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Unformatted text preview: Public Health 6450 Fall 2011 Andrew Mugglin and Lynn Eberly Division of Biostatistics School of Public Health University of Minnesota ph6450@biostat.umn.edu Part 08 Review Revisiting Important Concepts When Is Unknown Where are we going? Previously: Using the Central Limit Theorem (Chapter 5.2) Interval estimates for when is known (Chapter 6.1) Current topics: Revisiting some important concepts Interval estimates for when is unknown (Chapter 7.1) (Interval estimates for the Binomial will be covered in Ch. 8.) Mugglin and Eberly PubH 6450 Fall 2011 Part 08 2 / 29 Review Revisiting Important Concepts When Is Unknown Point estimates vs. interval estimates For a population parameter of interest (e.g., ), a point estimate (e.g., X ) is a statistic calculated from an observed random sample. The best way to estimate a parameter can often be chosen based on the estimates properties, such as unbiasedness , consistency (Law of Large Numbers), etc. This is why we use X to estimate , p to estimate p , and s 2 to estimate 2 . A point estimate is a random variable, because it is computed from a random sample. Therefore we need to describe its distribution (e.g., its variability) to convey the uncertainty in the point estimate. This variability is often quantified via the confidence interval . Mugglin and Eberly PubH 6450 Fall 2011 Part 08 3 / 29 Review Revisiting Important Concepts When Is Unknown CI for population mean Definition A 100 C % confidence interval for the mean of a normal population with known variance 2 , based on a random sample of size n , is X z * n , where z * is the value of the standard normal variable such that Pr( z * Z z * ) = C . This formula can also be used when n is large enough that the CLT applies. For a 90% CI, use z * = 1 . 645. For a 95% CI, use z * = 1 . 96. For a 99% CI, use z * = 2 . 576. Mugglin and Eberly PubH 6450 Fall 2011 Part 08 4 / 29 Review Revisiting Important Concepts When Is Unknown Things to remember Correct interpretation: if we take many samples from the same population and use this method to construct a 95% CI based on each sample, then on average , 95% of the CIs will include the (true) population parameter. CIs demonstrate the uncertainty in our point estimate X . The confidence level itself (e.g., 95%) may or may not be correct, depending on whether any assumptions were violated. Violation of CLT assumptions (e.g., too small n for nonnormal data) or a biased sample or correlated (nonindependent) observations could lead to CIs with incorrect coverage for your parameter of interest. CAUTION: Many research papers will report summary statistics as estimate st.dev. , which is not the same as a CI computed from estimate margin of error ....
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This note was uploaded on 11/21/2011 for the course PUBH 6450 taught by Professor Andymugglin during the Fall '10 term at Minnesota.
 Fall '10
 AndyMugglin

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