AP Statistics Unit 3

Population

All individuals that are capable of being chosen

Sample

A chosen subset of a population

Convenience Sample

A sample that is easy to reach (ex; surveying the next 10 customers making a purchase)

Bias

A consistent over or underestimate in a specific direction

Simple Random Sample / SRS

Choosing a group from a population so that every individual and group of individuals is equally likely to be chosen

1. Label the individuals [assign numbers]

2. Randomizing [use rng]

3. Select the individuals with the random numbers

Unbias,=ed, sometimes easy or difficult, and sometimes imprecise

Stratified Random Sample

Splitting a population into groups (strata) and choose a SRS from each strata

• Each strata consists of individuals with shared attributes (homogenous)

  • “Sample some from all groups

Unbiased, very precise, low variability when homogenous

Low, Low

A sampling method works best if it has (low/high) variability and (low/high) bias

Cluster Sample

A sampling method that splits subjects into representative, heterogenous groups

• Performs a census of randomly chosen clusters

  • “sample some from all groups”

Unbiased, very high variability when homogenous clusters

Systematic Random Sample

Choose a random starting point and take a sample using equal intervals

Census

Surveying everyone in a population

Undercoverage Bias

Some people are less likely to be chosen: happens before sampling

Nonresponse Bias

People cannot be reached or do not answer a survey; happens during sampling

Response Bias

Problems with data gathering instrument or process (lies, leading questions, uniforms)

Parameter

A number that summarizes something about a population

Statistic

A number that summarizes something about a sample

Observational Study

A study where no treatment is imposed

Prospective

An observational study that looks ahead

Retrospective

An observational study that “looks back” (uses data that already exists)

Experiment

A study that has treatment imposed ==> is able to show causation

Explanatory Variable / Factor

What is being changed in an experiment (used to predict the response)

Response Variable

What is being measured (SAT Results)

Confounding variables

Other variables affecting the outcome

Experimental Units / Subjects

What or who a treatment is imposed on

Treatment

What is done or not done to subjects / experimental units

• Levels or combination of variables lead to the explanatory variable

Well Designed Experiment

1. Comparison (2+ Treatments)

2. Random assignment (equivalent groups)

3. Replication (>1 in each treatment group)

   1. Control: keeping other variables constant

Random Assignment

This can show causation:

1. Label

2. Randomize

3. Assign

Placebo Effect

When a fake treatment (placebo) works

Blinding

When subjects (single-blind) and/or experimenters (double-blind) don’t know which treatment is which

Block Design

(For experiments)

A way to experiment using groups of similar experimental units

Blocking

1. Separate subjects into blocks

   1. Randomly assigns treatments within each

Variability

If done correctly, blocking reduces _______

Matched Pairs Design

Blocks of size 2

1. Subjects are paired by similarity

2. Randomly assign treatment

OR: each subject gets both treatments but the order is randomized

• ELIMINATES subject variability

Sampling Variability

Different samples yield different results

• Larger samples provide more accurate estimates

Statistically Significant

Results of an experiment are unlikely (<5%) to happen by chance

• If _______ → convincing evidence that the treatment caused a difference

Random Selection

___________ Allows us to generalize conclusions to the population from which we sampled

Random Assignment

_________ Allows us to conclude that a treatment causes changes in the response variable

Association

If an experiment does not use random assignment, only an __________ can be determined

Variation

How much distance is there between estimates?

Question Wording Bias

When survey questions are confusing or leading

Self-Reporting Response Bias

When individuals inaccurately report their own traits

Completely Randomized Design

Experiment: This tends to balance effects of confounding variables so that results can be attributed to treatments

Replication

Requires that multiple experimental units recieve the same treatment

Statistical Inference

Decisions from the sample can be attributed to their population

Sampling Frame

A portion of the target population: the group of people being selected from

Target Population

Entire set of individuals in the population that meet the sampling criteria