AP Statistics

Random Outcomes

Outcomes that occur by chance; every possible outcome has a known probability of occurring.

Response Variable

The variable that measures the outcome or result of interest in a study.

Population

The entire group of individuals or items about which we want information.

Sample

A smaller subset of the population, selected to represent the whole.

Sample Survey

A study that collects data from a sample to learn about a population.

Bias

A systematic error that causes estimates to differ consistently from the true population value.

Randomization

The use of chance to assign individuals to groups or treatments, reducing bias.

Sample Size

The number of observations or individuals in a sample.

Census

A study that collects data from every member of a population.

Population Parameter

A numerical value that describes a characteristic of the entire population (e.g., μ, p).

Statistic (Sample Statistic)

A numerical value that describes a characteristic of a sample (e.g., x̄, p̂).

Representative Sample

A sample that accurately reflects the characteristics of the population.

Simple Random Sample (SRS)

Every individual and group of individuals has an equal chance of being selected.

Sampling Frame

The list or set of all individuals from which a sample is actually drawn.

Sampling Variability

Natural variation in statistics from one sample to another due to random selection.

Stratified Random Sample

The population is divided into groups (strata), and random samples are taken from each.

Cluster Sample

The population is divided into clusters, some clusters are randomly selected, and all individuals in chosen clusters are sampled.

Multistage Sample

Sampling carried out in several stages, combining different methods (e.g., choosing schools, then students).

Systematic Sample

Selecting every kth individual from a list after a random starting point.

Pilot Survey

A small, preliminary study to test survey methods or questions before the full survey.

Voluntary Response Bias

Bias that occurs when only people who choose to respond are included, often those with strong opinions.

Convenience Sample

Choosing individuals who are easiest to reach, often producing bias.

Undercoverage

When some members of the population are not included in the sample frame.

Nonresponse Bias

When selected individuals do not respond, and their responses would have differed from those who did.

Response Bias

When the wording of questions or interviewer behavior influences responses inaccurately.

Observational Study

Researchers observe individuals without influencing them or imposing treatments.

Retrospective Study

Looks backward in time at existing data on past behaviors or outcomes.

Prospective Study

Follows individuals into the future to record outcomes as they occur.

Experiment

A study where researchers deliberately apply treatments to measure their effect on a response variable.

Random Assignment (Treatment)

Using chance to assign subjects to different treatments in an experiment.

Factor

An explanatory variable that is controlled and varied by the experimenter.

Experimental Units

The individuals or objects to which treatments are applied (subjects if they're people).

Level

A specific value of a factor (e.g., 10mg, 20mg, 30mg of a drug).

Treatment

A specific combination of factor levels applied to experimental units.

Principles of Experimental Design

The key ideas: control, randomization, and replication to reduce bias and variability.

Completely Randomized Design

All experimental units are assigned to treatments completely by chance.

Statistically Significant

An observed effect large enough that it is unlikely to have occurred by random chance.

Control Group

A group that does not receive the treatment, used for comparison.

Blinding

Keeping participants (and sometimes experimenters) unaware of which treatment is given to avoid bias.

Single-blind / Double-blind

Single-blind: either subjects or experimenters don't know treatment assignment. Double-blind: both are unaware.

Placebo

A fake treatment given to control groups to test the psychological effect of treatment.

Placebo Effect

When subjects respond to a placebo because they believe they are receiving real treatment.

Blocking

Grouping experimental units by a known variable before random assignment to control its effect.

Randomized Block Design

Random assignment of treatments occurs separately within each block.

Matching

Pairing subjects that are similar in key ways to compare treatment effects directly.

Confounding (Variable)

When the effects of two variables cannot be separated, making it unclear which caused the outcome.

Lurking Variable

A variable not included in the study that may influence the relationship between explanatory and response variables.