R

4.1: Sampling and Surveys

Introductory Terms

  • Population: an entire group of people about which information is sought
  • Sample: the actual part of the population studied in order to gather information
    • Information from the sample is used to draw conclusions about the entire population
    • Subset of total population
  • Census: an attempt to contact everyone in a population
    • Very difficult to obtain
    • US only attempts national censuses once every 10 years
  • It is only appropriate to generalize about a population if the sample is randomly selected or otherwise representative of that population
    • A sample is only generalizable to the population from which it was selected
  • Sample design: the method used to choose a sample from a population
  • Sampling frame: the list of individuals from which a sample is drawn
  • Biased sample/biased study: a sample or study which systematically favors certain individuals or outcomes
    • Does not represent the population
    • Consistently overestimates or underestimates the value sought

Replacement Sampling

  • Sampling with replacement: when an item from a population can be selected more than once
  • Sampling without replacement: when an item from a population cannot be selected more than once

Types of Sampling

Relatively Ineffective Methods

  • Convenience sampling: choosing individuals who are in close proximity or otherwise easy to reach
    • Often produces unrepresentative data
    • Almost guaranteed to show bias
  • Voluntary response sample: individuals choose themselves as participants by responding to a general appeal
    • Shows bias because people with strong opinions (often negative) are more likely to respond
    • Eg. call-in opinion polls

Generally Effective Methods (if used correctly)

  • Good sampling designs have the goal of creating a sample which is representative of the population
  • Random sample: an essential principle of statistical sampling
    • The use of chance to select a sample
    • Eg. dice, spinners, cards
  • Simple random sample (SRS): choosing individuals from a population in such a way that every individual in the population has an equal chance of being chosen and every possible sample has an equal chance of being chosen
  • The hat method is one type of SRS
    • Number the individuals on identical slips of paper
    • Place them in a hat
    • Mix thoroughly
    • Draw one at a time until the desired sample size has been selected
    • The numbers you draw represent the individuals that are chosen to be in the sample
  • Stratified random sample
    • More complicated than an SRS
    • Divide the population into groups of similar individuals based on something that might influence results
    • These groups are called strata (singular: stratum)
    • Select an SRS from each stratum and combine to form a full sample
    • Multiple hats; take a little from each
    • This way, you are guaranteed to have representation from each group
    • The individuals in each stratum are less varied than the population as a whole, but when you select an SRS from each stratum, you will definitely have people from each group
    • Can produce better information about the population than an SRS of the same size
  • Cluster sample
    • The population is naturally divided into groups that contain a mixture of individuals like mini populations, called clusters
    • Number each cluster, then choose an SRS from the clusters
    • Use all of the individuals in the chosen clusters for the sample
  • Multistage sample
    • Perform selection in stages, often done for national samples
  • Systematic sample
    • Order list according to some feature you want to ensure a range of responses from
    • Eg. height, GPA, income
    • Will be selecting every nth item from the ordered list
    • To figure out what n should be, take the total number in the list divided by the number you want to have in your sample
    • Starting point should be randomized
    • Will spread the sample more evenly throughout the population
  • Systematic Random Sample: a method in which sample members from a population are selected according to a random starting point and a fixed, periodic interval
    • Starting point should be randomized

Bias

  • Bias: when certain responses are systematically favored over others
  • When writing about bias, you must:
    • Identify the population and sample
    • Explain how the sampled individuals might differ from the general population
    • Explain how this leads to an overestimate or underestimate
  • Non-random sampling methods have the potential for bias because they do not use chance to select the individuals
    • Two such methods are voluntary response sampling and convenience sampling
    • Voluntary response bias: when a sample is comprised entirely of volunteers, the sample will typically not be representative of the population
    • Convenience bias: when those that are most convenient to access get selected for a sample

Types of Bias

  • In addition to the two types covered above:

  • Undercoverage bias: when some groups of the population are left out in the process of choosing a sample

  • Response bias: when the behavior of the respondent or the interviewer causes bias

    • Can be intentional or unintentional

  • Nonresponse bias: when an individual chosen for a sample can’t be reached or chooses not to respond

  • Question wording: when the complexity, style, or order that a question in influences a response

  • Self-reported responses: when individuals inaccurately report their own data