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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 7.17.2 ◮ Confidence intervals: MS Sections 7.37.4 ◮ Hypothesis testing: MS Sections 8.18.6, 8.9 ◮ Bayesian methods: these notes plus a bit in MS Section 8.13 Stat131A 4 Survey Sampling Survey Sampling: Introduction ◮ Realworld 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 HardyWeinberg 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 you’re 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 HardyWeinberg. 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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 Spring '08
 ISBER
 Statistics, Normal Distribution, Standard Deviation, Hypothesis testing, Yi, Stat131A

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