AP Statistics Unit 2 Review: Sampling and Experimental Design

Comprehensive vocabulary flashcards covering sampling methods, bias, experimental design, and statistical inference from AP Statistics Unit 2.

Population

All people, objects, or items about which information is desired.

Sample

A small portion of the population selected for study.

Convenience Sample

A sampling method selecting subjects who are easy to reach because they are nearby or in close proximity; this method can lead to bias.

Voluntary Response Sample

A sampling method in which the subjects decide whether they want to participate; this method can lead to bias.

Simple Random Sample (SRS)

A sampling method where individuals are chosen randomly, making it the best option to reduce bias. It involves labeling individuals (assigning numbers or writing names on paper) and randomizing (using a random number generator while ignoring repeats, or drawing names from a hat without replacement).

Bias

A systematic error in a study or sampling method that can lead to overestimates or underestimates.

Stratified Random Sample

A method where the population is split into groups (strata) based on shared attributes (homogeneous grouping), and a simple random sample is taken from each stratum ('sample some from all groups'). This produces low bias and low variability, reduces variability in what is measured, and guarantees all groups are represented.

Homogeneous Grouping

A grouping strategy where each group consists of individuals who share attributes or characteristics, as seen in strata.

Cluster Sample

A method where heterogeneous groups are formed and a simple random sample of entire groups is selected ('sample all from some groups'). It can produce results with high variability but low bias, and is easier because whole groups are located rather than individual people.

Heterogeneous Grouping

A grouping strategy where each group contains individuals with different characteristics, as seen in clusters.

Systematic Random Sample

A sampling method where selection begins at a random starting point and individuals are chosen using equal intervals until the desired sample size is met; it produces low variability and low bias.

Undercoverage

A potential sampling problem where certain members of the population are less likely to be chosen (e.g., calling landlines excludes cell-only users; surveying homeowners excludes renters and those living with family).

Non-response

A potential sampling problem occurring when selected individuals cannot be reached or refuse to answer (e.g., hanging up mid-conversation, or not answering calls and emails).

Response Bias

Problems in the data gathering instrument or process, such as self-reported responses where people lie or question wording that leads respondents to answer in a particular way.

Observational Study

A study in which no treatment is applied and results are gathered solely by observing or asking questions.

Experiment

A study in which one or more treatments are applied to experimental units; a well-designed experiment allows researchers to establish causation.

Experimental Units

The individuals, objects, or subjects to which treatments are applied in an experiment.

Treatments

The specific condition or action that is done (or not done) to the experimental units in an experiment.

Explanatory Variable (Factor)

The variable in an experiment that potentially changes or affects the response variable.

Response Variable

The variable that is measured at the conclusion of an experiment to assess the effect of the explanatory variable.

Confounding Variable

A variable that is related to the explanatory variable and influences the response variable, but is not part of the experiment itself.

Principles of Experimental Design: Comparison

A core experimental requirement to have two or more treatment groups in order to compare results.

Principles of Experimental Design: Random Assignment

An experimental procedure where participants do not choose their group; it helps decrease confounding variables and allows concluding that a treatment causes observed changes in the response variable.

Principles of Experimental Design: Replication

An experimental practice of using more than one participant per group or repeating the experiment entirely.

Principles of Experimental Design: Control

The practice of keeping other variables constant throughout an experiment, typically by using a control group or a placebo group.

Placebo Effect

A phenomenon that occurs when a fake or inactive treatment produces a measurable positive outcome.

Single Blind Experiment

An experiment in which the subjects do not know which group they are assigned to (treatment vs. control group), or, alternatively, the subjects know while the experimenters do not know.

Double Blind Experiment

An experiment in which neither the subjects nor the experimenters evaluating them know which group received the active treatment.

Completely Randomized Design

An experimental design in which the total number of subjects is randomized directly into an appropriate number of groups without the use of subcategories (blocks) or pairings.

Block Design

An experimental design where subjects are first separated into blocks (groups sharing similarities) and then randomly assigned treatments within each block; this lowers variability within blocks, making it easier to determine causation.

Matched Pairs Design

An experimental design where subjects are paired with a similar subject and randomly assigned treatment (one receives one treatment, the other receives the alternative), or where one subject receives both treatments in a randomized order.

Block Design vs. Stratification

A distinction in methodology: block design is used in experiments, whereas stratification is used in observational studies.

Statistically Significant

A term describing experimental results that are unlikely to occur purely by chance (specifically less than $5\%$ probability), providing convincing evidence that the treatment caused the observed difference in the response variable.

Scope of Inference

The boundaries of study conclusions: selecting a random sample allows generalizations to the population from which the sample was drawn (not outside it), while random assignment allows concluding that the treatment causes the outcome.