AP Stat Sampling/Bias Exam

Population

A targeted group of individuals (or objects) about whom we seek to study and make inferences.

Sampling frame

the group of individuals (or objects), based on our sampling technique who have the potential to end up in our sample.

Sample

a subset of the population from which we collect data.

Representative Sample

a sample whose statistics are reliable indicators of the population parameters we wish to measure

biased sample

inconsistent, i.e., very likely to underestimate or overestimate values of the population.

Randomization

the process of reducing sampling bias by ensuring that each member of the population has an equal likelihood of being selected.

Census

the process of sampling the entire population, i.e., every member of the population becomes a member of the sample

Why is a census often impractical?

The population is usually large, dynamic (not static over time), and infeasible from a time and/or budgetary constraint

Parameter

An unknown value of the population (e.g., mean, proportion, standard deviation) that we do not observe in practice.

Statistic

a value obtained from sampling the population (e.g., mean, proportion, standard deviation) that we hope will be a representative estimator of the population parameter.

Simple Random Sample (SRS)

Every individual in the population must have an equal chance of being selected and every possible sample size we draw has an equal chance of being selected and it must follow both independence criterion (observations should be independent of one another) and "the 10% condition" (no more than 10% of the population should be sampled).

sampling variability

the natural tendency for randomly drawn samples to differ from one another

Stratified random sampling

sampling design in which the population is first divided into subpopulations based on one or more characteristics (strata) and random samples are then drawn respectively from each stratum.

When and why is Stratified random sampling used

When it is heterogenous/diverse in terms of characteristics studied. Dividing the population into strata based on characteristics can ensure that the sample is representative of the overall population characteristics which reduces variability in the data and give more precise results.

cluster sampling

a sampling technique in which a randomly selected cluster closely resembles the population of interest.

When and why is cluster sampling used

When there is no reason to assume that a particular cluster differs in characteristics from another within the subset of the population. Ergonomic advantages: practical and economical. Random sampling should always be a component.

Multistage sample

sampling technique in which multiple methods are used. The sequence and methods should be determined beforehand (ex ante: Latin) and have a basis for doing so.

Systematic sampling

a sampling technique in which every (predetermined) 𝑛𝑡h member of the sampling frame is selected.

When is systematic sampling appropriate

If we have no reason to believe that the order in which we are sampling is associated with the responses sought

Voluntary Sampling

Individuals are motivated to respond or be opinionated on a particular question of interest. The bias results from the majority of interest whose opinions will be on the extreme end.

Convenience sampling

A selection process in which the sample is comprised of individuals who are the easiest or most convenient to reach.

Why is convenience sampling biased?

Systematically omits individuals of the population who are unavailable during the sampling time frame. It is never random

Undercoverage bias

some members of the population are less likely to be chosen or cannot be chosen in a sample. This is predetermined once the sampling frame has been established and whose effects cannot be mitigated by randomization.

Non response bias

Occurs when an individual selected either cannot respond or refuses to respond. Lack of response biases the results.

Response bias

when the wording of a question (or anything in the survey) influences the type of response given. A non neutral survey.

Bias

Sampling methods that, by their nature, tend to over- or under- emphasize some characteristics of the population

pilot

trial run of a survey you eventually plan to give to a larger group.

under coverage bias

Bias that occurs in sample results because a segment of the population with a certain characteristic is not sampled.

sampling error

a statistical error that occurs when an analyst does not select a sample that represents the entire population of data