SlideShare a Scribd company logo
1 of 28
Download to read offline
Probability
&
Probability
Distribution
Analytic View of
Probability
 If an event can occur in A ways and can fail
to occur in B ways, and if all possible
outcomes are equally likely to occur, then:
 Occurrence:
 A/(A+B)
 Fail to Occur:
 B/(A+B)
Frequentist View of
Probability
 Probability is defined in terms of one’s past
performance
 Uses sampling with replacement/independent
random sampling
Subjective Probability
 An individuals subjective belief in the
likelihood of occurrence
Key Terms
• Data used in analyzing probability
• Outcome of trial
Event
• Occurrence of one event is not dependent on the other
Independent Events
• Outcome of one event is related to the other
Dependent Events
• One way only
Mutually Exclusive Events
• All possible events
Exhaustive Events
Laws of Probability
The probability of the occurrence of one event or another is equal
to the sum of their separate probabilities.
Additive Law
The probability of the joint occurrence of two or more
independent events is the product of their individual probabilities.
Multiplicative
Law
Co-occurrence of two events
Joint Probability
The probability that one event will occur given the occurrence of
some other event.
Conditional
Probability
The probability of one event ignoring the occurrence or
nonoccurrence of some other event.
Unconditional
Probability
Laws of Probability: An
Example
Income and Happiness: Is there a
relationship?
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT IS NOT TOO HAPPY?
p
p = 315/1993 = 0.16
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT HAS A BELOW AVERAGE
INCOME?
p
p = 687/1993 = 0.34
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT HAS AN AVERAGE INCOME AND
IS PRETTY HAPPY?
p = 473/1993 = 0.24
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT HAS A BELOW AVERAGE
INCOME GIVEN THAT HE/SHE IS VERY HAPPY?
p = 132/687 = 0.19
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A PARTICIPANT HAS A
BELOW AVERAGE INCOME AND IS NOT TOO HAPPY?
p = 687/1993 = 0.34
p = 315/1993 = 0.16
p = (0.34) x (0.16) = 0.05
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
The Normal Distribution
 Symmetrical
 Bell-shaped
 Mean, Median, and Mode are equal to one
another
The Normal Distribution
The Normal Distribution
 The use of z-scores can help determine the
probability
 Can describe the proportions of area
contained in each section of the distribution
The Normal Distribution
 The use of z-scores can help determine the
probability
 Can describe the proportions of area
contained in each section of the distribution
z-scores
 Helps identify the exact location of a score
in a distribution
 To make raw scores meaningful, they are
transformed into new values
 Standardizes the entire distribution
z-scores
𝑧 =
𝑥 − 𝑥
𝜎
𝑥 = 𝜇 + 𝑧𝜎
Example 1
SAT scores for a normal distribution with
mean of 500 and a standard deviation of 100.
What SAT score separates the top 10% of the
distribution from the test?
Solution 1
X = mean + (z) (sd)
X = 500 + (z) (100)
X = 500 + (1.28) (100)
X = 500 + 128
X = 628
Example 2
IQ test scores are standardized to produce a
normal distribution with a mean of 100 and a
standard deviation of 15. Find the proportion
of the population in each of the following IQ
categories:
Genius or near genius: IQ over 140
Very superior: IQ 120-140
Average: IQ 90-109
Solution 2
Genius or near genius:
z = 140-100/15
z = 2.67
p = 0.0038 or 3.8%
Very Superior:
z = 120-100/15 = 1.33
z = 140-100/15 = 2.67
p (120 < X < 140) = 0. 0918 – 0.0038
p = 0.0880 or 8.8%
Average:
z = 90-100/15 = -0.67
z = 109-100/15 = 0.60
p = (90 < X < 109) = 0.2486 + 0.2257
p = 0.4744 or 47.44%
Sampling Error
 Discrepancy between a sample statistic and
its corresponding population parameter
 If the population is normal, you should be
able to determine the probability of
obtaining any individual score
Sampling Distribution
 Distribution of statistics obtained by
selecting all the possible samples of a
specific size from a population
Distribution of Sample
Means
 Collection of sample means for all possible
random samples of a particular size that can
be obtained from a population
 Characteristics:
 Piles up around population mean
 Forms a normal distribution
 The larger the sample size, the closer to the
population mean
Central Limit Theorem
 For any population with mean and standard
deviation, the distribution of sample means
for sample size will have a mean and a
standard deviation ( 𝜎 𝑛) that will
approach a normal distribution as the
sample approaches infinity.
Central Limit Theorem
 Expected Value of M
 The mean of the distribution of sample
means is equal to the mean of the
population of scores
 Standard Error of M
 Provides a measure on how much distance is
expected between sample mean and population
mean
Law of Large Numbers
 The larger the sample size, the more
probable it is that the sample mean will be
close to the population mean
 When n > 30, the distribution is almost
normal regardless of the shape
 As sample size increases, error decreases

More Related Content

What's hot (20)

The sampling distribution
The sampling distributionThe sampling distribution
The sampling distribution
 
Uniform Distribution
Uniform DistributionUniform Distribution
Uniform Distribution
 
Hypothesis Testing
Hypothesis TestingHypothesis Testing
Hypothesis Testing
 
Poission distribution
Poission distributionPoission distribution
Poission distribution
 
Hypergeometric probability distribution
Hypergeometric probability distributionHypergeometric probability distribution
Hypergeometric probability distribution
 
Sampling and sampling distribution tttt
Sampling and sampling distribution ttttSampling and sampling distribution tttt
Sampling and sampling distribution tttt
 
Discreet and continuous probability
Discreet and continuous probabilityDiscreet and continuous probability
Discreet and continuous probability
 
Statistical inference
Statistical inferenceStatistical inference
Statistical inference
 
STATISTICS: Normal Distribution
STATISTICS: Normal Distribution STATISTICS: Normal Distribution
STATISTICS: Normal Distribution
 
Continuous Random Variables
Continuous Random VariablesContinuous Random Variables
Continuous Random Variables
 
Point and Interval Estimation
Point and Interval EstimationPoint and Interval Estimation
Point and Interval Estimation
 
Hypothesis Testing
Hypothesis TestingHypothesis Testing
Hypothesis Testing
 
Point Estimation
Point Estimation Point Estimation
Point Estimation
 
Normal Distribution
Normal DistributionNormal Distribution
Normal Distribution
 
Sampling distribution
Sampling distributionSampling distribution
Sampling distribution
 
Methods of point estimation
Methods of point estimationMethods of point estimation
Methods of point estimation
 
Continuous probability distribution
Continuous probability distributionContinuous probability distribution
Continuous probability distribution
 
Probability.ppt
Probability.pptProbability.ppt
Probability.ppt
 
Cumulative distribution
Cumulative distributionCumulative distribution
Cumulative distribution
 
6. point and interval estimation
6. point and interval estimation6. point and interval estimation
6. point and interval estimation
 

Similar to Psych stats Probability and Probability Distribution

M.Ed Tcs 2 seminar ppt npc to submit
M.Ed Tcs 2 seminar ppt npc   to submitM.Ed Tcs 2 seminar ppt npc   to submit
M.Ed Tcs 2 seminar ppt npc to submitBINCYKMATHEW
 
5_lectureslides.pptx
5_lectureslides.pptx5_lectureslides.pptx
5_lectureslides.pptxsuchita74
 
Basic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docxBasic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docxjasoninnes20
 
Basic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docxBasic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docxgarnerangelika
 
Sriram seminar on introduction to statistics
Sriram seminar on introduction to statisticsSriram seminar on introduction to statistics
Sriram seminar on introduction to statisticsSriram Chakravarthy
 
Different types of distributions
Different types of distributionsDifferent types of distributions
Different types of distributionsRajaKrishnan M
 
Estimation in statistics
Estimation in statisticsEstimation in statistics
Estimation in statisticsRabea Jamal
 
Statistical Methods in Research
Statistical Methods in ResearchStatistical Methods in Research
Statistical Methods in ResearchManoj Sharma
 
Review & Hypothesis Testing
Review & Hypothesis TestingReview & Hypothesis Testing
Review & Hypothesis TestingSr Edith Bogue
 
Normal and standard normal distribution
Normal and standard normal distributionNormal and standard normal distribution
Normal and standard normal distributionAvjinder (Avi) Kaler
 
Inferential statistics
Inferential statisticsInferential statistics
Inferential statisticsMaria Theresa
 
Introduction to Statistical Methods
Introduction to Statistical MethodsIntroduction to Statistical Methods
Introduction to Statistical MethodsMichael770443
 
A Lecture on Sample Size and Statistical Inference for Health Researchers
A Lecture on Sample Size and Statistical Inference for Health ResearchersA Lecture on Sample Size and Statistical Inference for Health Researchers
A Lecture on Sample Size and Statistical Inference for Health ResearchersDr Arindam Basu
 
Sqqs1013 ch5-a122
Sqqs1013 ch5-a122Sqqs1013 ch5-a122
Sqqs1013 ch5-a122kim rae KI
 

Similar to Psych stats Probability and Probability Distribution (20)

Descriptive Statistics
Descriptive StatisticsDescriptive Statistics
Descriptive Statistics
 
M.Ed Tcs 2 seminar ppt npc to submit
M.Ed Tcs 2 seminar ppt npc   to submitM.Ed Tcs 2 seminar ppt npc   to submit
M.Ed Tcs 2 seminar ppt npc to submit
 
Statistics excellent
Statistics excellentStatistics excellent
Statistics excellent
 
5_lectureslides.pptx
5_lectureslides.pptx5_lectureslides.pptx
5_lectureslides.pptx
 
Basic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docxBasic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docx
 
Basic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docxBasic Statistics The z-Score and standard normal distribution.docx
Basic Statistics The z-Score and standard normal distribution.docx
 
Sriram seminar on introduction to statistics
Sriram seminar on introduction to statisticsSriram seminar on introduction to statistics
Sriram seminar on introduction to statistics
 
Different types of distributions
Different types of distributionsDifferent types of distributions
Different types of distributions
 
Basic statistics
Basic statisticsBasic statistics
Basic statistics
 
Estimation in statistics
Estimation in statisticsEstimation in statistics
Estimation in statistics
 
Statistical Methods in Research
Statistical Methods in ResearchStatistical Methods in Research
Statistical Methods in Research
 
Review & Hypothesis Testing
Review & Hypothesis TestingReview & Hypothesis Testing
Review & Hypothesis Testing
 
Freq distribution
Freq distributionFreq distribution
Freq distribution
 
Normal and standard normal distribution
Normal and standard normal distributionNormal and standard normal distribution
Normal and standard normal distribution
 
Inferential statistics
Inferential statisticsInferential statistics
Inferential statistics
 
Inorganic CHEMISTRY
Inorganic CHEMISTRYInorganic CHEMISTRY
Inorganic CHEMISTRY
 
Introduction to Statistical Methods
Introduction to Statistical MethodsIntroduction to Statistical Methods
Introduction to Statistical Methods
 
A Lecture on Sample Size and Statistical Inference for Health Researchers
A Lecture on Sample Size and Statistical Inference for Health ResearchersA Lecture on Sample Size and Statistical Inference for Health Researchers
A Lecture on Sample Size and Statistical Inference for Health Researchers
 
statistics
statisticsstatistics
statistics
 
Sqqs1013 ch5-a122
Sqqs1013 ch5-a122Sqqs1013 ch5-a122
Sqqs1013 ch5-a122
 

More from Martin Vince Cruz, RPm (20)

Multivariatetechniques01
Multivariatetechniques01Multivariatetechniques01
Multivariatetechniques01
 
Late adulthood
Late adulthoodLate adulthood
Late adulthood
 
Emerging and Early Adulthood
Emerging and Early  AdulthoodEmerging and Early  Adulthood
Emerging and Early Adulthood
 
Middle and Late Childhood
Middle and Late ChildhoodMiddle and Late Childhood
Middle and Late Childhood
 
infancy
infancyinfancy
infancy
 
Introto lifespandevt
Introto lifespandevtIntroto lifespandevt
Introto lifespandevt
 
Feminist therapy
Feminist therapyFeminist therapy
Feminist therapy
 
Paraphilias
ParaphiliasParaphilias
Paraphilias
 
Somatic sexdysphoria
Somatic sexdysphoriaSomatic sexdysphoria
Somatic sexdysphoria
 
Anxiety disorders
Anxiety disordersAnxiety disorders
Anxiety disorders
 
Person centered therapy
Person centered therapyPerson centered therapy
Person centered therapy
 
Organizational culture
Organizational cultureOrganizational culture
Organizational culture
 
Anxiety disorders
Anxiety disordersAnxiety disorders
Anxiety disorders
 
Counselor: Person and Professional
Counselor: Person and ProfessionalCounselor: Person and Professional
Counselor: Person and Professional
 
Abnormal Behavior in the Historical Context
Abnormal Behavior in the Historical ContextAbnormal Behavior in the Historical Context
Abnormal Behavior in the Historical Context
 
George kelly
George kellyGeorge kelly
George kelly
 
Raymond cattell
Raymond cattellRaymond cattell
Raymond cattell
 
Hypothesis Testing
Hypothesis TestingHypothesis Testing
Hypothesis Testing
 
Using SPSS: A Tutorial
Using SPSS: A TutorialUsing SPSS: A Tutorial
Using SPSS: A Tutorial
 
Review of Statistics
Review of StatisticsReview of Statistics
Review of Statistics
 

Recently uploaded

Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...raviapr7
 
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxPractical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxKatherine Villaluna
 
CAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxCAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxSaurabhParmar42
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice documentXsasf Sfdfasd
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxraviapr7
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17Celine George
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17Celine George
 
Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesMohammad Hassany
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17Celine George
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfYu Kanazawa / Osaka University
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfTechSoup
 
Benefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationBenefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationMJDuyan
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?TechSoup
 
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...Nguyen Thanh Tu Collection
 
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRADUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRATanmoy Mishra
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxraviapr7
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17Celine George
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 

Recently uploaded (20)

Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...
 
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxPractical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
 
CAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxCAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptx
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice document
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptx
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17
 
Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming Classes
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
 
Benefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationBenefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive Education
 
Prelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quizPrelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quiz
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?
 
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
 
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRADUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptx
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 

Psych stats Probability and Probability Distribution

  • 2. Analytic View of Probability  If an event can occur in A ways and can fail to occur in B ways, and if all possible outcomes are equally likely to occur, then:  Occurrence:  A/(A+B)  Fail to Occur:  B/(A+B)
  • 3. Frequentist View of Probability  Probability is defined in terms of one’s past performance  Uses sampling with replacement/independent random sampling
  • 4. Subjective Probability  An individuals subjective belief in the likelihood of occurrence
  • 5. Key Terms • Data used in analyzing probability • Outcome of trial Event • Occurrence of one event is not dependent on the other Independent Events • Outcome of one event is related to the other Dependent Events • One way only Mutually Exclusive Events • All possible events Exhaustive Events
  • 6. Laws of Probability The probability of the occurrence of one event or another is equal to the sum of their separate probabilities. Additive Law The probability of the joint occurrence of two or more independent events is the product of their individual probabilities. Multiplicative Law Co-occurrence of two events Joint Probability The probability that one event will occur given the occurrence of some other event. Conditional Probability The probability of one event ignoring the occurrence or nonoccurrence of some other event. Unconditional Probability
  • 7. Laws of Probability: An Example Income and Happiness: Is there a relationship? INCOME VERY HAPPY PRETTY HAPPY NOT TOO HAPPY TOTAL Above Average 164 233 26 423 Average 293 473 117 883 Below Average 132 383 172 687 TOTAL 589 1089 315 1993
  • 8. Laws of Probability: An Example WHAT IS THE PROBABILITY THAT A PARTICIPANT IS NOT TOO HAPPY? p p = 315/1993 = 0.16 INCOME VERY HAPPY PRETTY HAPPY NOT TOO HAPPY TOTAL Above Average 164 233 26 423 Average 293 473 117 883 Below Average 132 383 172 687 TOTAL 589 1089 315 1993
  • 9. Laws of Probability: An Example WHAT IS THE PROBABILITY THAT A PARTICIPANT HAS A BELOW AVERAGE INCOME? p p = 687/1993 = 0.34 INCOME VERY HAPPY PRETTY HAPPY NOT TOO HAPPY TOTAL Above Average 164 233 26 423 Average 293 473 117 883 Below Average 132 383 172 687 TOTAL 589 1089 315 1993
  • 10. Laws of Probability: An Example WHAT IS THE PROBABILITY THAT A PARTICIPANT HAS AN AVERAGE INCOME AND IS PRETTY HAPPY? p = 473/1993 = 0.24 INCOME VERY HAPPY PRETTY HAPPY NOT TOO HAPPY TOTAL Above Average 164 233 26 423 Average 293 473 117 883 Below Average 132 383 172 687 TOTAL 589 1089 315 1993
  • 11. Laws of Probability: An Example WHAT IS THE PROBABILITY THAT A PARTICIPANT HAS A BELOW AVERAGE INCOME GIVEN THAT HE/SHE IS VERY HAPPY? p = 132/687 = 0.19 INCOME VERY HAPPY PRETTY HAPPY NOT TOO HAPPY TOTAL Above Average 164 233 26 423 Average 293 473 117 883 Below Average 132 383 172 687 TOTAL 589 1089 315 1993
  • 12. Laws of Probability: An Example WHAT IS THE PROBABILITY THAT A PARTICIPANT HAS A BELOW AVERAGE INCOME AND IS NOT TOO HAPPY? p = 687/1993 = 0.34 p = 315/1993 = 0.16 p = (0.34) x (0.16) = 0.05 INCOME VERY HAPPY PRETTY HAPPY NOT TOO HAPPY TOTAL Above Average 164 233 26 423 Average 293 473 117 883 Below Average 132 383 172 687 TOTAL 589 1089 315 1993
  • 13. The Normal Distribution  Symmetrical  Bell-shaped  Mean, Median, and Mode are equal to one another
  • 15. The Normal Distribution  The use of z-scores can help determine the probability  Can describe the proportions of area contained in each section of the distribution
  • 16. The Normal Distribution  The use of z-scores can help determine the probability  Can describe the proportions of area contained in each section of the distribution
  • 17. z-scores  Helps identify the exact location of a score in a distribution  To make raw scores meaningful, they are transformed into new values  Standardizes the entire distribution
  • 18. z-scores 𝑧 = 𝑥 − 𝑥 𝜎 𝑥 = 𝜇 + 𝑧𝜎
  • 19. Example 1 SAT scores for a normal distribution with mean of 500 and a standard deviation of 100. What SAT score separates the top 10% of the distribution from the test?
  • 20. Solution 1 X = mean + (z) (sd) X = 500 + (z) (100) X = 500 + (1.28) (100) X = 500 + 128 X = 628
  • 21. Example 2 IQ test scores are standardized to produce a normal distribution with a mean of 100 and a standard deviation of 15. Find the proportion of the population in each of the following IQ categories: Genius or near genius: IQ over 140 Very superior: IQ 120-140 Average: IQ 90-109
  • 22. Solution 2 Genius or near genius: z = 140-100/15 z = 2.67 p = 0.0038 or 3.8% Very Superior: z = 120-100/15 = 1.33 z = 140-100/15 = 2.67 p (120 < X < 140) = 0. 0918 – 0.0038 p = 0.0880 or 8.8% Average: z = 90-100/15 = -0.67 z = 109-100/15 = 0.60 p = (90 < X < 109) = 0.2486 + 0.2257 p = 0.4744 or 47.44%
  • 23. Sampling Error  Discrepancy between a sample statistic and its corresponding population parameter  If the population is normal, you should be able to determine the probability of obtaining any individual score
  • 24. Sampling Distribution  Distribution of statistics obtained by selecting all the possible samples of a specific size from a population
  • 25. Distribution of Sample Means  Collection of sample means for all possible random samples of a particular size that can be obtained from a population  Characteristics:  Piles up around population mean  Forms a normal distribution  The larger the sample size, the closer to the population mean
  • 26. Central Limit Theorem  For any population with mean and standard deviation, the distribution of sample means for sample size will have a mean and a standard deviation ( 𝜎 𝑛) that will approach a normal distribution as the sample approaches infinity.
  • 27. Central Limit Theorem  Expected Value of M  The mean of the distribution of sample means is equal to the mean of the population of scores  Standard Error of M  Provides a measure on how much distance is expected between sample mean and population mean
  • 28. Law of Large Numbers  The larger the sample size, the more probable it is that the sample mean will be close to the population mean  When n > 30, the distribution is almost normal regardless of the shape  As sample size increases, error decreases