Experimental Design: Some Terminology and Examples

Read section 14.1 (8th ed.) in text (15.1 of 7th ed.) for background.

• Experiment: Process of collecting sample data.

• Experimental Design: Plan for collecting the data, where the independent (explanatory) variables are set in advance.

• Response Variable: Variable of interest to be measured in the experiment.

• Factors: Variables whose effect on the response is of interest; the independent or explanatory variables.

• Levels: Values of the factor.

• Treatments: The particular combinations of the levels of the factors in an experiment.

• Experimental Unit: Object on which the response and factors are measured.

• Designed Experiment: Analyst specifies the treatments and assignment of experimental units to the treatments.

• Observational Experiment: Analyst observes treatments and responses on a sample of experimental units. Difficult to determine cause and effect with such data.

In the following examples, identify the response variable, the factor(s) and treatments, and the experimental units.

ex. 1: The mean cholesterol level of four socio-economic classes is to be compared. Random samples of people from each class are selected for comparison.

ex. 2: A quality control engineer is interested in the quality of steel ingots (measured on a scale from 0 to 10) and its dependence on the temperature and pressure applied during the manufacturing process. The engineer designs an experiment in which 20 ingots are produced at each combination of 3 temperatures and 5 pressures.

Consider the following example:

ex. 3: Can aspirin help prevent heart attacks? To study this problem, a doctor took a random sample of 100 of his patients, and had 50 of them take an aspirin every second day. The other 50 patients took a placebo. After several years, the patients in the aspirin group had fewer heart attacks.

This example illustrates three principles behind experimental design:

1. Control (of outside variables). The placebo works as the control.

2. Randomization. We wouldn't want to simply place the first 50 patients that visited the doctor on a Monday morning in the aspirin group. (Why?)

3. Replication. We wouldn't want to base our results on giving aspirin to just one patient.