Lec0 Stats

Lec0 Stats - Physics 257 Lecture 0 Basic Statistics...

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Physics 257 Lecture 0: Basic Statistics & Introduction to Matlab Prof. Matt Dobbs Physics Department, McGill U. Prof. M. Dobbs, Physics 257 Lecture 0 Stats 2 Outline ± Orientation session was yesterday, Sept 6. If you missed it, download the information from WebCT. We covered: z z Brief intro to the interplay between theory & experiment + the scientific method TODAY ± Average behavior of data: Mean, median, mode ± Measures of spread: Variance, standard deviation ± Correlations: covariance, corr coefficient ± Significant Figures ± Matlab Introduction Basic Statistics Statistics is the mathematical treatment and analysis of large quantities of data. It provides us with a means of characterizing a distribution of data with a few parameters such as the average and standard deviation. Prof. M. Dobbs, Physics 257 Lecture 0 Stats 4 Why Statistics ± A couple centuries ago: “If your experiment needs statistics, you ought to have done a better experiment” (B. Russell) z First statistics conference was held in 1853. ± Today: To be a statistician is great ! You never have to be “absolutely sure” of something . .. Being “reasonably certain” is enough! (from Frank Lehner lecture) ± Our goal: learn to use statistics as a quantitative tool to report scientific results. Learn to understand what other people’s statistics mean – and when to trust them.
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Prof. M. Dobbs, Physics 257 Lecture 0 Stats 5 Basic Definitions ± A complete body of data to be analyzed is called a population . z E.g. all the red giant stars in our galaxy. ± Often, we must be satisfied with analyzing a sample of the population. z E.g. those red giant stars that have been observed with the CFHT telescope. z (class example) ± In this case we would like to know how likely it is that a statistic (mean, std dev) of the sample is characteristic of the whole population. z In physics we are most interested in knowing how good an estimation of a statistic (like the mean x) is of the true value (like the true mean μ ). z Convention: use greek letters ( μ , σ ) for true values and roman letters (x, s) for estimates. Prof. M. Dobbs, Physics 257 Lecture 0 Stats 6 Average and Expectation Values ± Arithmetic mean of data x i ± Expectation value for a variable x of a continuous function z <x> is the notation for the expectation value or average value. ± Both are linear operators
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Lec0 Stats - Physics 257 Lecture 0 Basic Statistics...

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