Design of Experiments

1. Design of Experiments Dr.... Mary Whiteside

2. Experiments • Clinical trials in medicine • Taguchi experiments in manufacturing • Advertising trials in market research • Comparisons of hybrid seeds in agriculture • Comparisons of training programs in management • Decision making tasks using IS • Comparisons of audit results

3. Observational vs. experimental studies • Key difference - an independent variable must be controlled, not observed • Observational studies - contributions, predictions • Methodology: Regression, Analysis of Variance • Experiments - treatment effects • Methodology: Analysis of Variance, Analysis of Covariance, GLM ANOVA

4. R2 - measures goodness of fit • Important in observational studies whose purpose is prediction • Less important in experiments whose purpose is identification of factor effects

5. Examples of research issues • Do pets help heart patients live? • Does hail suppression activity alter rainfall? • Are thin people healthier than people of average weight? • Does coffee increase risk of heart disease? • Do blood transfusions help or hurt patients? • Do smokers’ children face increased risk of lung cancer?

6. Definitions • Treatment • Factor • Levels • Response • Co-variate • Replication • Experimental Units • Repeat Tests

7. Treatment • A treatment is a particular combination of levels of the factors involved in an experiment • Examples • Transfusion when slightly anemic • Transfusion only when severely anemic • No coffee • Two cups of decaf

8. Factor • Independent variables, quantitative or qualitative, that are related to a response variable. • Examples • Indicated time for a transfusion • Cups of coffee • Type of coffee • Ad message • Ad medium

9. Levels • The intensity setting of a factor (i.e., the value assumed by a factor in an experiment) • Examples • Indicated time of transfusion • Slightly anemic, severely anemic • Amount of coffee • None, 2 cups, 4 cups • Type of coffee • Regular, decaf coffee

10. Response • The variable measured in the experiment • Examples • Level of LDL, HDL after the coffee drinking experiment • Whether a patient lives or dies • Brand recognition following an ad experiment • Number of defects per chip

11. Co-variate • A quantitative, independent variable observed in addition to the response in an experiment • Examples • Level of LDL, HDL before the coffee drinking experiment • Height of a manufacturing worker in a training program • Average yield of corn from a particular plot

12. Replication • The repeating of an entire experiment in a slightly different setting • Examples • Blood transfusions on a surgical wing • Coffee drinking among women • Ad campaigns in different countries • Manufacturing systems in different plants • Issues of homogeneous experimental units

13. Experimental units • The object upon which the response Y is measured • Examples • Coffee drinking man • Critically ill patient with anemia • An experiment can have “runs” rather than experimental units • Production run of manufacturing system • Batch of brownies

14. Repeat tests • Multiple observation of the response for a particular treatment, I.e. factor level combination • Examples • Twenty repeat tests were conducted for each coffee treatment • 418 repeat tests were conducted for the restricted transfusion treatment

15. Principles of Experimentation • Blocking - to remove extraneous variation • Completeness - to give balance and improve accuracy of error measurements • Randomization - to satisfy independence of error observations, to decrease likelihood of systematic bias, to improve validity of casual inferences

16. Designs are differentiated by the way randomization occurs • Completely randomized • Complete randomized block • Factorial • Incomplete randomized block • Latin Square • Split plot • Fractional factorial

17. Completely randomized • Treatments are randomly assigned to experimental units • Runs are randomly sequenced

18. Complete randomized block • Treatments are randomly assigned within blocks • Runs are randomly sequenced within blocks

19. Factorial • Definition-a factorial design is one that has all factor level combinations • Example • 3x4 factorial design has two factors, • one with 3 levels; one with 4 levels; and • 12 treatments • Treatments are randomly assigned to experimental units

20. Incomplete randomized block • Each block contains only a subset of all possible treatments • BIB - balanced incomplete block design Each pair of treatments appears together the same number of times • A particular BIB is randomly selected

21. Latin Square Design • A special BIB where 3 factors can be observed, each with k levels • Particular Latin Squares are randomly selected

22. Split plot design • Two factors - assigned to different kinds of experimental units • Examples • Seeds types are randomly assigned to fields, but insecticides are randomly assigned to farms • Machine B settings are changed in a random sequence for all of one manufacturing substance Manufacturing substance is also randomly sequenced

23. Fractional factorial • A particular “fraction” of the complete (factorial) set of treatments is randomly selected • Fractional factorial designs are precursors of Taguchi designs

24. Advantages of experiments • Casual inferences can be approached • Extraneous variation can be removed • Replication can extend generality

25. Disadvantages of experiments • For ethical and economic reasons, some variables cannot be manipulated • Experimental settings are sometimes only crude approximations of reality • Decision making outcomes of university students in an experiment with Executive Decision Support systems