AP Stats Chapter 5.2 Designing Experiments

Intro: Tire Blocking Experimental Design

A firm wishes to test the durability of four tire types that we’ll call A, B, C, and D for convenience. Here are four possible studies they might perform. In all cases, the cars are to be driven on a track under controlled conditions until its tires are deemed “worn out”. The response variable for each experimental unit (a car) is the number of miles the car drove with the tires. Each of the first three designs contains at least one serious weakness. Comment briefly on them. The fourth design is called a blocked design. State what the blocks are and explain what the advantage is of this design over design number 3.

1. Four Cadillacs of the same type are purchased new from four dealers. One gets tire A (ie: gets outfitted with four type A tires), one gets B, one gets C, and one gets D.

2. Twelve Cadillacs of the same type are purchased new from four dealers. Three get tire A, three get tire B, three get C, and three get D.

3. Twelve vehicles of different types are randomly selected from a list of many vehicle types and then are randomly allocated into four groups of three. One group gets tire A, one group gets tire B, one group gets tire C, and one group gets tire D.

4. Four Cadillacs, four Fords, and four Volkswagons are purchased. One of each type of car gets tire A, one gets tire B, one gets tire C, and one gets tire D.

Experimental units - individuals on which the experiment is done humans = subjects

Treatment - specific condition(s) applied to a subject a good experiment gives good evidence for causation

Principal for experimental designs:

I. Control – to try to eliminate confounding effects of lurking variables. a. Control group - gets a placebo (dummy treatment) eliminates placebo effect - response observed solely from being treated b. Blinding - subject doesn’t know which treatment he is getting double blinding - neither subject or experimenter know which treatment is given to whom. A way to control placebo effect. Person giving treatment doesn’t know, therefore avoid “bias attitude”. c. Blocking- separating into groups according to characteristics (natural differences: gender, age), then run the experiment on each group. NOT random!!! d. Other factors – diet, exercise, etc…

II. Randomization – reduce chance variation

Use random methods to assign subjects to the treatments (control group, treatment group 1, 2, etc..) Use unbiased methods to place them in group (RNT, hat, computer program)

III. Replication

Use enough subjects to reduce chance variation (larger groups = less variation) Repeat the experiment multiple times in different settings with different subjects

All 3 must be present in a well designed experiment!!

Example: Compare laundry detergent A vs. B. You run a lot of loads. A is used in washer 1 and B is used in washer 2. What is confounding about this experiment? EXAMPLE Testing a Breakfast Food A food company assesses the nutritional quality of a new “instant breakfast” product by feeding it to 30 newly weaned male white rats over a 28-day period. a) What is the response variable?

b) What will the treatment be for the control group?

c) What/how are you randomizing?

d) Set up an experiment using a diagram.

Homework: p 357 33 – 37 odds p 364 39, 40, 41, 43

Matched pairs design – form of block design in which just 2 treatments are compared.

1) match 2 subjects who are very similar (same age, sex, income,etc.) and assign each a different treatment; compare their response to the two different treatments

2) apply both treatments to the same subject so the subject acts as his own control example: coke vs. pepsi

example: compare old and new waterproofing treatments on boots of volunteers. EXAMPLE You want to study how girls’ bodies process calcium. At a summer camp of 60 girls, calcium can be given at either a high level or a low level.

1. Design an experiment to test it.

2. Design a match pairs experiment to test it.

EXAMPLE #3 You want to test a new diet pill. You have 100 overweight volunteers available. Design an experiment to test the pill.

EXAMPLE #4 Encouraging Energy Conservation Many utility companies have programs to encourage their customers to conserve energy. An electric company is considering placing electronic meters in households to show what the cost would be if the electricity use at that moment continued for a month. One cheaper approach is to give customers a chart and information about monitoring their electricity use. The company finds 60 single-family residences in the same city willing to participate. Will meters reduce electricity use? Would cheaper methods, such as the chart, work almost as well? The company decides to design an experiment and hires you to do it.

a) What is the response variable?

b) Is a control group needed? How many groups should there be?

c) What/how are you randomizing?

d) Set up an experiment using a diagram.

Twist: The executive of the electric company objects to including a control group. He says “It would be simpler to just compare electricity use last year (before the meter or chart was provided) with consumption in the same period this year. If households use electricity less this year, the meter or chart must be working.” Explain clearly why this design is inferior to that in the example above. Homework: p 371 45, 46, 48, 49, 50