Design of ExperimentsDesign of Experiments

Dr.... Mary Whiteside

ExperimentsExperiments

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

Observational vs. Observational vs. experimental studiesexperimental 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

RR2 2 - measures goodness of fit- measures goodness of fit

Important in observational studies whose purpose is prediction

Less important in experiments whose purpose is identification of factor effects

Examples of research issuesExamples 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?

DefinitionsDefinitions

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

TreatmentTreatment

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

FactorFactor

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

LevelsLevels

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

ResponseResponse

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

Co-variateCo-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

ReplicationReplication

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

Experimental unitsExperimental 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

Repeat testsRepeat 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

Principles of ExperimentationPrinciples 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

Designs are differentiated by Designs are differentiated by the way randomization occursthe way randomization occurs

Completely randomized Complete randomized block Factorial Incomplete randomized block Latin Square Split plot Fractional factorial

Completely randomizedCompletely randomized

Treatments are randomly assigned to experimental units

Runs are randomly sequenced

Complete randomized blockComplete randomized block

Treatments are randomly assigned within blocks

Runs are randomly sequenced within blocks

FactorialFactorial

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

Incomplete randomized blockIncomplete randomized block

Each block contains only a subset of all possible treatments

BIB - balanced incomplete block designEach pair of treatments appears together the same

number of times A particular BIB is randomly selected

Latin Square DesignLatin Square Design

A special BIB where 3 factors can be observed, each with k levels

Particular Latin Squares are randomly selected

Split plot designSplit 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

Fractional factorialFractional factorial

A particular “fraction” of the complete (factorial) set of treatments is randomly selected

Fractional factorial designs are precursors of Taguchi designs

Advantages of experimentsAdvantages of experiments

Casual inferences can be approached Extraneous variation can be removed Replication can extend generality

Disadvantages of experimentsDisadvantages 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