1. Warm Up
Imagine you want to conduct a survey of the students at Leland High School to find the most beloved and despised math teacher on campus.
Among your table, discuss and devise a plan to conduct your survey (Who, When, Where, How). Assume you will only be able to interview a small number (roughly 60) of students.
How will you choose a group of students that is representative of all students at Leland?

2. Chapter 4 – Designing Studies
Observational study: We observe individuals and measure variables of interest but do not attempt to influence responses.
Experiment: We deliberately impose some treatment on individuals in order to observe their responses.

3. Population vs. Sample
Population: the entire group of individuals that we want to learn about
Sample: a portion of the population that we actually gather data from
Sampling vs. Census: Sampling studies a portion in order to gain information about the whole; census gathers data on every individual in the population

4. Poor Methods for Choosing A Sample
Voluntary response: People choose themselves by responding to a request
Convenience sampling: Choosing individuals who are easiest to contact or measure
Bias: The sampling method is biased if it systematically favors certain outcomes

5. Issues When Choosing A Sample
Undercoverage: occurs when some groups in the population are left out in the process of choosing the sample (Many samples suffer from some degree of this)
Nonresponse: occurs when an individual chosen for the sample can’t be contacted or does not cooperate.

6. Good Methods for Choosing A Sample:
Simple Random Sample
The simplest way to use chance to select a sample is to place names in a hat (the population) and draw out a handful (the sample).
Definition of Simple Random Sample (SRS):
1) every individual has an equal chance of being selected.
2) every sample has an equal chance of being selected.

7. Random Digits
Table D: A long string of digits, 0-9. Each entry in the table is equally likely to be any of the 10 digits.
Choosing an SRS with Table D:
1. Assign a number to every individual in the population.
2. Choose a starting point in Table D to begin selecting random numbers.
3. Indicate the number of individuals required, toss out repeated numbers and numbers out of your range.
4. Use the random numbers to identify subjects to be selected from your population. This is your sample!

8. Practice with Table D
Imagine we want to select 6 of the 35 students in class for a sample. 1) Assign each student a number from 00 to 34. 2) Choose a starting point on Table D (for today choose Line 121). 3) Read each 2 digit number starting at Line 121: If it is 00 to 34 and has not been selected before this student is a match. If it is 35 to 99 or has been selected before move on to the next number. 4) Which 6 students are selected?

9. Other Good Methods for Choosing A Sample:
Stratified Random Sample
Divide population into several groups (aka strata). The different strata each contain a certain “type” of individual from within the population.
Choose a separate SRS from each strata, then combine these SRS’s to form the full sample.
Used when the responses are sensitive to a key characteristic of the population (e.g. gender).

10. Other Good Methods for Choosing A Sample:
Systematic Random Sample
Number every individual in the population from 1 to N. Determine the desired sample size (n) and calculate k = N/n
Randomly choose one individual from the first k individuals. Then choose the kth following individual until the sample is complete.
Example: We want a sample of size 10 from a population of size Randomly select one individual from the first 20 (say number 7). Then select individuals 27, 47, 67, , 187 to complete the sample.

11. Other Good Methods for Choosing A Sample:
Cluster Sample
Divide population into several groups (aka clusters). Each cluster is considered to be similar to the other clusters.
Several of these clusters are randomly selected. Then all the individuals in the chosen clusters are selected to be in the sample.
Used for ease of collecting data. It is often easier to collect data from a few clusters.

12. Other Good Methods for Choosing A Sample:
Multi-Stage Samples
Combine the three sampling methods we discussed. Each stage may use an SRS, stratified sample or a cluster sample.
These designs can be quite complex.

13. Summary of Sampling Methods
Simple Random Simple (SRS) – Conceptually the easiest method but often difficult to implement in practice.
Stratified Random Sample – The strata are DIFFERFENT from each other (wealthy vs. poor, men vs. women, etc.). Take a SRS from each strata.
Cluster Sample – One cluster is arguably THE SAME as another. Randomly select a few clusters and sample each individual in the cluster.

14. Activity – Sampling at Leland
Imagine you want to conduct a survey of the students at Leland High School to find the most beloved and despised math teacher on campus.
Among your table, discuss and devise a plan to conduct your survey. Assume you will only be able to interview a small number (roughly 60) of students.
What sampling method will you use (SRS, systematic, stratified, cluster)?
How will you avoid under coverage and non-response?
How will you avoid bias?
Be prepared to share your plan with the class and to critique the plans of others.