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chapter9_presentation - Introduction to Probability and...

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Introduction to Probability and Statistics II Instructor: John Snyder Office: Middlebush 35 Office hours: T/TH 8am - 9:30am Email: [email protected] 1 26 2016 John Snyder (MU) Stat —— 3500 — 1 26 2016 1 / 81

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Experimental Design & Analysis of Variance (ANOVA) 1 9.1 Elements of a Designed Experiment 2 9.2 Completely Randomized Design: Single Factor 3 9.3 Multiple Comparisons of Means 4 9.4 The Randomized Block Design (RBD) 5 9.5 Factorial Experiments John Snyder (MU) Stat —— 3500 — 1 26 2016 2 / 81
9.1 Elements of a Designed Experiment Section 1 9.1 Elements of a Designed Experiment John Snyder (MU) Stat —— 3500 — 1 26 2016 3 / 81

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9.1 Elements of a Designed Experiment Observational studies Observational studies Researchers observe experimental units in their natural setting and record the variable(s) of interest. A researcher simply observes behavior in a systematic manner without influencing or interfering with the behavior. Not reasonable to assess causation. Example: Asking people if they meditate and measuring their blood pressure to see if there is a difference between those two groups. John Snyder (MU) Stat —— 3500 — 1 26 2016 4 / 81
9.1 Elements of a Designed Experiment Designed experiment Designed experiment Researchers control the specification of the treatments and the method of assigning experimental units to each treatment. More reasonable to assess causation. Example: Selecting people to meditate/not meditate and measuring their blood pressure to see if there is a difference between those two groups. John Snyder (MU) Stat —— 3500 — 1 26 2016 5 / 81

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9.1 Elements of a Designed Experiment Advantages of designed experiments When we design a study, we want to maximize the amount of information obtained about the relationship between the treatments and the response. If we conduct a designed experiment, rather than an observational study, we can choose the treatments and factor levels to accomplish this. Additionally, the randomization that occurs in a designed experiment eliminates the bias inherent in observational studies. John Snyder (MU) Stat —— 3500 — 1 26 2016 6 / 81
9.1 Elements of a Designed Experiment Definitions Response variable (dependent variable) : Variable of interest to be measured in an experiment (e.g. SAT scores) Factors (independent variables) : the variables whose effect on the response is of interest (e.g Socio-Economic-Status) Quantitative: Numerical nature (e.g. high school GPA) Qualitative: Non-numerical nature (e.g. gender) Factor levels : the values of a factor Example: Factor Factor levels GPA Under 3.5, Over 3.5 Gender Male,Female John Snyder (MU) Stat —— 3500 — 1 26 2016 7 / 81

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9.1 Elements of a Designed Experiment More Definitions Treatments : Factor-Level combinations Gender: 2 treatments (F & M) Gender × GPA(Under 3.5, Over 3.5): 4 treatments (M-Under 3.5, M-Over 3.5, F-Under 3.5, F-Over 3.5) m factors, n 1 ,..., n m levels: n 1 × . . . n m treatments.
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