Probability, population and sample
-
Upload
rizwan-s-a -
Category
Health & Medicine
-
view
32 -
download
1
Transcript of Probability, population and sample
![Page 1: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/1.jpg)
Basic concepts: Probability, Population & SampleDr. S. A. Rizwan, M.D.
PublicHealthSpecialistSBCM, JointProgram– Riyadh
MinistryofHealth,KingdomofSaudiArabia
![Page 2: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/2.jpg)
Learningobjectives
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Familiarisewithtermsusedinprobability• Defineprobability• Describethe3approachesofprobability• Understandthebasiclawsofprobability• Solveproblemsbasedonabovelaws
• DescribetheconceptsofPopulationandSample
2
![Page 3: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/3.jpg)
Section1:Probabilitybasics
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 3
![Page 4: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/4.jpg)
Afewimportantterms
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Randomexperiment• Samplespace• Event
• exhaustive,impossible,elementary,composite,certain,mutuallyexclusive,independent,dependent,favourable,equallylikely
4
![Page 5: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/5.jpg)
Afewimportantterms
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Eventtype ExampleIndependent Twoseedsaresown,germinationofoneis
notaffectedbytheother.
Dependent Ifwedrawacardfromapackofwellshuffledcards,ifthefirstcarddrawnisnotreplacedthentheseconddrawisdependentonthefirstdraw.
Mutuallyexclusive
Inobservationofseedgerminationtheseedmayeithergerminateoritwillnotgerminate.
5
![Page 6: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/6.jpg)
Probability– whatisit?
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Chancethatsomethingwillhappen,howlikelyaneventwillhappen
• Canbemeasuredwithanumberlike"10%chanceofrain",orusingwordslikeimpossible,unlikely,possible,evenchance,likelyandcertain
6
![Page 7: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/7.jpg)
Probability– whatisit?
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Exampleofafairdie• P(landinga5)• P(landinganevennumber)
• Exampleofmarbles
7
![Page 8: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/8.jpg)
Probability– approachestocalculate
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Theoretical probability• Relativefrequency• Subjectiveprobability
8
![Page 9: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/9.jpg)
LawsofProbability– Setanalogy
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Union• Intersection• Complement
9
![Page 10: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/10.jpg)
Thoughtexercises:
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Example1.Abagcontains5redmarbles,3bluemarbles,and2greenmarbles.
Q1.pr (red)+pr (blue)+pr (green)Q2.pr (red)+pr (notred)Q3.pr (redorgreen)
10
![Page 11: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/11.jpg)
Thoughtexercises:
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Example2.Rolladieandflipacoin.
Q1.pr (headsandrolla3)
11
![Page 12: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/12.jpg)
Thoughtexercises:
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Example3.Thereare20peopleintheroom:12girls(5withblondhairand7withbrownhair)and8boys(4withblondhairand4withbrownhair).Thereareatotalof9blondsand11withbrownhair.
Q1.pr (girlorblond)Q2.pr (girlwithbrownhair)andpr (girl)
12
![Page 13: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/13.jpg)
Thoughtexercises:
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Example4.tossacoin4times
Q1.Whatistheprobabilityofgettingatleastoneheadonthe4tossespr (atleastoneH)
13
![Page 14: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/14.jpg)
Thoughtexercises:
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Example5.Anindividualapplyingtoacollegedeterminesthathehasan80%chanceofbeingaccepted,andheknowsthatdormitoryhousingwillonlybeprovidedfor60%ofacceptedstudents.
Q1.Whatisthechanceofthestudentbeingacceptedandreceivingdormitoryhousing?
14
![Page 15: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/15.jpg)
Thoughtexercises:
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Example6.A =“Patienthasliverdisease.”Pastdatatellsyouthat10%ofpatientsenteringyourclinichaveliverdisease.B =“Patientisanalcoholic.”Fivepercentoftheclinic’spatientsarealcoholics.Amongpatientsdiagnosedwithliverdisease,7%arealcoholics.
Q1.Findoutapatient’sprobabilityofhavingliverdiseaseiftheyareanalcoholic.
15
![Page 16: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/16.jpg)
LawsofProbability- 1
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Theprobabilityofaneventisbetween0and1
• Aprobabilityof1isequivalentto100%certainty
• Probabilitiescanbeexpressedatfractions,decimals,orpercentage
16
![Page 17: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/17.jpg)
LawsofProbability- 2
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Thesumoftheprobabilitiesofallpossibleoutcomesis1or100%.• IfA,B,andCaretheonlypossibleoutcomes,
• thenp(A)+p(B)+p(C)=1
Example: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. p (red) + p (blue) + p (green) = 1
17
![Page 18: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/18.jpg)
LawsofProbability- 3
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Thesumoftheprobabilityofaneventoccurringanditnotoccurringis1.• p(A)+p(notA)=1• p(notA)=1- p(A)
Example: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. p (red) + p (not red) = 1
18
![Page 19: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/19.jpg)
LawsofProbability- 4
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• IftwoeventsAandBareindependent• thentheprobabilityofAandBoccurringistheproductoftheirindividualprobabilities.
• p(AandB)=p(A)Xp(B)
Example: roll a die and flip a coin. p (heads and roll a 3) = p (H) X p (3)
*MultiplicativeTheorem
19
![Page 20: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/20.jpg)
LawsofProbability- 4a
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• IftwoeventsAandBaredependent• thentheprobabilityofAandBoccurringis• p(AandB)=p(B|A)Xp(A)=p(A|B)Xp(B)
• Anindividual applyingtoacollegedeterminesthathehasan80%chanceofbeingaccepted,andheknowsthatdormitoryhousingwillonlybeprovidedfor60%ofacceptedstudents.
• Whatisthechanceofthestudentbeingacceptedandreceivingdormitoryhousing?• P(AcceptedandDormitoryHousing)• =P(DormitoryHousing|Accepted)*P(Accepted)• =(0.60)*(0.80)=0.48
*MultiplicativeTheorem
20
![Page 21: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/21.jpg)
LawsofProbability- 5
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• IftwoeventsAandBaremutuallyexclusive• thentheprobabilityofAorBoccurringisthesumoftheirindividualprobabilities.
• p(AorB)=p(A)+p(B)
Example: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. p (red or green) = p (red) + p (green)
*AdditionTheorem
21
![Page 22: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/22.jpg)
LawsofProbability- 6
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• IftwoeventsAandBareNOT mutuallyexclusive• thentheprobabilityofAorBoccurringisthesumoftheirindividualprobabilitiesminustheprobabilityofbothAandBoccurring
• p(AorB)=p(A)+p(B)– p(AandB)
Example: 12 girls (5 with blond hair and 7 with brown hair) and 8 boys (4 with blond hair and 4 with brown hair). There are a total of 9 blonds and 11 with brown hair. One person from the group is chosen randomly. p (girl or blond) = p (girl) + p (blond) – p (girl and blond)
*AdditionTheorem
22
![Page 23: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/23.jpg)
LawsofProbability- 7
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Theprobabilityofatleastoneeventoccurringoutofmultipleeventsisequaltooneminustheprobabilityofnoneoftheeventsoccurring.• p(atleastone)=1– p(none)
Example: What is the probability of getting at least one head on the 4 throw of a coin?p (at least one H) = 1 – p (no H) = 1 – p (TTTT)
23
![Page 24: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/24.jpg)
LawsofProbability- 8
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• IfeventBisasubsetofeventA,• thentheprobabilityofBislessthanorequaltotheprobabilityofA.• p(B)≤p(A)
Example: There are 20 people in the room: 12 girls (5 with blond hair and 7 with brown hair) and 8 boys (4 with blond hair and 4 with brown hair).p (girl with brown hair) ≤ p (girl)
24
![Page 25: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/25.jpg)
ConditionalProbability
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• TwoeventsAandBaresaidtobedependent,whenBcanoccuronlywhenAisknowntohaveoccurred(orviceversa)
• TheprobabilityattachedtosuchaneventiscalledtheconditionalprobabilityandisdenotedbyP(A/B)
*BayesTheorem
25
![Page 26: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/26.jpg)
ConditionalProbability
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
*BayesTheorem
26
![Page 27: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/27.jpg)
ConditionalProbability- Example
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• A =“Patienthasliverdisease.”Pastdatatellsyouthat10%ofpatientsenteringyourclinichaveliverdisease.P(A)=0.10.
• B =“Patientisanalcoholic.”Fivepercentoftheclinic’spatientsarealcoholics.P(B)=0.05.
• Amongpatientsdiagnosedwithliverdisease,7%arealcoholics.Thisisyour B|A.
• Findingoutapatient’sprobabilityofhavingliverdiseaseiftheyareanalcoholic.
• P(A|B)=(0.07*0.1) / 0.05=0.14
*BayesTheorem
27
![Page 28: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/28.jpg)
Section2:Population&Sample
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 28
![Page 29: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/29.jpg)
Population
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 29
• Thepopulationisthesetofentitiesunderstudy• Apopulationincludesalloftheelementsfromasetofdata.• Ameasurablecharacteristicofapopulation- parameter
![Page 30: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/30.jpg)
Sample
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 30
• Asampleconsistsofoneormoreobservationsfromthepopulation• Ameasurablecharacteristicofasampleiscalledastatistic.
![Page 31: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/31.jpg)
Sample
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 31
![Page 32: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/32.jpg)
Descriptivestatistics
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 32
• Descriptivestatisticsprovideaconcisesummaryofdata.• Youcansummarizedatanumericallyorgraphically
![Page 33: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/33.jpg)
Descriptivestatistics
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 33
![Page 34: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/34.jpg)
Inferentialstatistics
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 34
• Inferentialstatisticsusearandomsampleofdatatakenfromapopulationtodescribeandmakeinferencesaboutthepopulation.
![Page 35: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/35.jpg)
Inferentialstatistics
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 35
![Page 36: Probability, population and sample](https://reader034.fdocuments.net/reader034/viewer/2022051520/58f9b1341a28abc3328b45d7/html5/thumbnails/36.jpg)
Takehomemessages
Demystifying statistics! – Lecture 1 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Understandingprobabilityanditslawsareimportanttounderstandingbiostatistics
• Theconceptsofpopulationandsampleareessentialforunderstandinginferentialstatistics
36