unit3 - Stat131A 1 Statistics 131A, Spring 2011 Unit 3:...

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Unformatted text preview: Stat131A 1 Statistics 131A, Spring 2011 Unit 3: Statistical Inference Chris Paciorek Stat131A 2 Outline of Material Survey Sampling Point estimation Overview and Criteria Simple methods Maximum Likelihood Estimation Confidence intervals Hypothesis testing Ideas and implementation Conceptual Issues Bayesian methods Stat131A 3 Sources Survey sampling: these notes plus Agresti and Franklin, Section 4.2 for the conceptual issues Point estimation: MS Sections 7.1-7.2 Confidence intervals: MS Sections 7.3-7.4 Hypothesis testing: MS Sections 8.1-8.6, 8.9 Bayesian methods: these notes plus a bit in MS Section 8.13 Stat131A 4 Survey Sampling Survey Sampling: Introduction Real-world importance Clear motivation for the conceptual model (sample from a population) In other settings the idea of sampling from a population will often be more abstract Introduce core statistical concepts in a simple setting Stat131A 5 Survey Sampling Bias in samples Suppose I want to know what proportion of Berkeley students know the Hardy-Weinberg law of genetics. I take this class as a sample of the population of Berkeley students and find out the proportion of you that know the law. Is this proportion a good estimate of the proportion amongst the Berkeley student body? In 1936 Literary Digest magazine mailed questionnaires to 10 million people asking if they preferred President Franklin Roosevelt or challenger Alf Landon in the 1936 presidential election. The mailing addresses were based on telephone directories, country club memberships, and automobile registrations. Based on the 2.3 million returned questionnaires, the magazine predicted Landon would win with 57% of the vote. In reality, FDR won in a landslide with Landon getting 36%. What went wrong? (There are multiple possibilities.) Suppose youre a field biologist and you want to assess the proportion of animals in a population that have a disease of interest. What will be the difficulties in getting a representative sample? Stat131A 6 Survey Sampling Variance in samples Suppose I actually take a random sample of Berkeley students and ask them whether they know Hardy-Weinberg. 1. If I ask 5 students and base my estimate of the proportion in the student body based on the proportion in my sample, would that be ok? 2. If I ask 500 students, and do the same, would that be ok? 3. What statistical result is relevant here? Stat131A 7 Survey Sampling Why use random samples? Why sample? Why random? Stat131A 8 Survey Sampling Populations and Sampling Frames The population is the group for which you would like to draw conclusions. Next you need a list of the subjects in the population from which to take the sample; this is called the sampling frame....
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unit3 - Stat131A 1 Statistics 131A, Spring 2011 Unit 3:...

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