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)

Experiment  An experiment is characterized by: 1)Manipulation of the researcher of one or more independent variables 2)Use of control such as random assignment of subjects to experimental conditions to minimize nuisance variables 3)Careful observation or measurement of one or more dependant variables

Causality  We infer that A causes Y if: 1)A precedes Y (Temporal precedence) 2)Whenever A is present Y occurs (sufficiency of A) 3)A must be present for Y to occur (necessity of A)

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.

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

Completely Randomized Design CR-p p = treatment levels

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

Randomized Block Design RB-p p = treatment levels

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

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

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

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

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

Yield of a variety of Corn -CRF 3x3  Interaction

Interaction

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