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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 computationSat, 09 Oct 2010 09:00:55 +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/09/t1286614864724eg7f2wj1fr0y.htm/, Retrieved Mon, 29 Apr 2024 06:12:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=82078, Retrieved Mon, 29 Apr 2024 06:12:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [Task 2: Babies Ca...] [2010-10-09 09:00:55] [8eb352cba3cf694c3df89d0a436a2f1b] [Current]
Feedback Forum
2010-10-15 08:20:51 [7d66e2e510b144c68ca0882fd178e17c] [reply] 
Oplossing werd correct uitgevoerd. We kunnen hieraan toevoegen dat we de nauwkeurigheid kunnen merken aan de verhoogde convergentie van de beide grafieken, vooral van het grote ziekenhuis.

Binomial distribution:

Ik zal mijn oplossing als voorbeeld geven. Link met benodigde info: http://www.freestatistics.org/blog/index.php?v=date/2010/Oct/14/t1287043525y4cscghkdhyqsfz.htm/

De definitie van de binomial distribution vind je terug in het feedback report. De uitwerking ervan vind je hieronder:

Groot ziekenhuis:
x= de stochastische variabele (27= 60% van 45)
n= aantal experimenten (45)
p= de waarschijnlijkheid op een geboorte van een jongen (50%)
q= de waarschijnlijkheid op een geboorte van een meisje (50%)

We berekenen de binomiale verdeling in Excel. Deze formule staat standaard ingesteld in Excel.
De uitkomst van deze formule p(x<=27) = 0.9324
Dan moeten we vervolgens deze waarschijnlijkheid aftrekken van 1: 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%)

We berekenen de binomiale verdeling in Excel. Deze formule staat standaard ingesteld in Excel.
De uitkomst van deze formule p(x<=9) = 0,849121
Dan moeten we vervolgens deze waarschijnlijkheid aftrekken van 1: 1 – 0,849121= 0,150879.
De waarschijnlijkheid dat in het klein ziekenhuis meer dan 60% van de geboortes per dag jongens zijn, is 15%.

Conclussie: Deze resultaten komen in grote mate overeen met de tabel die je terugvindt in de freestatistic software. Maar via de software kunnen er afrondingsfouten voorkomen in tegenstelling tot deze wiskundige berekening.




2010-10-17 17:25:45 [ac60b0733d04acb78c99358c3a0e1148] [reply] 
De waarschijnlijkheid op een geboorte van een jongen/meisje is allebei gelijk aan 50% (en dus niet gelijk aan respectievelijk 60%/40%). Bovendien moet het aantal experimenten n en de stochastische variabele x aangepast worden naargelang het een klein of groot ziekenhuis is.

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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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82078&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82078&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






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 Hospital82219
#Males births in Large Hospital82031
#Female births in Small Hospital27411
#Male births in Small Hospital27339
Probability of more than 60 % of male births in Large Hospital0.076986301369863
Probability of more than 60 % of male births in Small Hospital0.14986301369863
#Days per Year when more than 60 % of male births occur in Large Hospital28.1
#Days per Year when more than 60 % of male births occur in Small Hospital54.7

\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 & 82219 \tabularnewline
#Males births in Large Hospital & 82031 \tabularnewline
#Female births in Small Hospital & 27411 \tabularnewline
#Male births in Small Hospital & 27339 \tabularnewline
Probability of more than 60 % of male births in Large Hospital & 0.076986301369863 \tabularnewline
Probability of more than 60 % of male births in Small Hospital & 0.14986301369863 \tabularnewline
#Days per Year when more than 60 % of male births occur in Large Hospital & 28.1 \tabularnewline
#Days per Year when more than 60 % of male births occur in Small Hospital & 54.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82078&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]82219[/C][/ROW]
[ROW][C]#Males births in Large Hospital[/C][C]82031[/C][/ROW]
[ROW][C]#Female births in Small Hospital[/C][C]27411[/C][/ROW]
[ROW][C]#Male births in Small Hospital[/C][C]27339[/C][/ROW]
[ROW][C]Probability of more than 60 % of male births in Large Hospital[/C][C]0.076986301369863[/C][/ROW]
[C]Probability of more than 60 % of male births in Small Hospital[/C][C]0.14986301369863[/C][/ROW]
[ROW][C]#Days per Year when more than 60 % of male births occur in Large Hospital[/C][C]28.1[/C][/ROW]
[C]#Days per Year when more than 60 % of male births occur in Small Hospital[/C][C]54.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82078&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 Hospital82219
#Males births in Large Hospital82031
#Female births in Small Hospital27411
#Male births in Small Hospital27339
Probability of more than 60 % of male births in Large Hospital0.076986301369863
Probability of more than 60 % of male births in Small Hospital0.14986301369863
#Days per Year when more than 60 % of male births occur in Large Hospital28.1
#Days per Year when more than 60 % of male births occur in Small Hospital54.7


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')