AP Statistics Unit 3

Population

group being observed

Sample

Part of said group to gain information about the population

Statistic

A value that describes a sample

Parameter

A value that describes a population (-estimated from the statistic)

Observational Study

• no treatments

• studies correlation, but cannot imply causation

• lurking variables make it difficult to establish causal links

• measured in a natural setting

Sample Surveys

• research use questionnaires or interviews to collect information from a sample to learn about the entire population

• Census - A type of survey meant to collect data for ALL individuals in the population.

  • Difficulties — Collecting responses cost resources, and time consuming.

    • Best used when it sample is randomly selected.

    • Bias can be introduced if sample is not randomly selected.

3 points to a good survey

1. Speak the audience’s language

2. Keep it simple

3. Stay unbiased

Advantages of Surveys

• Various forms of collecting data:

• Efficient for collecting data from a large population in a timely manner

• Can be designed to focus only on needed response questions

• Applicable to wide range of topics.

Disadvantages of Surveys

• Dependent on respondents’ honesty and motivation when answering

• Can be flawed by bias

Experiments

• Purpose is to study whether a treatment causes a change in the response of an experimental unit.

• Human experimental units are called subjects.

• All experimental units need to believe they are experiencing the same condition.

• The best experiments use random assignment into treatments, are comparative, double—blind, placebo controlled.

Confounding Variable

Lurking Variable

Placebo

“fake” treatment that appears to be the actual treatment, but has no effect.

• Placebo Effect — Favorable response to the placebo.

Single-Blind Study

Double-Blind Study

SB — Researchers are aware which group has placebo. Subj don’t

DB — Both researchers and subjects are not aware which group has the placebo.

Simple Random Sample

• Sample needs to be representative of the population

  • SRS allows every member to have an equal chance.

    • technology or table of rand digits.

Systematic Random Sampling

• Is a form of SRS, but you pick units by increments.

Stratified Random Sampling

• Divide the population into homogeneous groups; by characteristic

  • SRS from each strata

Cluster Random Sampling

• Divide the population into heterogeneous groups; random grouping/not by characteristic

  • SRS from each cluster

Multistage Sampling

Combination of Cluster and Stratified

• Stratified comes first.

The bigger the sample…

The better the estimate

Bias

Producing inaccurate information that systematically favors one outcome over other outcomes.

Coverage Bias

Over or under representation

i.e. Only seniors responded

Non-response Bias

Can’t be contacted or don’t participate.

i.e. Don’t fill out Google form on classroom

Response Bias

Underestimate or exaggerate

Hidden Bias (Implicit Bias)

Unconscious or automatic attitudes towards something or someone

Voluntary-response bias

Members of the population volunteer to be in the sample.

• Individuals with strong pro/anti opinions are willing to participate

Convenience Sample

Easy-to-reach members of a population — Often does not question the entire population

• i.e. Dr. Williams only sample her AP Calc students to represent all math students at our school.

Leading Question

Prompts or encourages you to answer in a certain way.

Loaded Question

Controversial or unjustified assumption and normally requires more information

Double-Barreled Question

Asking more than one question but looking for one response

Choice Bias

Repeated — Intervals overlap

Limited — Only a few choices.

3 types of experimental designs

• Completely Randomized Design

• Randomized Block Design

• Matched Pairs Design

Principles of Experimental Design; how many are there?

4

1. Comparison

• Groups don’t differ greatly before experiment begins

• Factor — Explanatory variable; is manipulated

• Levels — Various groups factors can take

• Treatment — Combination of levels from all the factors an experimental unit receives.

2. Randomization

• Must be incorporated in the selection process or distribution of experimental units into treatment and control groups

• Minimizing differences allows measured differences to be correlated to treatment or by chance of RA.

3. Control

• A group that is treated the same as the treatment groups, but doesn’t receive the treatment.

• Control Group — Baseline

• Reduces variability in the response variable.

4. Replication

• Using enough experimental units so that differences in the effects of treatments can be distinguished from chance between groups

• Natural variability can still occur

Experimental Units

Individuals or objects that are assigned treatments

Completely Randomized Design

→ Identify sample

→ Randomly Assign Subjects

→ Identify the treatments

→ Compare results

Randomized Blocked Design

→ Identify the sample

→ Block the subjects/units

→ Randomly Assign Subjects

→ Identify the treatments

→ Compare results

→ Combine results

Matched Pairs Design

Subjects receive both the control and the treatment

Selection Bias

When a sample doesn’t accurately represent a population from which it was drawn.

Explanatory Variable

The variable that is being manipulated; independent variable

Response Variable

The variable that changes in response to the explanatory variable; dependent variable

Why are control groups used in experiments?

Inference

Drawing conclusions beyond the data at hand

A Confounding/Lurking Variable

A variable that is present in an experiment that is

• Tied to the explanatory variable in some way

• Has an effect on the response variable

• Difficult to seperate from the explanatory so we don’t know if it was the explanatory or confounding variable that caused the observed response.

Were individuals randomly selected — Were individuals randomly assigned?

Inference about the population

Inference about cause and effect

Laws when dealing with human subjects

Revied by the IRB

Informed consent

Confidentiality

Replacement

the practice of returning a selected item back into the pool of possible selections before making another choice