunstig = 9 (60% van 15), experimenten = 15 en kans-gunstig = 0,5. De uitkomst van deze formule = 0.849121. Daarna wordt de waarschijnlijkheid van 1 afgetrokken: 1-0.849121 = 0,150879. De waarschijnlijkheid dat in het klein ziekenhuis meer dan 60% van de geboortes per dag jongens zijn, is 15%.
2010-10-19 16:15:45 [] [reply] 
Let op, door de periode langer te maken, wordt de oplossing niet alleen duidelijk maar wordt het betrouwbaarder! Het kan zijn dat je slechte metingen had in uw eerste jaar maar het is bijna onmogelijk dat je 10 jaar lang slechte metingen maakt. Hoe meer metingen, hoe meer de grafiek geconvergeerd geraakt en dus hoe betrouwbaarder. De binomiaal verdeling (zaols hier boven perfect uitgelegd) kan hier zeker gebruikt worden, het is niet alleen wetenschappelijker maar ook nauwkeuriger dan de software.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 7 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82232&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82232&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 time7 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)
Number of simulated days3650
Expected number of births in Large Hospital45
Expected number of births in Small Hospital15
Percentage of Male births per day(for which the probability is computed)0.6
#Females births in Large Hospital82397
#Males births in Large Hospital81853
#Female births in Small Hospital27251
#Male births in Small Hospital27499
Probability of more than 60 % of male births in Large Hospital0.0668493150684931
Probability of more than 60 % of male births in Small Hospital0.152602739726027
#Days per Year when more than 60 % of male births occur in Large Hospital24.4
#Days per Year when more than 60 % of male births occur in Small Hospital55.7

\begin{tabular}{lllllllll}
\hline
Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.) \tabularnewline
Number of simulated days & 3650 \tabularnewline
Expected number of births in Large Hospital & 45 \tabularnewline
Expected number of births in Small Hospital & 15 \tabularnewline
Percentage of Male births per day(for which the probability is computed) & 0.6 \tabularnewline
#Females births in Large Hospital & 82397 \tabularnewline
#Males births in Large Hospital & 81853 \tabularnewline
#Female births in Small Hospital & 27251 \tabularnewline
#Male births in Small Hospital & 27499 \tabularnewline
Probability of more than 60 % of male births in Large Hospital & 0.0668493150684931 \tabularnewline
Probability of more than 60 % of male births in Small Hospital & 0.152602739726027 \tabularnewline
#Days per Year when more than 60 % of male births occur in Large Hospital & 24.4 \tabularnewline
#Days per Year when more than 60 % of male births occur in Small Hospital & 55.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82232&T=1

[TABLE]
[ROW][C]Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)[/C][/ROW]
[ROW][C]Number of simulated days[/C][C]3650[/C][/ROW]
[ROW][C]Expected number of births in Large Hospital[/C][C]45[/C][/ROW]
[ROW][C]Expected number of births in Small Hospital[/C][C]15[/C][/ROW]
[ROW][C]Percentage of Male births per day(for which the probability is computed)[/C][C]0.6[/C][/ROW]
[ROW][C]#Females births in Large Hospital[/C][C]82397[/C][/ROW]
[ROW][C]#Males births in Large Hospital[/C][C]81853[/C][/ROW]
[ROW][C]#Female births in Small Hospital[/C][C]27251[/C][/ROW]
[ROW][C]#Male births in Small Hospital[/C][C]27499[/C][/ROW]
[ROW][C]Probability of more than 60 % of male births in Large Hospital[/C][C]0.0668493150684931[/C][/ROW]
[C]Probability of more than 60 % of male births in Small Hospital[/C][C]0.152602739726027[/C][/ROW]
[ROW][C]#Days per Year when more than 60 % of male births occur in Large Hospital[/C][C]24.4[/C][/ROW]
[C]#Days per Year when more than 60 % of male births occur in Small Hospital[/C][C]55.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82232&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:

Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)
Number of simulated days3650
Expected number of births in Large Hospital45
Expected number of births in Small Hospital15
Percentage of Male births per day(for which the probability is computed)0.6
#Females births in Large Hospital82397
#Males births in Large Hospital81853
#Female births in Small Hospital27251
#Male births in Small Hospital27499
Probability of more than 60 % of male births in Large Hospital0.0668493150684931
Probability of more than 60 % of male births in Small Hospital0.152602739726027
#Days per Year when more than 60 % of male births occur in Large Hospital24.4
#Days per Year when more than 60 % of male births occur in Small Hospital55.7


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 3650 ; par2 = 45 ; par3 = 15 ; par4 = 0.6 ;
Parameters (R input):
par1 = 3650 ; par2 = 45 ; par3 = 15 ; par4 = 0.6 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
numsuccessbig <- 0
numsuccesssmall <- 0
bighospital <- array(NA,dim=c(par1,par2))
smallhospital <- array(NA,dim=c(par1,par3))
bigprob <- array(NA,dim=par1)
smallprob <- array(NA,dim=par1)
for (i in 1:par1) {
bighospital[i,] <- sample(c('F','M'),par2,replace=TRUE)
if (as.matrix(table(bighospital[i,]))[2] > par4*par2) numsuccessbig = numsuccessbig + 1
bigprob[i] <- numsuccessbig/i
smallhospital[i,] <- sample(c('F','M'),par3,replace=TRUE)
if (as.matrix(table(smallhospital[i,]))[2] > par4*par3) numsuccesssmall = numsuccesssmall + 1
smallprob[i] <- numsuccesssmall/i
}
tbig <- as.matrix(table(bighospital))
tsmall <- as.matrix(table(smallhospital))
tbig
tsmall
numsuccessbig/par1
bigprob[par1]
numsuccesssmall/par1
smallprob[par1]
numsuccessbig/par1*365
bigprob[par1]*365
numsuccesssmall/par1*365
smallprob[par1]*365
bitmap(file='test1.png')
plot(bigprob,col=2,main='Probability in Large Hospital',xlab='#simulated days',ylab='probability')
dev.off()
bitmap(file='test2.png')
plot(smallprob,col=2,main='Probability in Small Hospital',xlab='#simulated days',ylab='probability')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of simulated days',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Expected number of births in Large Hospital',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Expected number of births in Small Hospital',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Percentage of Male births per day
(for which the probability is computed)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Females births in Large Hospital',header=TRUE)
a<-table.element(a,tbig[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Males births in Large Hospital',header=TRUE)
a<-table.element(a,tbig[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Female births in Small Hospital',header=TRUE)
a<-table.element(a,tsmall[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Male births in Small Hospital',header=TRUE)
a<-table.element(a,tsmall[2])
a<-table.row.end(a)
a<-table.row.start(a)
dum1 <- paste('Probability of more than', par4*100, sep=' ')
dum <- paste(dum1, '% of male births in Large Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, bigprob[par1])
a<-table.row.end(a)
dum <- paste(dum1, '% of male births in Small Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, smallprob[par1])
a<-table.row.end(a)
a<-table.row.start(a)
dum1 <- paste('#Days per Year when more than', par4*100, sep=' ')
dum <- paste(dum1, '% of male births occur in Large Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, bigprob[par1]*365)
a<-table.row.end(a)
dum <- paste(dum1, '% of male births occur in Small Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, smallprob[par1]*365)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')