Table of Contents

Chapter 12 - Sample Surveys

Thursday, 20 October 2022
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Sample surveys occur in the real world in the form of opinion polls.

A well-constructed sample survey can provide useful information, but it is very possible to fail to set up a reasonable survey and create results that are far from the intended truth.

For example, a Literary Digest poll surveyed 10 million people that would predict Alf Landon winning the 1936 U.S. Election over Franklin D. Roosevelt. However, those 10 million surveyees came from a phone book and drivers' registrations. This would sway the sample to richer people which was not representative of the entire population.

Biases

Types of biases:

  • Selection bias

    • Faulty mechanism when choosing a sample

  • Response bias

    • The surveyor influences the surveyee (who may provide a false response)

  • Non-response bias & voluntary response bias

    • People would not respond to questions/surveys they are not interested in
    • Groups of people who do not respond would throw off the sample

Problems that may occur in sampling include:

  • Convenience sampling
  • Under coverage

Parameters vs. Statistics

Parameters come from populations, while statistics come from samples.

\begin{array}{l l l} & \textrm{Population Parameter} & \textrm{Sample Statistic} \\ \textrm{Mean} & \mu & \bar{x} \\ \textrm{Standard Deviation} & \sigma & S \\ \end{array}

Ideas About Sampling

  • Sampling frame

    • List or group of people that could represent the population
    • e.g. list of students at a high school
    • e.g. all the students at the cafeteria at 12:00

  • Sampling variability

    • What groups of people did you sample? How much of the population do they represent?

Types of Sampling

  • Simple Random Sample (SRS)

    • Every person has an equal chance of being sampled

  • Stratified Random Sample

    • Proportions of different groups (strata) being sampled

  • Cluster Sampling

    • Choosing a specific collective group (clusters) of people

  • Systematic Sampling

    • "1 in k"'
    • A specific counting rule/pattern implemented to find a sample
  • Multi-stage Sampling