ROCHESTER PHY 113 - Lecture Notes - Statistics (53 pages)

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Lecture Notes - Statistics



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Lecture Notes - Statistics

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Pages:
53
School:
University of Rochester
Course:
Phy 113 - General Physics I

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Is statistics relevant to you personally Month 1 Month 2 Bush 42 41 Dukakis 40 43 Undecided 18 16 4 Headline Dukakis surges past Bush in polls Is statistics relevant to you personally Global Warming Analytical medical diagnostics Effect of EM radiation What kinds of things can you measure quantitatively What kinds of things can you measure qualitatively What is the difference between a qualitative and quantitative measurement Which of these types of measurement are important in science In so far as possible physics is exact and quantitative though you will repeatedly see mathematical approximations made to get at the qualitative essence of phenomena 1 2 2 A quantitative measurement is meaningless without a unit and error Accuracy A measure of closeness to the truth Precision A measure of reproducibility Accuracy vs precision accurate precise Types of errors Statistical error Results from a random fluctuation in the process of measurement Often quantifiable in terms of number of measurements or trials Tends to make measurements less precise Systematic error Results from a bias in the observation due to observing conditions or apparatus or technique or analysis Tend to make measurements less accurate time True value Parent distribution infinite number of measurements time True value The game From N not infinite observations determine and the error on without knowledge of the truth time True value The parent distribution can take different shapes depending on the nature of the measurement The two most common distributions one sees are the Gaussian and Poisson distributions Most probable value Highest on the curve Most likely to show up in an experiment Probability or number of counts x Most probable value Median Value of x where 50 of measurements fall below and 50 of measurements fall above Probability or number of counts x Most probable value Median Mean or average value of x Probability or number of counts x The most common distribution one sees and that which is



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