Unit 3 AP Stats

Population

All subjects of interest

Sample

A smaller subset of the population

Observational study

No treatments are administered

Two kids of observational studies

Retrospective- Looking at past and current

Prospective- Following a sample of current subjects

What does it mean for something to be representative?

It diversely represents a population, meaning that you can generalize the results.

Random selections vs. assignment

Random selection- Used in studies

Random assignments- Used in experiments

Causal associations vs. relationships

Causal association- Determined by studies

Causal relationships- Determined by experiments.

Sampling w/o repetition

Subjects are/aren’t counted more than once, everyone has an equal chance of being selected

Simple random sample

Everyone has an equal chance of being selected.

What is the calculator function for simple random samples?

Math —> Prb —> 5: randInt

Stratified random sample

Subjects are grouped homogeneously, then certain individuals are selected. 

Cluster sample

Subjects are grouped heterogeneously, and a certain number of clusters are selected.

Systematic random sample

Starting from a random point, pick every n_th person from there.

Bias

When a certain resopnse is systematically favored over another

Voluntary response bias

Anyone can respond to a survey, so responses skewed to the extremes are more likely to be present.

Undercoverage bias 

Part of the population has a reduced chance of being selected. (i.e if you survey households, homeless people are much less likely to be represented.)

Nonresponse bias

Everyone has equal opportunity to respond, but some people choose to not respond (usually due to sensitive content)

Response bias

Confusing or misleading questions cause bias, either that or self-reported responses.

Experimental units

Objects of study

(Humans are called subjects/participants)

Explanatory variable

The treatment being administered

Response variable

The symptoms being measured

Confounding variable

Something that can affect the response v., but isn’t the explanatory variable.

How do confounding variables affect experiments?

They make it so you cannot determine a causal relationship.

What are 4 aspects of a well-designed experiment?

• 2+ treatment groups

• Patients are randomly assigned to treatment groups

• Replication

• Controlling confounding variables as much as possible.

Control group

Experimental units not receiving any new treatment.

Single blind

Only one group is unaware as to what treatment is being administered.

Double blind

Neither the experimental units nor the people conducting the experiment know what kind of treatment is being administered.

Placebo

Something that is physically identical to the treatment but does not offer any actual treatment.

Blocking

Separating subjects into specific groups based on shared characteristics they have, in order to eliminate confounding. 

Matched pairs design

Subjects are put in pairs, and each unit within it gets a different treatment.

What are the three types of experiment design?

1- Completely randomized

2- Randomized blocks

3- Randomized matched pairs

Is bias involved with experiments?

No

Statistical significance

Results are significantly different enough to prove a causal relationship, the result is not just a pure coincidence.

Statistical Inference

Observations from a sample can be applied to a different group.