AP Stats - Chapter 4

Population

the entire group of individuals the information collected is about.

Census

a survey collecting data from each individual in a population.

Sample

a subset of individuals in a population from which data is collected.

Sample Survey

a study that collects data from a sample that is chosen to represent a specific population.

Convenience Sample

Choosing individuals from a population who are easy to reach; introduces bias to the survey.

Bias

A likelihood to under or overestimate the value wanted to study.

Voluntary Response Sample

Samples are designated by offering an optional survey to an entire population, leading to bias.

Simple Random Sample (SRS)

Samples are chosen such that every group of individuals in the population has an equal chance to be selected as a sample.

Choosing an SRS through Technology

1. Label each individual in the population with a set, lowest value.

2. Randomly select individuals through RNG on calculator.

3. Select individuals from those chosen randomly by matching them with their assigned value.

Choosing an SRS through Table D

1. Label each individual in the population with a set, lowest value.

2. Randomize by reading consecutive groups of digits at the appropriate length, ignoring duplicates and values beyond the population boundaries.

3. Select individuals from those chosen by their value.

Stratified Random Sample

Individuals within strata are sampled by SRS and combining these chosen individuals into one random sample.

Strata

Groups of individuals in a population who share characteristics thought to be associated with variables measured.

Usage of Stratified Random Sample

• Individuals are similar within a sample, but not between stratums.

• Homogeneous groups rather than heterogeneous.

• Accounts for variability in specific categories surveyed.

Cluster Sampling

Selects a sample by randomly choosing clusters and including each member of the selected clusters in a sample.

Cluster

Group of individuals located near each other with random, evenly varying opinions that mirror the whole population.

Usage of Cluster Sampling

• Individuals who are close in proximity, but not in opinion, are chosen to represent the population.

• Heterogeneous groups rather than homogeneous.

• Accounts for variability in the population by choosing representative sample.

Undercoverage

Some members of a population are less likely to be chosen or cannot be chosen.

Nonresponse

Individuals chosen cannot be contacted or refuse to respond.

Response Bias

A systematic pattern of inaccurate answers.

Retrospective

A study examining existing data.

Prospective

A study examining data going into the future.

Confounding

Two variables are associated in a way such that their effects cannot be distinguished on a response variable.

Sample Surveys v. Experiments

• Sample surveys can only establish correlation.

• Controlled testing environment v. a survey of data that has no outlined causation.

Experiment

A study deliberately imposing some treatment on individuals to measure their response.

Treatment

the explanatory variables in an experiment

Experimental Units

individuals receiving a treatment in an experiment.

Factors

Variables used in an experiment.

Levels

Severity of variables used in an experiment.

Control Group

a group used to a provide a baseline for comparing the effects of other treatments, usually via a placebo or no treatment.

Placebo Effect

Some individuals will respond favorably to any treatment without being given an active treatment.

Double-blind

Neither the subject nor recorder measuring response variables know the treatment received.

Single-blind

Only the subject or the recorder measuring response variables knows the treatment received.

Random Assignment

Explanatory groups are given treatment by random selection.

Control

The constants within an experiment.

Replication

Using enough experimental units to distinguish a difference in treatment effects.

Principles of Experimental Design

1. Comparison

2. Random Assignment

3. Control

4. Replication

Completely Randomized Design

Subjects are randomly assigned a treatment.

Block

A group of experimental units with estimated similar effects from an explanatory variable.

Randomized Block Design

subjects grouped into blocks based on a variable, then randomized within blocks

Matched Pairs Design

each subject receives both treatments (order randomized), or matched with another subject with similar traits.

Sampling Variability

Differences in random samples of a population lead to different estimates of response variables.

Statistically Significant

Observed results of a study are too unusual to be coincidental.