Experimental Design: Terminology, Principles

Read Chapter 1 of Montgomery's book for more details.

• Experiment (Simple Definition): Process of collecting sample data.

• Experiment (Complex Definition): A test(s) in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reasons for changes that may be observed in the response.

• 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.

What This Course is About: Planning and conducting experiments and analyzing the resulting data so that valid and objective conclusions are obtained.

Three principles of experimental design

1. Replication.

   
   
   
   
   
   
   
   
   
   
   
   
   
   

2. Randomization.

   
   
   
   
   
   
   
   
   
   
   
   
   
   

3. Blocking.

Examples

1. I'm sure everyone has (a) spent an enjoyable evening at Plaza Bowl and (b) is dying to regularly have a bowling score in triple digits. Suppose we want to come up with a way to discover what factors are important in improving your bowling score.

   What factors might be important?

   How could we test the factors, assuming we can only bowl a limited number of games?

2. ``Gastric freezing'' is a treatment for ulcers in the upper intestine. The patient swallows a deflated balloon with tubes attached, then 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. Experiments showed this worked. The treatment was safe, easy and widely used for several years.

   Could this experiment have been designed better?

3. Two keyboards (A and B) are being compared in terms of typing efficiency. Six different reports denoted by 1-6 are given to the same typist. The test is arranged in the following sequence:

   1. A, B $\quad$ 2. A, B $\quad$ 3. A, B $\quad$ 4. A, B $\quad$ 5. A, B $\quad$ 6. A, B

   What are the factor(s) in this experiment? The response variable?

   Does this seem like a reasonable design?