AP Statistics: Sampling and Experimental Design

Comprehensive vocabulary flashcards covering sampling methods, bias, experimental design, and statistical inference concepts.

Population

In a statistical study, the entire group of individuals we want information about.

Census

Collects data from every individual in the population.

Sample

Subset (smaller group) chosen from the population to collect data from.

Sample Survey

A study that collects data from a sample that is chosen to represent a specific population.

Convenience Sampling

A sampling method where members of a population are not chosen at random, but are chosen because they are easy to access.

Voluntary Response Sampling

Allows people to choose to be in the sample by responding to a general invitation (such as internet polls, Yelp reviews, or call-in/write-in responses).

Bias

When design flaws in a study lead to likely overestimates or underestimates of the value we want to know. This design flaw would continue to cause problems even if another sample was taken.

Random Sampling

Using a chance process to determine which members of a population are included in the sample.

Simple Random Sample

A type of random sampling where every sample of size $n$ has an equal chance to be selected.

Strata

Groups of individuals in a population who share characteristics thought to be associated with the variables being measured in a study.

Stratified Sampling

Selects a sample by choosing a Simple Random Sample from each strata and combining the samples into one overall sample.

Cluster

A group of individuals in the population that are located near each other. Ideally, each cluster would be roughly representative of the population.

Cluster Sampling

Selects a sample by randomly choosing clusters and including each member of the selected clusters in the sample.

Undercoverage

When some members of the population are less likely to be chosen or cannot be chosen in a sample.

Nonresponse

When an individual chosen for the sample cannot be contacted or refuses to participate.

Response Bias

When there is a systematic pattern of inaccurate answers to a survey question.

Observational Study

Observes individuals and measures variables of interest but does not attempt to influence the responses.

Response Variable

Measures an outcome of a study.

Explanatory Variable

May help explain or predict changes in a response variable.

Confounding

When two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.

Experiment

Deliberately imposes some treatment on individuals to measure their responses.

Treatment

A specific condition applied to the individuals in an experiment (could be an active treatment or inactive treatment).

Experimental Units

The object to which a treatment is randomly assigned; these are the participants in an experiment.

Subjects

Experimental units when they are human beings.

Factor

A variable that is manipulated and may cause a change in the response variable in an experiment.

Level

The different values of a factor.

Fundamental Counting Principle

Describes the number of different combinations of factors and levels to describe the total number of outcomes by multiplying the number of factors by the number of levels in each factor.

Control Group

Used to provide a baseline for comparing the effects of other treatments.

Control

When other variables are kept constant for all experimental units (regardless of treatment group) to minimize the effects of confounding.

Placebo

A treatment that has no active ingredient, but is otherwise like other treatments; used as an inactive treatment in a control group.

Placebo Effect

When some subjects in an experiment respond favorably to any treatment, even an inactive treatment.

Double-Blind

Neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.

Single-Blind

Either the subjects do not know which treatment they are receiving, or the people who interact with them and measure the response variable do not know which subjects are receiving which treatment.

Random Assignment

Experimental units are assigned to treatments using a chance process.

Completely Randomized Design

An experimental design in which the sample is divided into $t$ treatment groups by creating a simple random sample of size $\frac{n}{t}$ for each treatment until all members are assigned.

Randomized Block Design

An experimental design that breaks the sample into groups based on some characteristic thought to affect the response, then breaks each block into $t$ number of groups and assigns each to a treatment.

Block

A group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.

Matched Pairs Design

A common experimental design for comparing two treatments that uses blocks of size 2, where either two very similar experimental units are paired and assigned treatments randomly, or each experimental unit receives both treatments in a random order.

Replication

Using enough experimental units to distinguish a difference in the effects of the treatments from chance variation due to the random assignment.

Sampling Variability

Different random samples of the same size from the same population produce different estimates due to inherent differences between people or items.

Statistical Significance

When the observed results of a study are too unusual to be explained by chance alone.