Design of Experiments Dr.... Mary Whiteside. Experiments l Clinical trials in medicine l Taguchi...
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Transcript of Design of Experiments Dr.... Mary Whiteside. Experiments l Clinical trials in medicine l Taguchi...
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