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Lec4 Chi2

# Lec4 Chi2 - Outline Physics 257 Lecture 4 2 Prof Matt Dobbs...

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Physics 257 Lecture 4: χ 2 Prof. Matt Dobbs Physics Department, McGill U. Prof. M. Dobbs, Physics 257 Oct 5, 2006 2 Outline ± Questions ? ± Comments from Assignment and Lab reports. z Be careful not to round off numbers in intermediate calculations! ± Review of χ 2 and DoF ± The Language of Probability – rolling dice. ± Linearizing Fits z Power law fits z Exponential fits ± Lab Break next week. z Class at NORMAL TIME will be more fun than usual. z Assignment 4 will be due TWO weeks from now (available from WebCT by the weekend) Prof. M. Dobbs, Physics 257 Oct 5, 2006 4 Prof. M. Dobbs, Physics 257 Oct 5, 2006 5 χ 2 ± The χ 2 is used to evaluate the level of compatibility between observed data and a theoretical hypothesis for the PDF of that data. z E.g. given the errors of my measurements, does my data agree with a straight line hypothesis? ± Inferential statistics : the use of statistics to make inferences concerning some unknown aspect (usually a parameter) of a population. z E.g. Does this best fit line accurately describe the data? z What is the statistical significance of this measurement?

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Prof. M. Dobbs, Physics 257 Oct 5, 2006 6 χ 2 () 2 1 2 2 2 1 2 2 2 1 2 2 1 reduced ) ; ( 1 reduced ) ; ( = = = Δ + = = Δ = = Δ = N i i i i N i i i i i N i i i i i y b ax y N DOF y a x f y M N DOF y a x f y χ ± Quantifies the degree to which a theoretical function (like a straight line ax+b) agrees with the data.
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Lec4 Chi2 - Outline Physics 257 Lecture 4 2 Prof Matt Dobbs...

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