AP Statistics Unit 3 Notes
Sampling Methods
Simple Random Sample (SRS):
Randomly selected subset of the population.
All members have an equal chance of selection.
Process:
Define the population and label individuals (assign numbers or use names).
Randomize (random number generator, names in a hat, etc.).
Select members for the sample.
Stratified Random Sampling
Split the population into groups (strata) based on shared traits (homogeneous groups).
Example: Dividing PrepWorks viewers into subscribers and non-subscribers.
Randomly select samples from each group.
Ensures everyone in the group has an equal chance of selection.
Example: Divide a school by grade level and randomly pick students from each grade.
Cluster Sampling
Divide the population into groups (clusters) and randomly select ENTIRE clusters.
Important: Select entire clusters to sample.
Example: Splitting a city into neighborhoods and surveying everyone in a few randomly chosen neighborhoods.
Key Difference:
Stratified: Homogeneous groups (e.g., all red or all blue).
Cluster: Heterogeneous groups (mixed representation).
Diagrammatic Depiction
Stratified: Split into red and blue, then SRS within each.
Cluster: Clusters contain both red and blue; entire clusters are selected.
Systematic Random Sampling
Select individuals at regular intervals, starting at a random point.
Example: Surveying every fifth person entering a school.
Bad Sampling Methods
Convenience Sample:
Choose people who are easy to reach.
Example: Surveying people at a nearby mall.
Voluntary Response Sampling:
Allow people to choose to participate.
People who feel strongly are more likely to respond, introducing bias.
Example: Online polls where respondents self-select.
Shortcomings in Sampling
Undercoverage:
Some groups are left out or underrepresented.
Example: Surveying only people with internet access.
Non-response:
Selected individuals don't or can't respond.
Example: People refusing to participate in a phone survey.
Response Bias:
People give false or misleading answers.
Example: A friend reviewing your YouTube channel.
Wording in the Question:
Poorly phrased or biased questions influence answers.
Example: "Do you want to subscribe to Prep's Education to receive $1 million?"
Observational Studies and Experiments
Observational Study:
Observe and collect data without influencing subjects.
Example: Watching people use seatbelts in their cars.
Experiment:
Manipulate variables or apply treatments to subjects.
Observe and measure the effects.
Principles of Experimental Design
Comparison: Compare two or more groups to see the difference in the treatment.
Random assignment: Randomly assign subjects to groups to reduce bias. You can also be randomly assigning treatments.
Control: Keep all variables constant.
Replication: Ensure a sufficient number of subjects.
Key Vocabulary
Factor:
Explanatory or independent variable (when there are multiple).
Level:
Specific value or category of the factor.
Example: Sunlight (factor), low/high sunlight (level).
Confounding:
Another variable affects the results, making it hard to determine the true cause.
Placebo:
A fake treatment where participants may react favorably.
Single Blind:
Subjects don't know their group, but researchers do.
Double Blind:
Neither subjects nor researchers know group assignments.
Randomized Block Design
Subjects are divided into blocks based on specific characteristics.
Each block is randomly assigned a treatment.
A block is a group of experimental units with the same characteristic.
Example: PrepWorks viewers split into subscribers and non-subscribers.
Treatments are then randomly assigned (e.g., using a random number generator).
Matched Pairs Design
Subjects are paired based on specific characteristics.
Each pair is randomly assigned a treatment.
One subject in each pair can be a control.
Example: Pairing a male and female to eliminate gender bias; assigning treatments or control status randomly within each pair.