Math 143 C/E, Spring 2001
IPS Reading Discussion Questions
Chapter 3, Section 3



  1. How are the concepts of population and sample related?

    The population is the group of objects (perhaps people) about which a question has been asked. In order to answer the question, a subset of these objects (a sample) is selected for the study or survey. The sample comes from the population, but is not the full population.

  2. The voluntary response sample discussed in Example 3.15 (p. 256) is not an SRS (Simple Random Sample). What, in your own words, is an SRS, and how does this sample miss out on being one?

    A sample is an SRS when the manner in which it was chosen made it equally-likely for each member of the population to be included. The nature of the headline in Example 3.15 makes it appear that the intent was to make a statement about all parents (or, at least, all parents in the U. S.). If we take the population to be all parents in the U. S., it seems clear that not every parent is equally likely to have been included in the sample. Even if we restrict our view to the population consisting of Ann Landers' readers, the fact that those included in the sample are so because they volunteered means that a sizable portion of her readers - those who love their children but are not prone to trumpeting it, for example - are unlikely to be included in the sample.

  3. Neither stratified random sampling nor multistage sampling are truly examples of SRS, but, carried out correctly, they are considered (for many purposes) to be random enough to produce a representative sample.

    1. What are the similarities you notice between stratified sampling (a term associated with survey samples) and blocking (a term associated with the design of experiments)?

      Both involve the identification of groups of individuals (strata in the case of surveys, blocks in the case of experiments) who have some common trait that may lead to similar behavior among individuals of the group. Both lead to the selection of individuals across groups (strata or blocks) for inclusion in a sample.

    2. Describe a typical multistage sampling design for a survey. Is it possible to implement both multistage and stratified sampling in the same design?

      The list of Stages 1-4 on p. 259 in IPS is an adequate example of how a typical multistage design might look. While they are different things, it is certainly possible to carry out both multistage and stratified sampling in the same design. A modification to the description on p. 259 that would accomplish this: In preparation for Stage 1, classify the 3000 counties into 3 distinct strata - urban, suburban and rural counties. Then carry out Stages 1-4 on each stratum, taking the sample to be the households that arise from the three selection processes.

  4. List and describe (briefly) the types of sampling errors mentioned in the section that can result in a biased survey process.

    Deliberate bias: purposefully selecting a sample that leans toward a certain view or goal.
    Voluntary response: people are self-selected for inclusion in a sample.
    Undercoverage (bad sampling frame): list from which individuals are selected is incomplete for population.
    Nonresponse: individuals selected for the sample do not participate.
    Response bias: interviewer may somehow sway the answers of respondent, or respondent may lie. Wording of questions: they may have confusing wording, or lead the respondent towards a certain answer.