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ASTR-3030 Methods & Instrumentation

ASTR-3030 Methods & Instrumentation. Day 5. Errors. In science, uncertainty and error are the same - unfortunately Systematic Errors: Consistent inaccuracies introduces a constant bias in data Random Errors: Outcome of one trial differs from the next in an unpredictable fashion

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ASTR-3030 Methods & Instrumentation

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  1. ASTR-3030Methods & Instrumentation Day 5

  2. Errors In science, uncertainty and error are the same - unfortunately Systematic Errors: Consistent inaccuracies introduces a constant bias in data Random Errors: Outcome of one trial differs from the next in an unpredictable fashion Propagation of Errors: Add in quadrature. Beware of unequal sizes (magnitudes going to WDLF) “If your experiment needs statistics, you ought to have done a better experiment.” - Ernest Rutherford

  3. Statistics Probability is the heart of analysis – if the system obeys Nature. Mean (average): Median Mode Variance Standard Deviation Standard Deviation of the Mean “The only uniform CCD is a dead CCD” – George Jacoby “God does not play dice with the Universe” – Albert Einstein

  4. Distributions Gaussian (a normal distribution function) Probable Error (0.6745 PGauss) Poisson (random behavior – photon counting) “Lies, damned lies and statistics.” – Benjamin Disraeli

  5. Trends Correlation Functions Partial Correlations Double-correlations Principal Component Analysis Parametric Tests –vs. – Non-Parametric tests “How do our data look?” “I’ve carried out a Kolmogorov-Smirnov test …” “Ah. That bad.” – interchange between Peter Scheuer and his then student..

  6. Data Rejection Chauvenet’s Criterion Be VERY careful in rejecting data when you don’t know how the system you’re dealing with is expected to act… astronomy may be the severe outlier in data rejection caution. Weighted averages Least Squares fitting (minimizing the deviation from a fit) Chi-Square test: Goodness of Fit Indicator (example) “But what about the errors on your errors?” – Graham Hine at a Mark Birkinshaw colloquium, Cambridge 1979

  7. Chi-Square Fit Measured Values of x (cm) 731 772 771 681 722 688 653 757 739 780 709 676 760 748 672 687 678 748 689 810 805 778 764 753 698 770 754 830 725 710 738 638 742 645 675 712 733 766 709 787

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