The Design of Experiments

1. The Design of Experiments

2. A designedexperiment is a controlled study in which one or more treatments are applied to experimental units. The experimenter then observes the effect of varying these treatments on a response variable. Control, manipulation, randomization and replication are the key ingredients of a well-designed experiment.

3. The experimental unit (or subject) is a person, object or some other well-defined item upon which a treatmentis applied.

4. The experimental unit (or subject) is a person, object or some other well-defined item upon which a treatmentis applied. The treatment is a condition applied to the experimental unit.

5. The experimental unit (or subject) is a person, object or some other well-defined item upon which a treatmentis applied. The treatment is a condition applied to the experimental unit. A response variable is a quantitative or qualitative variable that represents our variable of interest.

6. The experimental unit (or subject) is a person, object or some other well-defined item upon which a treatmentis applied. The treatment is a condition applied to the experimental unit. A response variable is a quantitative or qualitative variable that represents our variable of interest. An experiment is double-blind when neither the experimental unit nor the experimenter knows what treatment is being administered to the experimental unit.

7. The experimental unit (or subject) is a person, object or some other well-defined item upon which a treatmentis applied. The treatment is a condition applied to the experimental unit. A response variable is a quantitative or qualitative variable that represents our variable of interest. An experiment is double-blind when neither the experimental unit nor the experimenter knows what treatment is being administered to the experimental unit. A placebo is an innocuous medication such as a sugar tablet given to patients that serve in a control group.

8. Steps in Conducting an Experiment • Step 1: Identify the problem to be solved. • Should be explicit • Should provide the researcher direction • Should identify the response variable and the population to be studied.

9. Steps in Conducting an Experiment • Step 2: Determine the factors that affect the response variable. • These factors are called the predictor variables. • Once the factors (predictor variables) are identified, it must be determined which factors are to be fixed at some predetermined level (the control), which factors will be manipulated and which factors will be uncontrolled.

10. Steps in Conducting an Experiment Step 3: Determine the number of experimental units.

11. Steps in Conducting an Experiment • Step 4: Determine the level of the predictor variables • 3 LEVELS • Control their levels so they remain fixed throughout the experiment. These are variables whose affect on the response variable is not of interest. • Manipulate or set them at predetermined levels. These are the variables whose affect on the response variable interests us. These variables comprise the treatment in the experiment. • Randomize so that the effects of variables whose level cannot be controlled is minimized. The idea is that randomization “averages out” the affect of uncontrolled predictor variables.

12. Steps in Conducting an Experiment • Step 5: Collect and process the data • This is the replication. Repeat the experiment on each experimental unit. • Measure the value of the response variable. • Organize the results. • Any difference in the value of the response variable can be attributed to differences in the level of the treatment.

13. Steps in Conducting an Experiment • Step 6: Test the claim. • This is the subject of inferential statistics.

14. EXAMPLEDesigning an Experiment The octane of fuel is a measure of its resistance to detonation with a higher number indicating higher resistance. An engineer wants to know whether the level of octane in gasoline affects the gas mileage of an automobile. Assist the engineer in designing an experiment.

15. EXAMPLEDesigning an Experiment The octane of fuel is a measure of its resistance to detonation with a higher number indicating higher resistance. An engineer wants to know whether the level of octane in gasoline affects the gas mileage of an automobile. Assist the engineer in designing an experiment. Step 1: The response variable in miles per gallon. Step 2: Factors that affect miles per gallon: Engine size, outside temperature, driving style, driving conditions, characteristics of car

16. Step 3: We will use 12 cars all of the same model and year. • Step 4: We list the variables and their level. • Octane level - manipulated at 3 levels (87, 89, 92) • Engine size - fixed • Temperature - uncontrolled, but will be the same for all 12 cars. • Driving style/conditions - all 12 cars will be driven under the same conditions on a closed track - fixed. • Other characteristics of car - all 12 cars will be the same model year, however, there is probably variation from car to car. To account for this, we randomly assign the cars to the octane level.

17. Step 5: Randomly assign 4 cars to the 87 octane, 4 cars to the 89 octane, and 4 cars to the 92 octane. Give each car 3 gallons of gasoline. Drive the cars until they run out of gas. Compute the miles per gallon. Step 6: Determine whether any differences exist in miles per gallon.

18. Completely Randomized Design 87 octane 4 cars Random assignment of 12 cars Compare MPG 4 cars 89 octane 4 cars 92 octane

19. EXAMPLE Designing an Experiment Suppose we discovered that the cars were not running at the same temperature. We would say that engine temperature is confounded with octane rating because we cannot tell whether differences in miles per gallon are attributed to temperature or octane. To resolve this, we might want to control engine temperature at, say, 4 different levels - 170, 185, and 200, and 215 degrees Fahrenheit. We will randomly assign temperature to the 4 cars at each octane level. This is an example of a randomized block design.

20. Randomized Block Design 170 degrees 215 degrees 4 cars (87 octane) 185 degrees 200 degrees 215 degrees Random assignment of 12 cars 200 degrees Compare MPG 4 cars (89 octane) 185 degrees 170 degrees 200 degrees 215 degrees 4 cars (92 octane) 185 degrees 170 degrees

21. A matched pairs design is a randomized block design in which the experimental units are somehow related (i.e. the same person before and after a treatment, twins, husband/wife, etc.)

22. EXAMPLE A Matched Pairs Design A psychologist wishes to know whether the IQs of twins differs. She randomly selects 10 twins. She administers IQ tests to all 20 participants, computes the IQ score and computes the absolute difference in IQ scores for each pair of twins for a total of ten scores.