DRILLDRILLIf you needed to select 5

students from a group of 6250, how could you use the table of random digits to carry out the selection process.

Starting at line 118 what are the numbers of the five students.

Section 5.2Designing Experiments

AP StatisticsOctober 27th, 2014

TerminologyTerminology The individuals on which the experiment is

done are the experimental unitsexperimental units. When the units are human beings, they

are called subjectssubjects. A specific experimental condition applied

to the units is called the treatmenttreatment.

Units Treatment Observe Response

ExperimentsExperiments

The explanatory variables in an experiment are often called factors.

Each treatment is formed by combining a specific value (often called a level) of each of the factors.

Comparative ExperimentsComparative Experiments When first conducting an experiment you first

must state the explanatory and response variables.

Treatment Observation Observation 1 Treatment Observation 2

The Physicians’ Health StudyThe Physicians’ Health Study Does regularly taking aspirin help protect people

against heart attacks? The Physicians’ Health Study looked at the effects of two drugs: aspirin and beta carotene. The body converts beta carotene into vitamin A, which may help prevent some forms of cancer. A combination of the drugs were given to 21,996 male physicians.

The Physicians’ Health StudyThe Physicians’ Health Study Subjects? Physicians Treatments? 4 (the groups) Factors? 2 (aspirin & beta carotene)

The Placebo EffectThe Placebo Effect“Gastric freezing” is a clever treatment for ulcers in the

upper intestine. The patient swallow a deflated balloon with tubes attached, the a refrigerated liquid is pumped through the balloon for an hour. The idea is that cooling the stomach will reduce its production of acid and so relieve ulcers.

An experiment reported in the Journal of the American Medical Association showed that gastric freezing did reduce the acid production of and relieve ulcer pain.

The Placebo EffectThe Placebo EffectThe “Gastric freezing” experiment was poorly

designed. The patients’ response may have been due the placebo effect. A placebo is a dummy treatment. Many patients respond favorably to any treatment, even a placebo.

This may be due to trust in the doctor and expectations of a cure, or simply to the fact that medical conditions often improve without treatment.

Groups in an ExperimentGroups in an Experiment Sometimes a group will be used in an

experiment, where they think they are receiving a treatment but they are really receiving a placebo. This group is called the control group.

The control group may also be a group that is not receiving the treatment.

People who receive the “real” treatment are the treatment group.

Aspirin/Beta CaroteneGroup 1

UnitsCompare Response

ExperimentsExperiments

Aspirin/PlaceboGroup 2Placebo/Beta Carotene

Group 3Placebo/PlaceboGroup 4

Principles of Experimental DesignPrinciples of Experimental Design1. Control of effects of lurking variables on

the response, most simply by comparing several treatments.

2. Randomization, the use of impersonal chance to assign subjects to treatments.

3. Replication of the experiments on many subjects to reduce chance variation in the results.

Statistical SignificanceStatistical Significance An observed effect so large that it would

rarely occur by chance is called statistically significant.

Double-Blind ExperimentDouble-Blind Experiment In a double-blind experiment

neither the subject or the person in contact with them knows which treatment a subject received if any.

Experiments without placebosExperiments without placebos Matched pair design

In a matched pair design, subjects are paired by matching common important attributes.

Often the results are a pre-test and post-test with the unit being “matched” to itself.

Block DesignBlock Design A block design is a group of

experimental units or subjects that are similar in ways that are expected to affect the response to the treatments.

In a block design, the random assignment of units to treatments is carried out separately within each block.

Groups in an ExperimentGroups in an Experiment Sometimes in experiment they will use

matchingmatching to create the groups of individuals.

Matching is when you try to match the two groups up so that they have the same number of people in different categories such as age, sex, race, etc…

MatchingMatching When matching is combined with a

block design you create a matched-pairs design.

Each block would consist of two people who each have similar traits. One would get the treatment

HomeworkHomeworkPage

Section 5.3Simulations

Honors Statistics

AP Statistics, Section 5.3 23

SimulationSimulation “The imitation of chance behavior, based

on a model that accurately reflects the experiment under consideration, is called simulation.”

AP Statistics, Section 5.3 24

Simulation StepsSimulation Steps State the problem or describe the

experiment. State the assumption. Assign digits to present outcomes. Simulate many repetitions.

AP Statistics, Section 5.3 25

ExampleExample Toss a coin 10 times. What is the likelihood of a run of 3 or more

consecutive heads or tails.

AP Statistics, Section 5.3 26

AP Statistics, Section 5.3 27

ExampleExample Unemployment as defined by the Treasury

Department means that someone is out of work and is actively seeking employment.

About 27% of teenagers are unemployed. Simulate selecting a group of 20 teens. Repeat 10 times. How often are more than half unemployed?

AP Statistics, Section 5.3 28

AP Statistics, Section 5.3 29

ExampleExample A couple plans to have children until they

have a girl or until they have 4 children. What is the likelihood of having a girl.

AP Statistics, Section 5.3 30

AP Statistics, Section 5.3 31

ExampleExample Shaquille O’Neal has a free-throw percentage

of 58% (He makes approximate 58 free-throws for every 100 attempted)

Simulate selecting 10 groups of 20 shots. How often does he miss more than half his

shots?

AP Statistics, Section 5.3 32

SamplingSampling1. Identify the population being sampled.2. Recognize bias due to voluntary response

and other methods of sampling.3. Use Table B or other appropriate method to

take a SRS from the population.4. Recognize the presence of undercoverage or

nonresponse, and wording of the question.5. Use random digits to select a stratified

random sample from a population when the strata are identified.

ExperimentsExperiments1. Recognize if something is an experiment or

observational study.2. Recognize bias due to lurking variables3. Identify factors (explanatory variables,

treatments, response variables or subjects.4. Outline a design of a completely randomized

experiment.5. Randomly assign subjects to groups6. Recognize the placebo effect, recognize when

a double-blind experiment should be used.