1. What is statistics? Statistics is the science of dealing with data.
Data is any type of info packaged in numerical form.
Common examples: Political polls, Health/medical studies

2. Some Basic Definitions
Population: collection of individuals or objects we want to study statistically
“What is the population to which the statistical statement applies?”
N-value: how many individuals/objects there are in the population

3. Example Study: What percentage of the M&Ms in the jar are blue?
Population: all of the M&Ms in the jar
N-value: 4392

4. Census
Census: the process of collecting data by going through every member of the population
Our example: Count all M&Ms in the jar, count all of the blue ones, find percentage.
Drawbacks:
Expensive
Too much work
Almost impossible for large populations

5. Census vs Survey
Census: the process of collecting data by going through every member of the population
Survey: process of collecting data only from some members of the population (and use that data to draw conclusions & make inferences about the entire population)
Poll: data collection done by asking questions

6. Use samples!
Sample: a subgroup of the population chosen to provide the data
Sampling: the act of selecting a sample
Finding a good sample is EXTREMELY DIFFICULT!!!!
Sampling frame: the actual subset of the population from which the sample will be drawn

7. Example Study: What percentage of our class likes cheeseburgers?
Population: all members of our class
N-value: 20
Sampling frame: all of the women in our class
A Sample: all of the women in our class who are present today

8. Sampling frames make a difference!
CNN/USA Today/ Gallup Poll, Nov 2004:
If the election for Congress were being held today, which party’s candidate would you vote for in your district?
Asked of 1866 registered voters nationwide: 49% for Dem, 47% for Rep, 4% undecided
Asked of 1573 likely voters nationwide: 50% for Rep, 46% for Dem, 3% undecided
Differences: sampling frames for each was different…..sampling frame for the second poll more representative of people who actually voted, and closely predicted actual results. However, it’s much easier to get a list of registered voters as opposed to likely voters

9. Representative Samples
When a population is highly homogeneous, a very small sample may be representative
Ex: blood samples, thoroughly mixed cake batter, etc
More heterogeneous populations -> more difficult to find representative samples

10. Are these samples representative?
Question: What is the average time it takes a UNL student to walk to class?
Samples:
All students living in dorms
All students who use city buses
All students in the Union at noon
All students currently taking math classes

11. 1936 Literary Digest Poll
US presidential election: Alfred Landon (R) vs
incumbent Franklin D Roosevelt (D)
Sampling frame included:
Every person listed in a telephone directory anywhere in the US
Every person on a magazine subscription list
Every person listed on the roster of a club or professional association
List of 10 million people created to whom mock ballots were mailed

12. 1936 Literary Digest Poll
Poll predicted Landon with 57% of vote vs Roosevelt’s 43%
Reality: 62% for Roosevelt and 38% for Landon
What went wrong?!
Think about the sample.
Representative?
Biased?
During the depression, those people with phones, magazine subscriptions, club memberships were RICH

13. Bias
Selection bias: when the choice of the sample has a built-in tendency to exclude a particular group or characteristic within the population
Literary Digest poll only had 24% response rate
Low response rate -> nonresponse bias (selection bias)
People selected themselves out of the survey. Always low response rate for mail surveys. Also, people more passionate about a topic are more likely to respond.

14. Lots of different kinds of bias
Leading-question bias:
Are you in favor of paying higher taxes to bail the federal government out of its disastrous economic policies and its mismanagement of the federal budget?
Question order bias
Afraid to answer bias:
Have you ever cheated on your income taxes?

15. Morals Bigger samples aren’t necessarily better samples!
Watch out for different types of bias!
A representative sample is key!

16. Lots of Sampling Methods
Convenience sampling: selection of individuals included in the sample is dictated by what is easiest or cheapest
Notoriously bad!
Ex: Want to know the average score on the last quiz? Sample: Look at the scores of the people sitting next to you.
Ex: Want to know how people feel about making the switch to the Big Ten? Sample: Set up a table outside of your house for people to come by and fill out questionnaire

17. Quota sampling
Quota sampling: the sample should have so many women, so many men, so many Christians, so many Muslims, so many urban-dwellers, so many rural farmers, etc
The proportions in each category in the sample should be the same as those in the population

18. Example of quota sampling
Intro to Stats has 120 students
40 freshman
30 sophomores
30 juniors
20 seniors
To fill out questionnaire, prof selects
24 freshman
18 sophomores
18 juniors
12 seniors

19. 1948 US Presidential Election
Gallup poll used detailed quota sampling
Sample size: 3250 people
Prediction vs reality:
Thomas Dewey: 49.5% / 44.5%
Harry Truman: 44.5% / 49.9%
What went wrong?
Missing criterion wrt the categories considered for quota. Interviewers we free to choose whom to interview -> selection bias

20. Simple Random Sampling
SRS: all members of the population have an equal chance at being included in the sample
How were previous examples not SRS?
Examples of methods:
Pull names from a hat
Flip a coin
Random number generator

21. Stratified Sampling
Break the sampling frame into categories (strata), then randomly choose a sample from these strata
Those chosen strata are subdivided into substrata, and a random sample taken.
Subdivide again and take a random sample, etc
End up with clusters, but usually reliable

22. Stratified Sampling Example

25. Now survey these houses!

26. More Definitions Statistic: Numerical information drawn from a sample
Parameter: unknown measure (numerical info) from the population
Hopefully, the statistic will be close to the parameter so conclusions made about the sample will be true for the whole population.

27. Error and Bias
Sampling error: the difference between the parameter (estimated) and the statistic
Sampling error attributed to:
Chance error
Sampling variability: different samples give different results
Sampling bias: bad sample chosen

28. Sample Size Population size = N Sample size = n
Sampling proportion = n/N
Modern public opinion polls: 1000 ≤ n ≤ 1500

29. Capture-Recapture Used to estimate the N-value Steps:
Choose a sample of size , tag the members, and release.
After some time, capture a new sample of size
and take an exact head count of tagged individuals. Call that number k.
The N-value is approximately
Proportion is sample approximately the proportion in the population

30. Small fish in a big pond A pond of fish! Capture = 200 fish. Tag them.
Capture = 150 fish. Notice that k = 21 of these fish have tags.
There are approximately N ≈ (200*150)/21 ≈ 1428 fish

31. CORRELATION DOES NOT IMPLY CAUSATION!!!!!!!!!!
Clinical Studies
Try to study cause and effect, whereas surveys just observe and report
CORRELATION DOES NOT IMPLY CAUSATION!!!!!!!!!!

32. Alar Scare Alar: chemical used by apple growers
1973: mice exposed to active chemicals in Alar at 8 times greater than the max tolerated dosage
A child would have to eat 200,000 apples per day to get that dosage
Alar doesn’t really cause cancer, but no longer used. Washington State apple industry lost $375 million.

33. Clinical studies
Concerned with determining whether a single variable or treatment (vaccine, drug, therapy, etc) can cause a certain effect (disease, symptom, cure, etc)
Confounding variables: all other possible contributing causes that could produce the same effect
First step: isolate the treatment under investigation from confounding variables

34. Controlled Study Subjects are divided into two different groups:
Treatment group: consists of subjects receiving the actual treatment
Control group: consists of subjects that are not receiving any treatment (for comparison only)
Randomized controlled study: subjects are assigned to the treatment group or control group randomly....hopefully groups are representative samples

35. Placebos
Placebo: fake treatment intended to look like the real treatment
Controlled placebo study: controlled study in which control group is given a placebo
Placebo effect: just the idea of getting treatment can produce positive results

36. Don’t tell them about the placebo!
Blind study: neither the members of the treatment group nor the members of the control group know to which of the two groups they belong
Double-blind study: the scientists conducting the study don’t know either

37. Homework
Read Chapter 13
Answer the questions on the Vocabulary worksheet
Exercises beginning on page 515:
1-4, 13, 17-25, 30-32, 45-48, 57-60, 70