DRILL If 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 5.2 Designing Experiments AP Statistics October 27th, 2014

Terminology The individuals on which 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 the treatment.

Experiments Units Treatment Observe Response 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 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 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 Study Subjects? Physicians Treatments? 4 (the groups)  Factors? 2 (aspirin & beta carotene)

The 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 Effect The “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 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.

Experiments Aspirin/Beta Carotene Group 1 Aspirin/Placebo Group 2 Compare Response Units Placebo/Beta Carotene Group 3 Placebo/Placebo Group 4

Principles of Experimental Design Control of effects of lurking variables on the response, most simply by comparing several treatments. Randomization, the use of impersonal chance to assign subjects to treatments. Replication of the experiments on many subjects to reduce chance variation in the results.

Statistical Significance An observed effect so large that it would rarely occur by chance is called statistically significant.

Double-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 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 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 Experiment Sometimes in experiment they will use matching 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…

Matching 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

Homework Page

Section 5.3 Simulations Honors Statistics

Simulation “The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration, is called simulation.” AP Statistics, Section 5.3

Simulation Steps State the problem or describe the experiment. State the assumption. Assign digits to present outcomes. Simulate many repetitions. AP Statistics, Section 5.3

Example 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

AP Statistics, Section 5.3

Example 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

AP Statistics, Section 5.3

Example 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

AP Statistics, Section 5.3

Example 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

AP Statistics, Section 5.3

Sampling Identify the population being sampled. Recognize bias due to voluntary response and other methods of sampling. Use Table B or other appropriate method to take a SRS from the population. Recognize the presence of undercoverage or nonresponse, and wording of the question. Use random digits to select a stratified random sample from a population when the strata are identified.

Experiments Recognize if something is an experiment or observational study. Recognize bias due to lurking variables Identify factors (explanatory variables, treatments, response variables or subjects. Outline a design of a completely randomized experiment. Randomly assign subjects to groups Recognize the placebo effect, recognize when a double-blind experiment should be used.