Experimental Design Notes



AP Statistics: Unit 3 Producing Data Ms. Matrone

Name___________________            Date_________________ Period____________

Experimental Design Guided Notes

Important Definitions

Observational study -

Experiment –

Experimental unit –

Factor –

Level –

Response variable –

Treatment –

Control group –

Placebo Effect –

Blinding –

Double blind –

The Four Principals of Experimental Design

1)

2)

3)

4)

Types of Experimental Designs

Completely Randomized Design -

Randomized Block Design -

Matched Pairs Design -

How to Design an Experiment:

1) Indentify the important ___________________ of the experiment.

2) Draw a ______________________for the randomized design

3) Explain how the design utilizes the _____________________________________________.

Example 1: Randomized Design

A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared.

Identification of Features:

What are the experimental units?

What is the factor (explanatory variable)?

How many levels?

What is the response variable?

How many treatments?

Diagram:

Four Principals of Design:

Quick Check! Create a completely randomly designed experiment.

1. Suppose a consumer group wants to test cake pans to see which works the best (bakes evenly). It will test aluminum, glass, and plastic pans in both gas and electric ovens.

Identification of Features:

What are the experimental units?

What is the factor (explanatory variable)?

How many levels?

What is the response variable?

How many treatments?

Diagram:

Four Principals of Design:

Example 2: Randomized Block Design

A pharmaceutical company has developed a new medicine that they believe will be more effective in treating people who suffer from migraine headaches. Researchers plan to enlist several people who suffer from migraines in a test.

Identification of Features

What are the experimental units?

What is the factor (explanatory variable)?

How many levels?

What is the response variable?

How many treatments?

What are we blocking by?

Diagram

Four Principals of Design:

Quick Check! Create a Randomized Block Design Experiment

A pharmaceutical company has developed a new medicine that they believe will be more effective in treating people who suffer from migraine headaches. Researchers plan to enlist several people who suffer from migraines in a test.

Identification of Features:

What are the experimental units?

What is the factor (explanatory variable)?

How many levels?

What is the response variable?

How many treatments?

What are we blocking by?

Diagram:

Four Principals of Design:

Independent Practice

Please identify the following for each scenario.

a) type of experimental design

b) if blocked, what blocked by

c) experimental units

d) factor(s) and levels

e) treatments

f) response variable

g) was blinding used

h) how randomization & replication is used

1. Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, he or she will take a pill that may be a standard pain reliever or a placebo. Half of each group will also drink a large glass of ice water. Participants will then report the level of pain relief they experience. (Stats, Modeling the World, 2nd edition by Bock, Velleman & De Veaux, p. 314)

2. After menopause many women take supplemental estrogen. There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two groups, as were 12 other volunteers not on estrogen. In each case, one group drank an alcoholic beverage, the other a non-alcoholic beverage. An hour later everyone’s estrogen level was checked. Only those on supplemental estrogen who drank alcohol showed a marked increase.

3. Some gardeners prefer to use non-chemical methods to control insect pests in their gardens. Researchers have designed two kinds of traps, and want to know which design will be more effective. They randomly choose 10 locations in a large garden and place one of each kind of trap at each location. After a week they count the number of bugs in each trap.

4. Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were randomly assigned to a special no-dessert diet; the others continued desserts as usual. Half of the people in each of these groups were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvements.

For the following questions: Identify whether it is an experiment or an observation study/survey. If experiment: identify experimental design, experimental units, factors & levels, response variable, and blocks (if any). If study/survey, identify sampling method and one possible source of bias.

1. In marketing children’s products, it’s extremely important to produce television commercials that hold the attention of the children who view them. A psychologist hired by a marketing research firm wants to determine whether differences in attention span exist among advertisements for different types of products. Fifteen children under 10 years of age are randomly asked to watch one 60-second commercial for one of three types of products, and their attention spans are measured in seconds.

2. Upon reconsidering the above problem, the psychologist decides that the age of the child may affect the attention span. Consequently, the psychologist randomly assigns fifteen 10-year-olds, fifteen 8-year-olds, fifteen 6-year-olds, and fifteen 4-year olds to watch one of the commercials, and their attention spans are measured.

3. An economist wants to determine if differences exist among the salaries of university professors in different departments. Data is collected from a random sample of six professors from each of the departments of business, history, and psychology.

4. The editor of the student newspaper was in the process of making some major changes in the newspaper’s layout. He was also contemplating changing the typeface of the print used. To help him make a decision, he asked six individuals to read four newspaper pages, with each page printed in a different typeface. If the reading speed differed, then the typeface that was the fastest would be used. However, if there was not enough evidence to allow the editor to conclude that such differences existed, the current typeface would be continued. (Where should randomization be implemented?)

5. For many years automobile insurance companies have charged young men higher premiums, reflecting this group’s relatively poor driving record. An executive in the insurance industry believes that different premiums should be charged according to age for all drivers, because drivers in some age groups drive considerably more than others. To examine this issue, 50 young (25- to 40-year olds), 50 middle-age (40- to 55-year-olds), and 50 older (over 55-years-old) drivers were questioned concerning the number of miles they drove in the previous 12 months.

6. In a recent report, a group of scientists claimed that Americans are consuming an excessive amount of selenium in their diets. The National Science Foundation has stated that the safe upper limit is 200 micrograms per day. In order to determine the extent of the problem in Plano, researchers divided the town into five regions based on economic levels and drew random samples of households from each region. They then interviewed an adult at the residence and measured their daily consumption of selenium.

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