Other Sampling Methods

1. Other Sampling Methods Section 3.1B

2. Why not SRS? • Sometimes it’s just not feasible or practical. • Sometimes there are statistical advantages to using more complex sampling methods.

3. Stratified Random Sample • Divide the population into groups of individuals that are similar in some way that is important to the response. • Choose a separate SRS in each stratum • Combine these to form the full sample

4. Example To survey radio station about the most requested songs we randomly choose 100 radio stations from each geographic location.

5. Cluster Sample • Divide the population into groups or clusters. • Randomly choose some of these clusters. • All individuals in the chosen clusters are the sample

6. Example of Cluster Survey AP students to see if they had enough time to take the test. We randomly pick some of the schools that took the test & every student at the selected schools are surveyed.

7. Systematic Sampling This is where you survey every kth person. You randomize it by randomly choosing where to start.

8. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. • Tell what type of sampling was used and what biases (if any) might result. • Don’t forget convenience and voluntary.

9. Put a big ad in the newspaper asking people to log their opinions on the PTA web site.

10. Randomly select one of the elementary schools and contact every parent by phone.

11. Send a survey hoe with every student, and ask parents to fill it out and return it the next day.

12. Randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week.

13. Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they favor or oppose the plan.

14. Hold a PTA meeting at each of the 20 elementary schools and tally the opinions expressed by those who attend the meetings.

15. Randomly select one class at each elementary school and contact each of those parents.

16. Go through the district’s enrollment records, selecting every 40th parent. PTA volunteers will go to those homes to interview the people chosen.

17. Activity: Sampling Sunflowers • Use Table D or technology to take an SRS of 10 grid squares using the rows as strata. Then, repeat using the columns as strata. Sampling and Surveys

18. Example: Sampling at a School Assembly • Describe how you would use the following sampling methods to select 80 students to complete a survey. • (a) Simple Random Sample • (b) Stratified Random Sample • (c) Cluster Sample Sampling and Surveys

20. Inference • It is the process of drawing conclusions about a population on the basis of sample data. • Inferences from convenience samples or voluntary samples would be misleading because the methods are biased.

21. Activity • One at a time, each student will take a SRS of 20 chips and record the proportion of chips obtained that are red. • Dotplot of sample proportions:

22. Trusting Random Samples • Laws of probability all us to say how likely it is that sample results are close to the true population. • Laws of probability allow trustworthy inference about the population with a margin of error.

23. Margin of Error • Sets bounds on the size of the likely error. • Larger random samples give better information about the population than smaller samples.

24. Homework • Page 227 (17-25) odd • Page 230 (37-42)