Experimental Design

1. Experimental Design • The term experimental design refers to a plan for assigning subjects to experimental conditions and the statistical analysis associated with the plan. (R. Kirk, 1995)

2. Experiment • An experiment is characterized by: • Manipulation of the researcher of one or more independent variables • Use of control such as random assignment of subjects to experimental conditions to minimize nuisance variables • Careful observation or measurement of one or more dependant variables

3. Causality • We infer that A causes Y if: • A precedes Y (Temporal precedence) • Whenever A is present Y occurs (sufficiency of A) • A must be present for Y to occur (necessity of A)

4. Examples of Experimental Design • A consumer testing Agency decides to evaluate the wear characteristics of four major brands of tires • The agency selects four cars of a standard car model and four tires of each brand • The tires will be placed on the cars and driven 20,000 miles on a 2 mile track.

5. Examples of Experimental Design (2) • The decrease in tread thickness is the variable of interest in this study • The drivers, weather conditions, smoothness of track, and the maintenance are essentially the same • All extraneous factors that may affect the tires are nearly the same for all four brands

6. Completely Randomized Design CR-p p = treatment levels

7. Randomized Block Design RB-p • The procedure forms n block of p homogeneous experimental units • p = levels of treatments • n = levels of the nuisance variable • The blocks are formed so that the experimental units are more homogenous with respect to the nuisance variable than are those in different blocks

8. Randomized Block Design RB-p p = treatment levels

9. Latin Square Design (1) • Each letter appear only once on each row and once in each column • The name comes from an ancient puzzle that dealt with the number of different ways that Latin letters could be arranged on a square matrix • This design allows the researcher to isolate the effects of two nuisance variables. Variation associated with rows and associated with columns

10. Latin Square (2) • The efficiency of the Latin square relative to the CR and RB was 222% and 137% (Cochran) • Used in Agricultural and Industrial Research, less frequently in behavioral and educational research

11. Latin Square Design LS-p P treatments and two nuisance variables with p levels each

12. Completely Randomized Factorial Design CRF-pq • A factorial design occurs when all the possible combinations of two or more treatments occur together on the design • 1)- Two or more treatments • 2)- Each treatment is investigated with two or more levels (p levels x q levels) • Random assignment of experimental units to treatment combinations

13. Example CRF-3x3 • Suppose that we want to determine the combination of nitrogen and phosphorus that produces the maximum amount of corn per plot • We have three levels of each factor • The experimental units are small, relatively homogeneous plots • We examine the levels of these two variables and observe all possible combinations of these levels

14. Yield of a variety of Corn -CRF 3x3 • Interaction

15. Interaction

16. Yield of a variety of Corn -CRF 3x3 No Interaction

17. No Interaction