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