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If we can reduce our desire, then all worries that bother us will disappear. Design of Experiments I Topic: Introduction Prof. Shenghua(Kelly) Fan California State University Representative Sample • (Simple) random sample: Each group of units of the required size from the population has the same chance to be the selected sample. Research studies Observational studies Sample surveys Randomized experiments Case control studies Case Study: Baldness and Heart Attacks “A really bad hair day: Researchers link baldness and heart attack.” “Men with typical male pattern baldness … are anywhere from 30 to 300 % more likely to suffer a heart attach than men with little or no hair loss at all.” Newsweek, March 8, 1993. Q: What type of study is it? Which Type of Study? • Ethical concerns • Resource limitations • Desired conclusion: – cause and effect – relationship I want to slim down. Should I do exercise or limit my fat intake? Problem: What are the factors affecting the taste of a soft drink beverage? • Type of sweetener • Ratio of syrup to water • Carbonation level • Temperature • Others?? Iterative Nature of Experimentation Conjecture Conjecture Design Analysis Experiment Conjecture Design Analysis Design Experiment Increasing knowledge Design = Analysis of conjecture & synthesis of experiment Analysis = Interpretation of data & synthesis of new conjecture The Phases/Objectives of Experimentation Increase knowledge about process under study. Phase Objective # of variables Design type Screening (which) •Identify key variables •Estimate effects 2-15; Numerical/ Categorical Factorial design Empirical (how) •Fit/test empirical model •Determine local optimum 2-6; Numerical Response surface design 1-5; Numerical/ Categorical Optimal design Theoretical •Estimate parameters in mechanistic model (why) •Model testing What Is an Experiment? • An inquiry in which an investigator chooses the levels (values) of input or independent variables and observes the values of the output or dependent variable(s). The Six Steps of Experimental Design • • • • • • Plan the experiment. Design the experiment. Perform the experiment. Analyze the data from the experiment. Confirm the results of the experiment. Evaluate the conclusions of the experiment. Plan the Experiment • Identify the dependent or output variable(s). • Translate output variables to measurable quantities. • Determine the factors (input or independent variables) that potentially affect the output variables that are to be studied. • Identify potential combined actions between factors. Problem (Cont.): soft drink beverage •What is the output variable? Taste of the drink; score 1 to 10 (from poor to good) •What factors and at which levels should we study? • • • • Type of sweetener Ratio of syrup to water Carbonation level Temperature A, B Low, High Design the Experiment Determine the levels of independent variables (factors) and the number of experimental units at each combination of these levels according to the experimental goal. Experimental unit: the unit we apply the factors on to get the response. Problem (Cont.): soft drink beverage •What combinations of factors should be studied? All 2x2x2x2 combinations. •How should we assign the studied combinations to experimental units? Assign equal number of units to each combination. (unit: the “null” beverage or say the plain water) More on Experimental Design • Randomizing the condition assigned to a unit – the type of treatments – the order of treatments • Adding control groups – placebo; standard treatment; both • Preventing bias: blinding – double blind; single blind • Reducing the variability/ Increasing the accuracy – blocking; adding covariates (nuisance variables) Complete Randomized Design (CRD) The treatments are randomly assigned to (experimental) units. Randomized Block Design (RBD) Within each block, conduct CRD using an equal number of units. Eg. Block factor: the age group Basic Terminology • Factors: the controlled variables; must be categorical • Treatments: conditions constructed from the factors • Replications: observations or measurements in the observational study Analysis of Variance (ANOVA) Example: Y = battery life X = battery brand Objective: the impact of X on Y study how the value of Y changes according to X study how much of the variability in Y is due to the different levels of X ANOVA: Analyze the variability in Y (output variable) to find the reasons of it (input factors). Example: Y = LIFETIME (HOURS) 3 replications per level 1 BRAND 2 3 4 5 6 7 8 1.8 4.2 8.6 7.0 4.2 4.2 7.8 9.0 5.0 5.4 4.6 5.0 7.8 4.2 7.0 7.4 1.0 4.2 4.2 9.0 6.6 5.4 9.8 5.8 2.6 4.6 5.8 7.0 6.2 4.6 8.2 7.4 5.8 The total variability in life (Y) How the variability in life is associated with brand (X):