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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 [email protected] Part 05 Review Probability Random Variables Where are we going? Previously: • Overview of the study cycle • Specifics: sampling and study design Current topics: • Probability! • More on random variables Mugglin and Eberly PubH 6450 Fall 2011 Part 05 2 / 51 Review Probability Random Variables Randomness Definition A phenomenon or trial is random if its outcome is uncertain. Examples • The outcome of a single flip of a coin. • The next participant’s blood type. • Your blood pressure. • Tomorrow’s weather. Mugglin and Eberly PubH 6450 Fall 2011 Part 05 3 / 51 Review Probability Random Variables Sources of Uncertainty Why are measurements of variables uncertain (i.e., variable)? • Sampling variability: different samples give different results. • Measurement variability: instrument calibration, observer skill or bias, metric being used,... • Intrinsic variability: circadian rhythm, hormonal cycles • Modeling variability: Different models, applied to the same data, can give different results. Handling such uncertainty constitutes the foundation of statistical theory. Mugglin and Eberly PubH 6450 Fall 2011 Part 05 4 / 51 Review Probability Random Variables Objective probability Definition The probability of random outcome is the proportion of times the outcome would occur in a very long (infinite) series of repetitions. This is known as objective probability. (Also frequency or empirical probability.) Mugglin and Eberly PubH 6450 Fall 2011 Part 05 5 / 51 Review Probability Random Variables Examples • The probability of head when tossing a coin ( ∼ . 5). • The probability of a randomly chosen newborn in the US being male ( ∼ . 513). • The probability of a new R01 proposal being funded by NIH ( ∼ . 16) (highest in NIDCD ∼ . 29, lowest in NCCAM ∼ . 06). Mugglin and Eberly PubH 6450 Fall 2011 Part 05 6 / 51 Review Probability Random Variables Example: Tossing a Fair Coin Example Tossing a fair coin: # tosses proportion of heads 10 0.4 100 0.49 1000 0.507 10000 0.4997 100000 0.50016 The proportion of heads in a finite sample is approaching the probability of a head that would be seen in an infinite sample. Mugglin and Eberly PubH 6450 Fall 2011 Part 05 7 / 51 Review Probability Random Variables Elements in probability We use ‘trial’ here to denote one instance of a random phenomenon. • The trial has some possible outcomes. The set of possible outcomes is the sample space (or outcome space). • The trials are independent if the outcome of one trial does not influence the outcome of another....
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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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