AP Stats

Simple Random Sample (SRS)

A sampling method where every individual and every possible group has an equal chance of being selected.

Stratified Random Sample

Divide the population into homogeneous groups (strata), then randomly sample from each group.

Cluster Sample

Divide the population into heterogeneous groups (clusters), randomly select some clusters, and sample everyone in them.

Systematic Sample

Choose a random starting point, then select every nth individual from a list.

Convenience Sample

Select individuals who are easiest to reach; often leads to bias.

Voluntary Response Sample

Individuals choose to participate by responding to a general invitation; usually biased.

Random Condition

Data must come from a random process (random sample or random assignment) to avoid bias.

10% Condition

The sample must be ≤10% of the population when sampling without replacement to maintain independence.

Large Counts Condition

For proportions: both np ≥ 10 and n(1 - p) ≥ 10 to ensure approximate normality.

Normal/Large Sample Condition

For means: if the population is normal or n ≥ 30, then the sampling distribution of the sample mean is approximately normal.

Convenience Sample Bias

Results are likely unrepresentative because the sample only includes easy-to-reach individuals.

Voluntary Response Bias

Overrepresents individuals with strong opinions, often leading to skewed or extreme results.

Undercoverage Bias

Some groups in the population are left out of the sampling frame entirely.

Nonresponse Bias

Chosen individuals do not respond, and those who do may differ in important ways from those who don’t.

Response Bias

Survey responses are influenced by wording, interviewer, or desire to give a socially acceptable answer.

Wording Bias

Confusing or leading questions influence responses and lead to inaccurate results.

Sampling Bias

A general term for when a sample is collected in a way that makes it unrepresentative of the population.

Effect of Bias on Results

Leads to inaccurate or misleading conclusions that do not reflect the true population.

How to Reduce Bias

Use random selection, neutral wording, and high response rates to improve sample quality.

Observational Study

A study where researchers observe and measure variables without assigning treatments.

Experiment

A study where researchers apply treatments to experimental units to observe their effects.

Purpose of Observational Study

To identify associations or correlations, but cannot prove causation.

Purpose of Experiment

To determine causation by controlling variables and randomly assigning treatments.

Confounding Variable

A variable that affects both the explanatory and response variables, making it hard to tell which causes the effect.

Control Group

A group that does not receive the treatment; used for comparison in an experiment.

Placebo

A fake treatment used to prevent subjects from knowing whether they’re receiving the actual treatment.

Blinding

Subjects (and sometimes experimenters) do not know which treatment was received to reduce bias.

Double-Blind

Neither subjects nor those measuring results know who received which treatment.

Random Assignment

Assigning treatments to experimental units by chance to reduce bias and create comparable groups.

Replication

Applying each treatment to enough subjects to reduce chance variation.

Control (in experiments)

Keeping all variables except the explanatory variable the same to isolate the treatment effect.

Experimental Unit

The individual or object to which a treatment is applied (often called a “subject” if human).

Statistical Significance

Results are unlikely to occur by random chance alone; suggests a real treatment effect.

Matched Pairs Design

A type of experiment where subjects are paired based on similarity, then randomly assigned different treatments OR the same subject receives both treatments in random order.

Block Design

Experimental units are grouped into blocks based on a variable that affects the response, then treatments are randomly assigned within each block.

Purpose of Blocking

To reduce variability by accounting for differences among known groups before comparing treatments.

Difference Between Blocking and Stratifying

Blocking is used in experiments to control for variation; stratifying is used in sampling to ensure representation.

Interpreting a Confidence Interval

We are [C]% confident that the true [parameter in context] is between [lower bound] and [upper bound].

Interpreting the Confidence Level

If we took many samples, about [C]% of the resulting confidence intervals would capture the true [parameter in context].

Interpreting the P-value

Assuming the null hypothesis is true, there is a [p-value]% chance of getting a result as extreme or more extreme than what we observed by random chance alone.