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Unformatted text preview: 1 Lecture 9 Introduction to Statistical Inference: The Bootstrap Lecture 9 1 Inference: The Bootstrap Lecture 9 Outline 1. Statistical Inference 2 Data as evidence 2. Data as evidence 3. Frequentist statistical reasoning 4. Bootstrap 5. Measuring precision 6. Bootstrap and confidence interval estimation estimation 7. References 2 2 1. Statistical Inference: Search for Truth Sampling/Probability Observed Value Truth for for a Population Representative Sample Statistical inference 3 1.1. Statistical Inference: Search for Truth Sampling/Probability Observed rate in a True survival rate representative in population sample Statistical inference 4 3 1.2 Statistical Inference An approach for using information (data) from the sample to make statements about the population sample to make statements about the population Which population? The one from which your sample was randomly drawn The one for which your sample is reasonably thought to be representative reasonably thought to be representative  like a random sample 5 6 4 2. Data as Evidence 2x2 Table Relapse within 400 days; from Figure 1 in Csernansky, et al. 2002 Risp Hal Total Relapse 41 67 108 No 136 121 257 Relapse Total 177 188 365 7 2.1 Observed Relative Rate of Relapse Risperidone: Relapse rate = 41/177 = 0 23 Risperidone: Relapse rate 41/177 0.23 Haloperidol: Relapse rate = 67/188 = 0.35 Relative rate = Risp rate/Hal rate = (41/177) / (67/188) = 0.65 8 5 2.2 Statistical Inference Frequentist Style Our observed rate is not the population rate! It deviates from the true population value It deviates from the true population value because we only have a sample of fixed size, not the whole population....
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 Spring '08
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