Design of Experiments Dr.... Mary Whiteside

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

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

R 2 - measures goodness of fit l Important in observational studies whose purpose is prediction l Less important in experiments whose purpose is identification of factor effects

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

Definitions l Treatment l Factor l Levels l Response l Co-variate l Replication l Experimental Units l Repeat Tests

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

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

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

Response l The variable measured in the experiment l 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

Co-variate l A quantitative, independent variable observed in addition to the response in an experiment l 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

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

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

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

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

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

Completely randomized l Treatments are randomly assigned to experimental units l Runs are randomly sequenced

Complete randomized block l Treatments are randomly assigned within blocks l Runs are randomly sequenced within blocks

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

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

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

Split plot design l Two factors - assigned to different kinds of experimental units l 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

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

Advantages of experiments l Casual inferences can be approached l Extraneous variation can be removed l Replication can extend generality

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