ap stats auh

Population

The entire group of individuals we want information about.

Sample

A smaller group selected from the population.

Census

Collecting data from every individual in the population.

Parameter

A numerical value that describes a population.

Statistic

A numerical value that describes a sample.

Sampling frame

A list of all individuals in the population from which a sample is selected.

Voluntary response sample

A sample in which people choose themselves to participate, often by responding to an open invitation.

Convenience sample

A sample chosen because the individuals are easy to reach.

Simple random sample (SRS)

A sample in which every group of a given size has an equal chance of being selected.

Stratified random sample

Divide the population into groups called strata based on a characteristic, then randomly select individuals from each stratum.

Cluster sample

Divide the population into groups called clusters, randomly select entire clusters, and survey everyone in the selected clusters.

Systematic random sample

Select individuals using a fixed interval after randomly choosing a starting point.

Undercoverage

When some groups in the population are left out or are less likely to be selected.

Nonresponse

When selected individuals cannot be contacted or do not respond.

Response bias

When people give inaccurate or dishonest answers.

Wording bias

When the wording of a question influences people's responses.

Sampling bias

A sample method that consistently produces a sample that does not represent the population.

Observational study

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

Experiment

A study where researchers impose treatments on individuals and measure their responses.

Experimental unit

The individual or object on which a treatment is imposed.

Subject

A human experimental unit.

Treatment

A specific condition applied to the experimental units in an experiment.

Control group

A group that does not receive the experimental treatment or receives a comparison treatment.

Explanatory variable

A variable that may help explain or predict changes in the response variable.

Response variable

The outcome being measured in a study.

Confounding variable

A variable whose effects cannot be separated from the effects of another variable.

Random assignment

Using chance to assign experimental units to treatment groups.

Randomization

Using chance to reduce the effects of variables that could influence the results.

Replication

Using enough experimental units or repeating an experiment to make results more reliable.

Control

Keeping other conditions similar between treatment groups so the treatment effect can be isolated.

Placebo

A treatment that has no active ingredient but is made to look like the real treatment.

Placebo effect

When subjects respond because they believe they are receiving a treatment, even though the treatment has no active effect.

Blinding

Keeping subjects, researchers, or both unaware of which treatment subjects receive.

Single-blind

Either the subjects or the researchers do not know which treatment is assigned.

Double-blind

Neither the subjects nor the researchers who interact with them know which treatment is assigned.

Completely randomized design

Randomly assign all experimental units directly to the treatment groups.

Block

A group of experimental units that are similar in an important way that could affect the response.

Randomized block design

Divide experimental units into blocks, then randomly assign individuals within each block to treatments.

Why use blocks?

To reduce variation caused by a variable that is related to the response variable.

Matched pairs design

A special type of randomized block design where each block contains two similar individuals, or the same individual receives both treatments.

Difference between blocking and stratifying

Blocking is used in experiments before random assignment; stratifying is used when selecting a sample.

Cluster vs. stratified sampling

In cluster sampling, randomly choose entire groups and survey everyone in them; in stratified sampling, randomly sample individuals from every group.

SRS vs. cluster sample

An SRS randomly selects individuals from the whole population; a cluster sample randomly selects groups and surveys everyone in those groups.

Why use an SRS?

To give every individual an equal chance of being selected and reduce selection bias.

Generalizability

The ability to apply results from a sample to the larger population.

Causation

A relationship where changes in one variable actually cause changes in another.

Association

A relationship between two variables where they tend to change together.

When can you generalize?

When a random sample is used, results can generally be generalized to the population from which the sample was selected.

When can you establish causation?

A well-designed randomized experiment can provide evidence of cause and effect.

Observational study and causation

An observational study can show an association but generally cannot establish causation because of possible confounding variables.

Random sampling

Helps make a sample representative of the population and allows generalization.

Random assignment

Helps create similar treatment groups and allows researchers to make cause-and-effect conclusions.

Sampling method vs. experimental design

Sampling methods determine who is studied; experimental designs determine how subjects are assigned to treatments.

Matched pairs example

Compare two treatments by having each subject receive both treatments in random order.

Blocking example

Separate students into freshmen and seniors, then randomly assign students within each group to treatments.

Cluster sample example

Randomly choose 5 classrooms and survey every student in those classrooms.

Stratified sample example

Divide students by grade level and randomly select students from each grade.

SRS example

Randomly select 50 students from the entire student roster.

Convenience sample example

Survey the first 50 students you see in the hallway.

Voluntary response example

Post an online survey and let anyone choose whether to respond.

Undercoverage example

Survey only landline phone users, leaving out people who only use cell phones.

Nonresponse example

Randomly select 100 people, but 30 never respond to the survey.

Response bias example

People underreport how much they drink because they are embarrassed.

Wording bias example

Asking "Don't you agree that school lunches are terrible?" can influence people toward a negative response.