1. Sample Design Section 4.1

2. Terminology
Observational Study – observes individuals and measures variables of interest but does not impose treatment on the individuals.
Experiment – deliberately imposes treatment on individuals and measures the responses

3. Observational vs. Experiment
Observational studies often have confounding variables.
Well-designed experiments, on the other hand, try to reduce confounding variables.

4. More terminology
Population – the entire group of individuals that we want information about
Sample – a part of the population that we actually examine in order to gather information
Census – attempts to contact every individual in the entire population

5. Sample Design
Sample design is the method used to select the sample from the population.
Some poor examples of sample design are as follows:

6. Voluntary Response Sample
What it is: people who choose themselves by responding to a general appeal.
Why it’s bad: people with strong opinions, especially negative opinions, are more likely to respond. Therefore, the sample is not likely to be representative of the whole population.

7. Convenience Sampling
What it is: a sample chosen because the individuals are the easiest to reach
Why it’s bad: It’s not likely to be representative of the entire population.
Example: Mall surveys… People at the mall tend to be wealthier. Also, those people who are attracted by mall surveys tend to be teens or the elderly.

8. Common Thread
Sample designs are bad when they are not representative of the whole population.
Sample designs are called BIASED if they systematically favor certain outcomes.
Some Other Problems:
Undercoverage: Who did we leave out?
Non-response: Can’t be contacted; refuses to participate.

9. Good Sample Designs
Probability Sample (any sample chosen by chance). We must know what samples are possible and what probability each sample has of being chosen.
Choosing a sample by chance allows neither favoritism by the sampler nor self-selection by respondents.

10. Examples of Probability Samples
SRS (Simple Random Sample)
The simplest way to use chance to select a sample
Analogous to putting names in a hat (the population) and drawing out a handful (the sample).
Each individual has an equal chance of being chosen and each sample is equally likely.

11. How to Choose an SRS Label Decide if you will throw out repeats.
Assign a number to each individual in the population. They must all have the same number of digits.
Decide if you will throw out repeats.
Random Selection:
Table
Use Table B to select numbers at random.
OR Calculator
Use calculator to find random digits

12. Random Digits from Table B
Each digit 0-9 is equally as likely.
If you need to have 1-10 individuals, look at numbers 0-9 (one digit). Have individuals use numbers (two digits). Have individuals, numbers (three digits) and so forth.
Choose a row in your table to start with (if you use this method on the AP exam you should state which row you start with).
Follow the row and choose individuals.

13. Let’s perform our own SRS
We will choose 5 students from the class at random. First, lets use Table D. How will we label?

14. Random Digits in Calculator
Go to Math
PRB
RandInt(1st #, last #, how many numbers)

15. Let’s perform our own SRS
We will choose 5 students from the class at random. Now let’s try using our calculator.

16. Another Probability Sample
Stratified Random Sample
Divide the population into groups of similar individuals, called strata. Then choose a separate SRS from each stratum and combine the SRSs to form a full sample.
Example: Choose an SRS from each class – freshmen, sophomores, juniors, and seniors.

17. And Another Cluster Random Sample
When you have items (or people) grouped into clusters and you choose a random sample of the clusters and examine all in the cluster.
Ex. You choose an SRS of 2nd period classes (clusters) at NCHS and sample everyone in those classes

18. Final Probability Sample
Multi-stage Sample
Chooses the sample in stages.
Example: Take a random sample of the counties in NC. Then, divide the counties into sectors. Take a random sample of the sectors. Then divide each sector into blocks. Take a random sample of blocks. On each block, take a random sample of households.

19. CAUTIONS: Response Bias:
People Lie! Especially with embarrassing or incriminating topics.
Wording of questions can be misleading:
Choose one:
Yes, I would like my taxes to stay the same and not support the schools.
No, I approve of passing the bond to fund new schools.
Larger random samples give more accurate results than smaller samples.

20. Homework
Chapter 4
# 2, 3, 8, 9, 10, 12, 17, 30