Chapter 12: Sample Surveys

1. Chapter 12: Sample Surveys -basic terminology -principles -Types of sampling

2. Basic Terminology Population � group of people/objects whose characteristics we are attempting to determine Often we are interested in estimating one of two population parameters: 1) population mean (�) 2) population proportion (p) = percent of a population which has a characteristic

3. Samples A sample is a subset of a population We use different symbols to summarize aspects of a sample: The sample mean (x-bar) The sample proportion (p-hat) Population parameters are generally unknowable � we use sample statistics to estimate these parameters

4. A basic principle of sampling Any good sampling method involves randomization - we can�t just pick and choose who we will survey for our sample One problem with picking and choosing is that we may end up with a sample that does not accurately represent the population � our sample may be biased We will discuss randomization and other principles of good sampling in our next class

5. Sampling methods Simple random sample Stratified random sampling Cluster sampling Multistage samples Systematic Sampling A few �bad� methods: - voluntary response sample - convenience sampling - bad sampling frame

6. Simple random sample Each member of population has an equal chance of being selected Furthermore, every possible combination of members of the population has a chance of being chosen as the sample Create a numbered list of population members, then generate random numbers to determine who will be surveyed For a long list, instead of numbering consecutively, assign each individual a single random digit, then survey everyone numbered with a certain digit, say 5

7. Stratified Sampling Stratified sampling allows us to account for different subgroups of the population, for example, ensuring that both men and women are represented in the sample We sort the population into groups that are homogeneous in some way (gender, race, age group, location, income level, etc.) called strata Then we select randomly within each strata Often this is done proportionately; for example if the population contains 60% women and 40% men, in a sample of 200, choose 120 women and 80 men

8. Cluster sampling Take advantage of �natural� groupings that are heterogeneous (that is, each group should contain variation that is representative of the variation in the population) For example, rather than survey the entire senior class, perhaps I will choose one homeroom (assuming anyone shows up for homeroom) The idea is that within each senior homeroom is a heterogeneous mix of students (some boys, some girls, different academic levels, different ethnic backgrounds, different economic backgrounds) so that the variation within the homeroom mirrors the variation in the entire senior class Each cluster is sort of a micro-version of the population

9. Clusters, continued How does randomization come into play? We select one or more clusters at RANDOM from within the population Another example: to determine the reading level of a textbook, we can select a few pages at random and assess the difficulty level of those pages (here the pages are the clusters)

10. Multistage sampling Combines other methods of random sampling For example, to survey U.S. opinion, stratify towns by location (northeast, southwest, etc.) then choose a few blocks (clusters) within each town, then select an SRS from each chosen block

11. Systematic Sampling Here there is a SYSTEM to whom is selected We list population and choose a random starting point, then survey every kth person on the list after that For example, start with the 3rd person on the list and then survey every 8th person after that

12. BAAAAAAAD sampling Voluntary response � rely on members of population to mail back a survey or call a phone number (american idol) Usually only those who are passionately concerned (or have a lot of time on their hands) respond � and the population as a whole may not have the same opinions/characteristics as the passionate responders, resulting in bias

13. Bad, bad, bad sampling continued Convenience sampling � survey the members of the population that are nearby or easy to contact For example, someone surveying people walking by them in a mall or outside a grocery store, or a student who just surveys his/her friends Those chosen may differ from the overall population in some significant way; those who do not frequent the particular mall or grocery store, or are not friends with the student doing the surveying, cannot be selected

14. Bad sampling again! Bad sampling frame The sampling frame is the list of population members from whom the sample is drawn If the list is incomplete, you�ve got a bad sampling frame! Suppose I am trying to determine U.S. attitudes regarding littering and decide to dial phone numbers using a random number generator Why is this an example of a bad sampling frame? Those without phone numbers cannot be contacted (homeless, etc.)� these people may have a different attitude about littering than those who are surveyed

15. HOMEWORK Read chapter 12!