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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismean3.wasp
Title produced by softwareTesting Mean with known Variance - Type II Error
Date of computationTue, 11 Nov 2008 06:46:49 -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/11/t1226411244pk2f0v16rgwkrrb.htm/, Retrieved Sun, 19 May 2024 12:14:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23472, Retrieved Sun, 19 May 2024 12:14:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Testing Mean with known Variance - Type II Error] [Q3] [2008-11-11 13:46:49] [2ba2a74112fb2c960057a572bf2825d3] [Current]
Feedback Forum
2008-11-18 18:52:51 [Glenn De Maeyer] [reply] 
De student loste de berekening correct op. We gaan onderzoeken wat de kans is dat wij de fraude niet detecteren (type II error). We gaan de alternatieve hypothese vooropstellen (15,2%). Een type II fout kan je enkel berekenen indien je de alternatieve hypothese kent.
De studente ging echter heel even de mist in bij haar interpretatie van het resultaat. Ze schreef namelijk 'Als we er vanuit gaan dat de getuigenis van de ex-werknemer klopt heeft de leverancier maar +-94% kans dat wij dit merken'. Dit moet uiteraard zijn +/- 94% dat wij dit niet merken. De pakkans is zeer klein.
We kunnen de type II fout verkleinen en de pakkans dus vergroten door ofwel onze meettechniek te verbeteren of door onze steekproefgrootte (sample size) te verhogen.
2008-11-20 22:05:59 [256f97d8b7c07ed49f142eff724c6520] [reply] 
goed opgelost, opletten met de zinsformulering. Dit is natuurlijk geen echte fout. Naarmate je in de volgende zin het toch rechtzet.
Een lichte aanvulling:
hierbij is het dus zeer verleidelijk voor de leverancier om te frauderen
2008-11-23 10:55:35 [Liese Tormans] [reply] 
Ik heb gebruik gemaakt van de juiste techniek, maar bij het vormen van mijn conclusie heb ik de waarde verkeerd geïnterpreteerd. Ik heb het probleem dus ook niet opgemerkt, bijgevolg ook geen oplossing gegeven.

Ik heb hier onderzocht hoe groot de kans is dat we de fraude niet gaan detecteren, dit heb ik gezien aan de hand van de type II Error waarde. Deze waarde bedraagt +-94%. De kans dat we de leverancier pakken bedraagt 6%. We kunnen dus concluderen dat de kans zeer klein is bijgevolg is de verleiding voor de leverancier zeer groot om te frauderen.

We hebben 2 mogelijke oplossingen om dit probleem te verhelpen.
De meettechniek verbeteren zodat de type II error verkleind en de pakkans groter wordt.
De meetproef (sample size) vergroten zodat de type II error verkleind en de pakkans vergroot.

Opmerking: De type twee fout kan je enkel detecteren indien je de alternatieve hypothese kent. In dit geval was de alternatieve hypothese 15,2% en de nul hypothese 15%.

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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 time0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23472&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]0 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=23472&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23472&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Testing Mean with known Variance
sample size27
population variance0.012
sample mean0.1547
null hypothesis about mean0.15
type I error0.05
alternative hypothesis about mean0.152
Type II Error0.93942747750307

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 27 \tabularnewline
population variance & 0.012 \tabularnewline
sample mean & 0.1547 \tabularnewline
null hypothesis about mean & 0.15 \tabularnewline
type I error & 0.05 \tabularnewline
alternative hypothesis about mean & 0.152 \tabularnewline
Type II Error & 0.93942747750307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23472&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]27[/C][/ROW]
[ROW][C]population variance[/C][C]0.012[/C][/ROW]
[ROW][C]sample mean[/C][C]0.1547[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]0.15[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]alternative hypothesis about mean[/C][C]0.152[/C][/ROW]
[ROW][C]Type II Error[/C][C]0.93942747750307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23472&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23472&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:

Testing Mean with known Variance
sample size27
population variance0.012
sample mean0.1547
null hypothesis about mean0.15
type I error0.05
alternative hypothesis about mean0.152
Type II Error0.93942747750307


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 27 ; par2 = 0.012 ; par3 = 0.1547 ; par4 = 0.15 ; par5 = 0.05 ; par6 = 0.152 ;
Parameters (R input):
par1 = 27 ; par2 = 0.012 ; par3 = 0.1547 ; par4 = 0.15 ; par5 = 0.05 ; par6 = 0.152 ;
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)
par5<-as.numeric(par5)
par6<-as.numeric(par6)
c <- 'NA'
csn <- abs(qnorm(par5))
if (par3 == par4)
{
conclusion <- 'Error: the null hypothesis and sample mean must not be equal.'
}
if (par3 > par4)
{
c <- par4 + csn * sqrt(par2) / sqrt(par1)
}
if (par3 < par4)
{
c <- par4 - csn * sqrt(par2) / sqrt(par1)
}
p <- pnorm((c - par6) / (sqrt(par2/par1)))
p
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm','Testing Mean with known Variance','learn more about Statistical Hypothesis Testing about the Mean when the Variance is known'),2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'sample size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'population variance',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'sample mean',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'null hypothesis about mean',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type I error',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alternative hypothesis about mean',header=TRUE)
a<-table.element(a,par6)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm#ex3','Type II Error','example'),header=TRUE)
a<-table.element(a,p)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')