1 stat 217 introduction to statistical concepts and methods

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Stat 217

Introduction to Statistical

Concepts and Methods

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What will you learn in this class?

• Evaluate claims

• Draw conclusions

• Make sense of numbers

• Monitor trends

• Support arguments

• Make comparisons

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What you will be asked to do

• Interpret, explain, justify, communicate

• Use algebra and computer as tools

• Practice developing and using tools

• Try things on your own

• Work together

• Ask questions

Warning: Often I answer with a question...

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What you will not be asked to do

• Memorize formulas

• Manipulate equations without understanding where they came from, what they mean, or why they are used

• Repeat back what I say to you

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Why are you being asked to do this?

BiologyEconomicsPsychologyAnthropologyEngineeringHistoryLawMedicine

PharmaceuticalsBusinessIndustryEnvironmental ScienceGeologyPolitical ScienceSports

Learn by Doing…

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What is (not) Statistics?

• TRUE cigarettes have 5 milligrams less tar

• Anacin contains more of the ingredient doctors recommend most

• Doctors specify Bufferin the most over other leading brands

• Dr. Bragg claims his patients have 50% fewer cavities

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What is (not) Statistics?

• General Motors advertises that JD Power picks the Lumina Coupe as the most trouble-free car in its class

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What is (not) Statistics?

• Science (1976): People over 65, now numbering 10 million, will number 30 million by the year 2000, and will constitute an unprecedented 25 percent of the population

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What is (not) Statistics?

• Dr. Fudge counted how many cars turned left at a certain intersection in groups of 20 cars at a time. In 6 different trials, he reported percentages of 53%, 58%, 63%, 46%, 48%, and 67% (of the 20 cars made left turns).

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What is (not) Statistics?

• CCC Information Service: Camrys, Accords still the top choices of car thieves

The top 6 stolen cars of 20001. 1989 Toyota Camry 2. 1990 Toyota Camry 3. 1991 Toyota Camry 4. 1988 Toyota Camry 5. 1994 Honda Accord EX 6. 1996 Honda Accord LX

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What is (not) Statistics?

• In 1989, 5326 drivers 65 years of age and over were involved in fatal accidents. In contrast, only 2900 drivers aged 16 and 17 had fatal accidents. Thus, young people are safer drivers.

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What is (not) Statistics?

• The Alabama Development Office reports that the state has attracted 422,657 new industrial jobs in the past 25 years.

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What is (not) Statistics?

• Schick Super Chromium razor blades commercial:A group of barbers shave with the same blade,

one after the other. The 12th, 13th, 15th, and 17th men to use the blade were interviewed and said the shave was satisfactory

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What is (not) Statistics

• The unemployment rate is 5.7 % in August

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Def: “Unemployed Persons” (bls.gov)

Persons 16 years and over who had no employment during the reference week, were available for work, except for temporary illness, and had made specific efforts to find employment sometime during the 4-week period ending with the reference week. Persons who were waiting to be recalled to a job from which they had been laid off need not have been looking for work to be classified as unemployed.

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What is (not) Statistics

• The AIDS Epidemic and its sub-epidemics

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What is (not) Statistics?

• Company report

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Last Year’s Expenses

Last Year's Expenses

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1 2 3 4 5 6 7 8 9 10 11 12

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Do

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Last Year’s Profits

Last Year's Profits

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20.5

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21.5

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1 2 3 4 5 6 7 8 9 10 11 12

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What is (not) Statistics?

• Describing voter opinion

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What is (not) Statistics?

Roper Poll: Does it seem possible or does it seem impossible to you that the … never happened

“One in five people in the United States is open to the idea that the Holocaust is a myth.” – USA Today

•83% said the Holocaust definitely happened•13% said it probably happened“Figure one out of five Americans

could be willfully stupid” –San Francisco Examiner

Gallup Poll: … did the Holocaust: definitely happen, probably happen, probably not happen, or definitely not happen?

•22% said “it seemed possible” that it never happened

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What is (not) Statistics?

• The Challenger AccidentWas O-ring failure related to temperature?

Examine the failures:

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Challenger Data

50 55 60 65 70 75

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temp

num

Number of failures vs. temperature

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Challenger Data

50 60 70 80

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failu

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Number of failures vs. temperature

Challenger launched at 31 degrees

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What is Statistics?

• Starting in 1916 polio claimed hundreds of thousands of lives, mainly children.

• In 1954, Jonas Salk’s vaccine seemed promising.• The Biggest Public Health Experiment Ever: The

1954 Field Trial of the Salk Poliomyelitis Vaccine– Randomized 1 million children to receive the

vaccination and 1 million to not receive the vaccination

• Evidence that vaccine worked – stopped early• Continued: is vaccine now (since 1980) causing

polio?

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What is Statistics?

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Evaluating Uses of Statistics

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Step 1: Obtain Data

• Make up data

• Anecdotes– Example: seat belts

• Available data– History report– Exploration

• Collect your own data

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Thought Question

• Want to determine if a new allergy medication reduces symptoms. How would you collect data to answer this question?

• Statistics: Even though results vary, can we see patterns or trends that still allow us to make decisions…

“distribution of data”

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Collecting your own data

1) What will you measure?

2) How will you measure the variable?

3) Which individuals will you measure?

4) How will you conduct the study?

5) How many measurements will you take?

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1) What will you measure?

• Def: variable = any characteristic that changes from observational unit/individual to observational unit

• Types of variables (p. 4)– Quantitative = numerical value and makes sense to

“average”– Categorical = places individuals into groups

• Special case: binary = two groups

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Example 1-1: Chocolate Lovers

• Observational units

people

men

• Variables

candy eating habits

number of years lived

weight, smoking habits…

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Example 1-2: Variables of State

Is it a characteristic that varies from state to state?

(b) each state could have a different percentage

(c) each state could have a different maximum speed limit

(a) there is one number that describes all of the states, it is not phrased as a question that could be posed to each state…

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2) How will you take the measurements?• Instruments or tools

– monitor meals? survey?

• Definitions– “abstain”– “trouble free rating”

– “intelligence”

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3) Which individuals will you measure?• Def: Population = the collection of

individuals you are interested inExample: all Cal Poly studentsExample: all US citizens

• Def: Census = obtain measurements for all individuals in the population

• Drawbacks– Cost, time, destructive, accuracy

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population

Which individuals, cont.

• Def: Sample = subset of individuals in the population

Key Idea: Use sample to gain information about the entire population

sample

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Example - Opinion Polls

• Gallup Polls (www.gallup.com)– Observational units - people– Variables – how respond to questions about

public issues– Method – telephone interviews– Population - U.S. residents over 18– Sample - About 1000-1500 people interviewed

weekly

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Example - Marketing Research

• Nielsen ratings (www.nielsenmedia.com)– Observational units - households– Variables – programs viewed, age, gender, race– Method – “people meter”– Population - All 102.2 million U.S. households

that have a TV set– Sample - About 5,000 households that agree to

use meter

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Example - Royalties

• ASCAP (www.ascap.com)– Observational units - Song– Variables - number of times played– Method – identify song by first few notes– Population - All songs played by all local

radio stations across nation each year (53 million hours)

– Sample - About 60,000 hours of songs

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Example 1-3: Elvis Presley

a) Sample = those who called in

(individuals = radio listeners)

Population = listeners of over 1000 radio stations

b) No, those who believe strongly in Elvis are probably more likely to call in and are more willing to pay the $2.50

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Example 1-4: Literary Digest

c) Population = all voters

Sample = 2.4 million respondents

d) In the 1930’s, only wealthier citizens had phones, cars and they tended to Republican as well.

Also, those unhappy with incumbent are more likely to make effort to voice opinion

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BIAS

• The sampling method is biased if samples tends to overrepresent certain segments of the population

• Common causes:– Voluntary response– Nonresponse– Bad sampling frame

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Example 1-5: Sampling CP

On a separate piece of paper, with two names on it, turn in your suggestions to:

• Sampling frame?

• Identify variables

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Assignments

• By Wednesday– Bring coursenotes to class– Reading in BPS, finish syllabus– Complete example 1-6

• By Friday– complete survey in Blackboard

• By Monday– HW 1– Bring floppy