warm up 2/20/2014

Warm Up 2/20/2014

Principles of Experimental Design (CRR)

1) Control the effects of lurking variables on the response, most simply by comparing two or more treatments.

2) Randomize – use impersonal chance to assign experimental units to treatments.

3) Replicate each treatment on many units to reduce chance variation in the results.

Experimental Units, Subjects, Treatment

• The individuals on whom the experiment is done are the experimental units.

• When the units are human beings, they are called subjects.

• A specific experimental condition applied to the units is called a treatment.

Factors and Levels• The explanatory variables in an experiment are often

called factors.

• Many experiments study the combined effects of several factors.

• Each treatment is formed by combining a specific value or level of each of the factors.

Do Anti-Depressants Help People Quit Smoking?• Suppose that you wanted to study the effects that anti-

depressants have on the relapse rate of individuals who are trying to quit smoking.

Smokers Anti-depressants Observe Relapse

• It would not be enough to give every individual a daily anti-depressant and then measure the rate of relapse after a period of time.

• You need a control group!

Control Group• The subjects of the experiment would need to be

divided into two groups: those who actually take anti-depressants and those who think that they are taking anti-depressants

• Those who are taking the fake anti-depressants are called the control group.

Placebo and Placebo Effect• The placebo in this case would be a pill that looks

exactly like the anti-depressant, but does not contain the active ingredient.

• Placebo Effect: People who take a placebo tend to respond better than those who take nothing, perhaps for psychological reasons.

Double Blind Experiment

• In a double-blind experiment, neither the subjects nor the people who have contact with them know which treatment a subject received.

• In the case of a medical study, neither the doctor nor the patient would know whether or not the patient was taking a placebo. This helps eliminate unconscious bias in the way the patient is treated.

Completely Randomized Comparative Experiments

When we introduce the control group to the smokers and anti-depressants experiment, we create a randomized comparative experiment with the following diagram:

RandomAssignmentof 400 Smokers

Group 1200 Smokers

Group 2200 Smokers

Treatment 1Anti-Depressant

Treatment 2Placebo

Compare relapse rateand repeat

Ex 1: Does regularly taking aspirin help protect people against heart attacks?

• This experiment studies the effects of aspirin and beta carotene on the prevention of heart attacks and certain types of cancer.

• The subjects were 21,996 male physicians.• There are two factors: aspirin and beta carotene.• Each factor has two levels: yes or no.• One-fourth of the subjects were assigned to each

treatment group.

Treatments in the Physician’s Health Study

On odd numbered days, the subjects took a white tablet that

contained aspirin or a placebo (dummy pill)

On even numbered days, they took a red

capsule containing either beta carotene

or a placebo.

Response Variables The study looked for…

• Heart attacks

• Several kinds of cancer

• Other medical outcomes

After several years, 239 of the placebo group vs. only

139 of the aspirin group had suffered heart attacks. This outcome is good evidence

that taking aspirin does reduce heart attacks. Beta carotene had no apparent

effect.

Statistically Significant• An observed effect so large that it would rarely

occur by chance is called statistically significant.

• This is one of the reasons why it is so important that we replicate experiments!

Ex 3: • A baker is trying to decide what chips to use in chocolate chip

cookies that he plans to offer for sale. A salesman has told him that more bakers are using milk chocolate chips in their cookies versus the traditional semisweet chocolate chips because of their extra creaminess. The milk chocolate chips are slightly more expensive than the traditional semi-sweet chips. After thinking about switching chips, the baker decides that what delights people most about chocolate chip cookies is the way the chocolate melts in their mouths. If the baker can be sure that the milk chocolate chips will melt faster in his customers’ mouths than the traditional semi-sweet chips, then he will use the milk chocolate chips in his cookies.

1) What is the treatment in this experiment?2) What will the response variable be?3) How will the response variable be measured?4) What will the experimental units be?5) Draw a diagram below that demonstrates an

appropriate design for this experiment. (BE SURE TO INCLUDE CRR!)

6) Should the baker switch chips? Why or why not?

Block Design • In general, men and women may react differently to

different medications or be able to lift different amounts of weight or on average do a different number of push ups.

• When comparing the number of push ups that a group of fitness students can do at the end of a training camp, it would make more sense to separate men and women into separate comparison groups.

• This type of separation is called blocking.

Block Design• A block is a group of experimental units or subjects

that are known before the experiment to be similar in some way that is expected to systematically affect the response of the treatments.

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

• Blocks are another form of control.

Ex: Comparing Cancer Therapies• The progress of a type of cancer differs in women

and men.• A clinical experiment will compare three different

treatments.• Men and women will first be separated into blocks.• Then each block will be randomly assigned to the

three different treatments.

Outline of block design for cancer therapies experiment

Matched Pairs Design• Completely randomized designs are the simplest statistical

designs that clearly demonstrate the principals of CRR.

• However, completely randomized designs are often inferior to more elaborate statistical designs.

• Using a matched pairs design, where subjects are matched in various ways, can produce more precise results.

Matched Pairs Design• The subjects are matched in pairs and only two

treatments are compared• For example, an experiment to compare two

advertisements for the same product might use pairs of subjects with the same age, sex, and income.

• It is not always easy to match subjects.• Matched pairs are an example of block design.• Sometimes, people are paired with themselves and

receive both treatments in a random order.

Ex: Cell Phones and Driving• In this experiment, the effects of driving while talking

on a cell phone are to be observed.• There are two treatments: driving in a simulator and

driving in a simulator while talking on a hands-free cell phone.

• The response variable is the time the driver takes to apply the brake when the car in front brakes suddenly.

• Since subjects differ in driving skill and reaction times, experimenters used a pairs design in which all subjects drove both with and without using the cell phone.

• They compared each individual’s reaction time with and without using the cell phone.

• The reason that subjects are separated into two groups, those who drive first without a cell phone and those who drive first with a cell phone is to reduce the possibility that talking on a cell phone would be confounded with driving a simulator for the first time.

Double Blind Experiment• In a double-blind experiment, neither the subjects

nor the people who have contact with them know which treatment a subject received.

• In the case of a medical study, neither the doctor nor the patient would know whether or not the patient was taking a placebo. This helps eliminate unconscious bias in the way the patient is treated.

• There is a great overview of all these terms on p. 305-306 in the textbook 3.2 section summary.

• Homework for tonight: Exercises 5.31, 35, 36, 37, 39, 43, 45, 50, 53a,c• Until the bell: group “quiz” on some 5.1 topics• Email me if you need a copy of the notes from

today or yesterday:– timothy.macarthur@dpsnc.net