Detailed Summary: Lectures and Readings STATISTICS 2.2 FSWPE2-022

| n f e r e n c e f O r
P r ◦ o r t i O n s
p
m m c c +, •




Large Sample Confidence internat for a population proportion

( Moose an SRS Of Size n from a large population with an unknown Proportion p of Success es


The Sample proportion is :
ß ¥
Innere ✗ is the humber of Success es .




The Standard error of B is SEß JFPFÖn

Ä
Pn
'
B
* *
margin Of is SEß
-




☐ no the error of at Confidence level C m =
2- = 2- 7
*
IN nere the Critical Valve 2- is the Value for the Standard Normal ☐ ensity Curve with area C

* *
between 2- ☐ na 2- .




An approximierte level C Confidence internat for p is ß± m
* * *
Use this intervall for 90% 2- -
1.645.95% 2- -

1.96 .
Or 99% 2- 2.576 Confidence when the humber


Of Success es ☐ no nvmber Of failure s are ☐ 0th at least to .




ve r wo r r e n e r w w w.t e




Confidence Intervalls based on large sample approacnofleninaccvraewnennumrerotsvccess.es and


failure ☐ rent botn at least to .
•
simple cicljvstments ; ☐ ssvming that Sample contains tour additional


Observations : HNO Successes ☐ no two failure s '
Agresti -

con est imac :
F¥ B± 2- * NÄF
SignifikanteFLVVTJimgleepmonpvthomitocakuc.it plus for
-




Confidence internat
for P

Large sample significcince
-

test for ☐ Population proportion

SRS Of Size n from large population with UMKMOINM Proportion P Of Success es .




Ä Po
TO test the nypotnesis Ho :p =
Po , Compute the Z Statistics :
2- pol , -

po
n


variable P
Interims of a Standard Normal random Z the approximierte Value for test of Ho against
-



.



""



Ha :p po is P Z ≥ 2- ÄError Large
-




sample 2- significance lest recommenclect


Ha :p < po is P 2- ≤ 2- Äh as long as expect.CI humber of Success , npo ,
☐ na



FEE
" "




Ha :p / po is 2012-712-1 fciwres.nu -

po ) ☐ rebotncitleastlcimmmnmhg Bh 90




Nummerischwww.nedhangimayermar


Level C Confidence internat for proportion p will have margin of error ☐ pproximcitety equal to ☐ specific
2
*
2-
Valve M When the Sample Size scitisfies n= Pt -
p
*

m

*
>
2-
*
Critical Valve for Confidence level C ☐ na p is Gvessecl Value for the proportion of

Successes in the future sample .




*
The margin of error will be less than or equal to m if P is cnosen to be 0.5 into the


formula above
gives : n
=L ¥2
Choo Sing Sample Size for a Sign .
test : !
sicnificcince level Cl vsvally 0.05 Power Prob Of rejecting Ho Innen it is false VSUGIIY 80%10.80) for power
• *
: .
:




-



Value of Po in the null hypotheseis Ho =p =p •

alternative hypotnesis ,
2- siciec ( Ha :p =/ p . )

One sictcd ( Ha :p >
po or Ha :p < po) Value of P for the alternative hypothese is
-
-

, C O m r I M G t IN o t O S
p ☐
p
r o p o r I n




Large Sample Confidence internat for Comp☐ ring HNO proportions :




cnoose ☐n SRS Of Size Ms from a large population having proportion pn Of Successes ☐ no o n independent


SRS Of Size Mz from ☐ not ner population having , proportion pz Of Success es


Estimcited difference in Population proportion s is :
D PI PI

The Standard Error Of D is : SED
'
Pitt Pi )-

Rz II -

Rz )


*
☐ no Margin of error of D for Confidence level C is m -
2- SED

*
innere the Critical Valve 2- is the Value for the Standard Normal density Curve with area C between


* *
2- ☐ ncl 2- .




Alexei C large -



Sample Confidence internat for Ps
-


Pz is : DEM

NominiertenFehlernaehrung 2
proportioniert


TO test the hypo thesis : Ho :
Ps =p ,

Ä -


PI
Computer the 2- Statistics 2- =



SEDP
IN here the POOKOI Standard Error is
SF-ip-NPI-pn.it ,


✗ + ✗2
estimcite Of pz is D=
^
☐ ncl IN here the pooted the Commons Value of Pn ☐ na
hr + MZ

Ha :p Pa is P Z ≥ 2- £ "" "
" "" "" " " " Peeta humber of successe s ☐ n a,
,




Ha :
A. < Da is P 2- ≤ 2- 4- faiivres in each Sample ☐
reatfm-n5.TW/- µ
Ha :p / is zp , z ≥ , z ,
.
pa E-
Mehrwertsteuerverdrehte


Level C Confidence intervall for ☐ clifference in TINO proportion s Will have a margin of error approximativ lava



to ☐ specific Value im innen Sample Size for each of the TINO proportion s is :




2
*
2-
n =

m
PI 1- p ? + PI 1- PI

Here ,
2-
* :
Critical Value for C and PI and PI are qvessect Hawes for piano pz ( Success es in future Sample

The margin of error INN be less than or equal to m if pfand PI are cnosen to be 0.5
* 2


f-
2-
the Commons Sample Size revised is then given by n = → Use
requires at least to tails + Success es
m

r e i a t i r e r i s k :
the CHIO Of two Sample Proportion S RR =
Ä
Rz

Confidence Intervalls for relative risk are Otten Used to summarize Campari son of 2 proportion s

,conduit.my/thivaeneseanehNUremberg Code :
Set of ethical Principles essential for a medical experiment to be
"

per missio e
"




con Sent most be Voluntary + free to without from Stray at any time
•




prior to Giving consent should be informell about pur pose + Potential risks
•



.




ICH vnnecessciry risks should be ☐ Void ed



Stvo y should yiekl results whose benefit to Society out Weichs risks Portici Ponts
'


to



Only Quali fiecl Scientists should Conduct the research
-




Belmont Report :
ethics COCK that providers the foundation for U.s. federal regulations Governing research on humans


'
such research Called :
human Subject s research

Principles and Guidelines : 1.
respect for persons 2. Den eficence 3. justice from : those Principles ,
Bet man Report

derNeo
guidelines for :
Obtaining conSent from portici ponts .
☐ssessingrisks + benefit s of Project +
selectingppl.in just INCH

American Psychologie at Associations APA) Ethics Code : ☐ escri Des General ethical Principles and specific ethical



standards to Guide psycnologist 's Professional behavior


General Principles :




Beneficience ☐ na nonmaleficience beneficience Means that Psycho 109 ists should Stine to benefit
•
:




those With IN nom they work ; Normale ficence Psych Should :
. be Core tut not to Cause harm


Fidelity Psych Should behave in Citrus HNO rtny Mannes ; Responsibility in 40111 es ☐ an ering professional Codes
-
:
.
:
to



Of Conduct and not exploring people
'



Integrity psych
:
.
De honest and trvtnfvl ☐ no not engage in fraud ; Justice Calls upon psych
:
.
to recognize that


the benefits of research should be mache ☐Vail ab k to all Persons


Respect for people's rights and dignity respect respect dignity :
and North Of all people and the rights
-
:




Of individual s to Privacy Confidential it 4 and Self determination
-




,




Deception :
with holding information or miste Going people in Ways that Might influence their ckcision to portici pale

> ethical / y Controller sich but , all 01N ed under Limited Conditions + to rechte PPI ☐ ctingunnatvrallyclvringstuc.ly

Debriefing :
Occvrs at conclvsion Of research Session ; Investigator s provider Partie IN itn more.
Complete information

about nature of the Stray ex Plains any ,
☐ eoeptions ☐ na ☐ Overse effects part Maybe .
experiencing

Animal research :
nos con tribute a to some of Psychology 's most im D. cliscoieries : ☐ EDGE over IN nether ☐no



when animal research is ethical Centers around Question of IN nether animal s have Moral stand in g


'
3 ethical perspectives :
Innere nt rights utilitaricinism ,
☐ no Pro
-

Use


Psycho 10cg ists IN no Conduct animal research mvst ☐ ☐ here to APA's ethics standards and güternmental

regulations .
LACU Cs review IN nether proposed animal research Comp lies with tnese regulation

Most Standards ☐ no regulations per tain to three principles ,
Known as the Three RS

'
Three Rs reduction refinement :
,
and re Placement


Psych 0104 ists are Obligatea to CNOICI false ☐ na cleceptiite statements incl those regard Ing their research find inqs
,
.
,




Publications + are as of expertise i no piagicrism innen IN riting papers +
citinq Sources properly