1. Lecture #1 Tuesday, August 23, 2016
Statistics 200
Lecture #1 Tuesday, August 23, 2016
Objectives:
Define Statistics and begin to appreciate why it is important.
Distinguish between a representative and unrepresentative sample.
Distinguish between an observational study and randomized experiment.

2. Definition of Statistics (page 1)
Statistics is a collection of procedures and principles for gathering data and analyzing information to help people make decisions when faced with uncertainty.

3. Statistical inference (page 150)
…data can be used to make inferences about a much larger group if the data can be considered to be representative with regard to the question(s) of interest.

4. Eight Statistical Stories (Section 1.2)
Case study 1.3: A sample survey that uses a representative sample
Case study 1.4: A sample survey that uses an unrepresentative sample
Case study 1.5: An observational study
Case study 1.6: A randomized experiment
We’ll focus on four of them
Compare:
1.3 vs 1.4
1.5 vs 1.6

5. Did anyone ask whom you’ve been dating?
What percentage of US teens have dated somebody in another race or ethnic group?
Population of all U.S. teens
Random sample of 602 teens
This is case study 1.3, page 3. What does the title mean?

6. Did anyone ask whom you’ve been dating?
Random sample of 602 teens
Of 496 who have dated, 57% have dated somebody of another race or ethnic group.
Accurate to within a margin of error of 5%
We are reasonably confident that the true percentage is between 52% and 62%

7. Case study 1.3: Some definitions
Population - a collection of individuals about which information is desired
Random sample - a subset of the population so that every individual has a specified probability of being included
Population
Random Sample
Random Sample

8. Moral of case study 1.3:
A representative sample of only a few thousand, or perhaps even a few hundred can give reasonably accurate information about a population of many millions.

9. Case study 1.4: Who are those angry women?
100,000 women were sent questionnaires about love, sex, and relationships.
Only 4.5% responded, and they were overwhelmingly fed up with men and eager to fight with them.
Can we use this data to make generalizations about all women in America?
NO!

10. Case study 1.4: Not random sample – unrepresentative.
Self-selected sample (or volunteer sample)
Nonparticipation bias (or nonresponse bias): occurs when many people who are selected for the sample either do not respond at all or do not respond to some of the key survey questions.

11. Moral of case study 1.4:
An unrepresentative sample, even a large one, tells you almost nothing about the population.
Example
It would be incorrect to conclude that the average adult drinks until they are intoxicated between 5 and 6 times a month based on a sample collected at 2am in downtown State College.

12. Case study 1.5: Prayer and Blood Pressure
Sample of 2391 people aged 65 or older
Form two groups based on religious activity
Group 1:
Frequent Religious Activity
Group 2:
Infrequent Religious Activity
40% less likely to have high blood pressure
More likely to have high blood pressure

13. Case study 1.5:
Can we say that prayer and religious activity caused lower blood pressure?
No!
Observational study - a study in which participants are merely observed and measured
Confounding variable: A variable that is not the main concern of the study but may be partially responsible for the observed results.

14. Moral of case study 1.5:
We cannot claim cause and effect from an observational study.

15. Case study 1.6: Does Aspirin reduce heart attack rates?
22,071 male physicians
Randomly assign each physician to one of two groups
Group 1:
Aspirin every other day
Group 2:
Placebo every other day
Heart attack rate: 9.42 per 1000 participating physicians
Heart attack rate: per 1000 participating physicians

16. Case study 1.6: Definitions
Randomized experiment - a study in which treatments are randomly assigned to participants.
Treatment – a specific regimen or procedure assigned to participants by the experimenter.
Placebo – a pill or treatment designed to look just like the active treatment but with no active ingredients.

17. Moral of case study 1.6: Unlike with observational studies
Cause-and-effect conclusions can generally be made on the basis of randomized experiments.
Question:
Could the previous case study on religious activity been randomized?

18. …and explain these objectives
Review: If you understood today’s lecture, you should be able to solve…
1.5, 1.11, 1.15, 1.25, 1.38 on pages 9 to 12
…and explain these objectives
Define statistics or, more importantly, explain what statistical inference means.
Distinguish between a representative and unrepresentative sample; describe consequences of each
Distinguish between an observational study and randomized experiment; describe consequences of each