AP Statistics Section 5.2 A Designing Experiments

AP Statistics Section 5.2 A Designing Experiments

Recall the primary difference between an observational study and an experiment. In an experiment, we deliberately do something to the individuals to observe their responses.

The individuals on which an experiment is conducted are called 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 Any specific treatment may have several different components to it. These different components are called _______ factors and will be the explanatory variable(s) in our study. Many experiments study the joint effects of several factors. In such an experiment, each treatment is formed by combining different amounts of each of the factors. Each specific value of a factor is called a _____. level

Example: What are the effects of repeated exposure to an advertising message? The answer may depend both on the length of the ad and how often it is repeated. An experiment investigated this question using undergraduate students. All subjects viewed a 40-minute television program that included ads for a digital camera. Some subjects saw a 30-second commercial, others, a 90-second version. The same commercial was shown 1, 3 or 5 times during the program.

How many different factors are present in the experiment and what are they?

2 factors: length of commercial and the number of repetitions What are the different levels of each of the factor?

Length: 30 secs. or 90 secs. Repetitions: 1, 3 or 5

By combining the information above describe the various treatments in this experiment. How many treatments were present in the experiment?

30 sec .- 1 rep. 30 sec. - 3 rep. 30 sec. - 5 rep. 90 sec. - 1 rep. 90 sec. - 3 rep. 90 sec. - 5 rep.

After viewing the 40-minute program, all of the subjects answered questions about their recall of the ad, their attitude toward the camera and their intention to purchase it. These are the ________ response variables.

This example shows how experiments allow us to study the combined effects of several factors. The inter-action of several factors can produce effects that could not be predicted from looking at the effects of each factor alone.

Some experiments have a simple design with only a single treatment which is applied to all of the experimental units. Such an experiment could be outlined in the following way.

treatment  response

Experiments that are conducted in the controlled environment of the laboratory are protected from lurking variables. When experiments are conducted in the field or with living subjects, simple designs can yield invalid data. That is, we cannot tell whether the response was due to the treatment or to lurking variables. This can be particularly true in medical experiments.

A placebo is a dummy treatment. The response to the dummy treatment is called the placebo effect. We can defeat confounding by comparing two groups of patients, one which receives the treatment and the other which receives the placebo.

The group of subjects who receives the treatment is called the treatment group while the group of ______________ subjects who receives the placebo is called a ____________ control group because it enables us to control the effects of outside variables on the outcome.

There are 3 basic principles to good experimental design:

Control is the first basic principle of statistical design of experiments. Don’t confuse control and control group. Control refers to the overall effort to minimize the variability in the way the experimental units are obtained and treated. Comparison of several treatments in the same environment is the simplest form of control.

Even with control, there will still be natural variability among experimental units. If each treatment is assigned to only one unit, you won’t know whether any systematic differences in responses were due to the treatments or to the natural variability in the units.

We would like to see units within a treatment group responding similarly to one another but differently from units in other treatment groups. Then we can be sure that the treatment groups really are responding differently from each other.

replication: the use of enough experimental units to reduce chance variation. The purpose of replication is not to eliminate chance variation but to reduce its role and increase the sensitivity of the experiment to differences between treatments.

randomization: the rule used to assign the experimental units to the treatment groups must involve randomization.

Comparison of the effects of several treatments is valid only when all treatments are applied to similar groups of experimental units. Statisticians rely on chance to make an assignment that does not depend on any characteristic of the experimental units and that does not rely on the judgment of the experimenter in any way. Randomization allows us to assert that treatment groups are essentially similar, that there is no systematic difference between them before treatments are administered.

Example: Design an experiment to measure whether listening to classical music while reading an unfamiliar piece of literature aids retention. Assume there are 40 students in the experiment. compare retention

Label 01-40. Skip > 40 and repeats. First 20 go in group 1 and next 20 in group 2

Example: Set up treatments to determine if regularly taking aspirin and/or beta-carotene help protect people against heart attacks and/or some forms of cancer. Assume there are 200 subjects in the experiment.