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Welcome to Stat 100.001

Joe Schafer

Associate ProfessorDepartment of Statistics and

The Methodology CenterThe Pennsylvania State University

Course website

All official information pertaining to this course—syllabus, announcements, lecture notes, assignments, etc.—are posted at the website:

http://www.stat.psu.edu/~jls/stat100/

Be sure to visit this website early and often.

Textbook

Utts, J. M. (2005) Seeing Through Statistics, Third edition. Duxbury Press.

We will follow this book closely, covering about one chapter per lecture. Additional material will be presented by the instructor as needed.

Students are responsible for all material covered in the lectures, whether or not it can be found in the textbook.

Quizzes

• no make-up quizzes for any reason

Near the end of every lecture, we will conduct a random experiment to determine whether or not a quiz will take place (probability between 1/3 and 2/3). If “yes,” you will receive a short quiz.

• missed quiz will be scored as zero

• ten best quiz scores will contribute to your final grade; remaining scores will be dropped

• quiz based solely on that day’s lecture

Exams

• exam may be missed only by prior written request and approval by instructor

Three in-class exams will be given during the semester (dates to be announced soon).

Final exam during finals week.

• no make-up exams for any reason

Homework

• solutions to some problems available in book or posted on website

Regular homework exercises will be assigned (approximately 5 problems per lecture)

• not collected or graded

• each exam will include some questions derived from the homework

Grading Scheme

• exams worth 100 points (20%) each

Overall grade based on a possible 500 points

• ten best quizzes worth 50 points (10%)

• final exam worth 150 points (30%)

Extra credit problems (worth 1 point each) may occasionally appear in various on the course website. Answers must be emailed to the instructor by the specified deadline.

Course rules

• Pay attention in class.

• Don’t disrupt the learning environment.

• You are responsible for all material and announcements given in class and/or posted on the website

For a complete list of rules and policies, see the syllabus posted on line at

http://www.stat.psu.edu/~jls/stat100

Office Hours

• Monday and Wednesday 2-3:30 pm in 422A Thomas

• By appointment at The Methodology Center (204 E. Calder Way, Suite 400)

Lecture 1

This lecture is not strictly based on material in the textbook, but it covers some of the same concepts that appear in Chapter 1. We will cover Chapter 1 next time.

Topic for today:

“The three C’s and the Three R’s”

• replication, randomization, representativeness

• co-occurrence, causation, counterfactuals

Co-occurrence and causation

Many questions in scientific research are of the following nature

• We want to know, “Does A cause B”? (causation)

• We observe something (A) together with something else (B) (co-occurrence)

Causation usually requires co-occurrence, but co-occurrence does not automatically imply causation.

Example 1

Light switch

You walk into a room and flip the switch on the wall. The lights come on. Can you immediately conclude that A (flipping the switch) caused B (the lights go on)?

No, because you cannot be sure that the lights would not have gone on anyway.

Example 2

Global warming and atmospheric CO2

Average surface temperatures around the world have apparently been increasing. Levels of carbon dioxide in the atmosphere have also been increasing. Can we conclude that increasing CO2 levels cause global warming?No, because you cannot be sure that global warming would not have taken place anyway.

Meaning of causation

Suppose A and B co-occur. What does it mean for A to have caused B?

“A caused B” means that B would not have occurred if A had not occurred.

Or, more generally, it means that B would have been less likely to occur if A had not occurred.

Counterfactual outcomes

Causation, therefore, is really statement about counterfactual outcomes.

If A and B occur together, the counterfactual outcome is what would have happened (either B or not B) if A had not occurred.

• Counterfactual outcomes cannot be observed. We cannot simultaneously observe what happens under A and not A.• Yet, using careful experimentation and statistical analysis, we can sometimes infer or prove beyond a reasonable doubt that A causes B. How?

The Three R’s

To infer or prove causation in a scientifically defensible manner, we rely on three R’s

• replication: Use multiple subjects or experimental units

• randomization: Randomly select some units to receive A, the others to receive not A

• representativeness: Make sure that the units in your experiment are similar to (representative of) the population to which you want to generalize

Example 1 (continued)

Light switch experiment

Designate ten moments in time. Randomly select five and flip the switch at those times, but not the others.

Suppose you observe that the light is on at the five moments at which you flipped the switch, and off at the other five moments. This is powerful evidence that flipping the switch caused the light to go on.

Analysis

Number of ways to select five units (without replacement) out of ten = 252

If the lights were going to be on regardless of what you did at five of the ten occasions, the probability that they would have been on at exactly the five moments you selected is

1/252 = .00397 = 0.397%

Beyond a reasonable doubt!

For now, the details of this analysis are not important. The important thing is that we were able to get strong evidence that A (flip switch) caused B (lights on) by using replication (multiple moments in time) and randomization (randomly selecting the moments at which to apply the treatment A).In order to conclude that A causes B, not just at those ten moments but in general (all the time), we must believe that the ten moments in time were not unusual—i.e, that they are representative.

Why the three R’s are important

Why replication?

Using of multiple subjects or experimental units decreases the chance that the effects we observe could be a product of mere chance.

• 1 out of 2: 1/2 = .5

• 5 out of 10: 1/252 = .00397

• 10 out of 20: 1/184756 = .00000541

Why the three R’s are important

Why randomization?

Using randomization to select the units to receive the alternative treatments ensures that the units receiving A are, on average, no different from those receiving not A.

Without randomization, the two groups could be systematically different even before the treatments are applied. Then we could not be sure that the different responses in the two groups were not caused by these prior differences.

Why the three R’s are important

Why representativeness?

Representativeness allows you to generalize from the units in your study to a broader population.

Studies with units that are not representative of the population may be criticized for lacking “external validity.”

Example 2 (continued)

Global warming and atmospheric CO2

Should we conclude that increasing CO2 levels have caused global warming?

From the standpoint of the three R’s, this will be very difficult to prove or disprove, because it is based on a sample of just one unit (our world). Nevertheless, it is an important question!

Today’s Quiz (not given)

(a) 3 points List the three R’s.

(b) 2 points “Last year, I decided to go on a diet (A). Now I weigh more than I did one year ago (B). Therefore, dieting made me fat.” Is this conclusion correct? What is the counterfactual outcome?

See you on Wednesday.