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Intermediate Lab PHYS 3870

Intermediate Lab PHYS 3870

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Intermediate Lab PHYS 3870

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  1. Intermediate Lab PHYS 3870 Lecture 5 Comparing Data and Models—Quantitatively Linear Regression

  2. Intermediate Lab PHYS 3870 Comparing Data and Models—Quantitatively Linear Regression References: Taylor Ch. 6, 7, 8 Also refer to “Glossary of Important Terms in Error Analysis”

  3. Intermediate Lab PHYS 3870 Errors in Measurements and Models A Review of What We Know

  4. Precision and Random (Statistical) Error

  5. Standard Deviation

  6. Standard Deviation of the Mean

  7. Comparison with Other Data Percent Error = |X1 – X2| / ½(X1 + X2)

  8. Direct Comparison with Standard Percent Error = |XMeasured – XStandard| / XStandard

  9. Errors in Models—Error Propagation

  10. Specific Rules for Error Propogation

  11. General Formula for Multiple Variables

  12. Intermediate Lab PHYS 3870 Rejecting Data Chauvenet’s Criterion

  13. Chauvenet’s Criterion Data may be rejected if the expected number of measurements at least as deviant as the suspect measurement is less than 50%.

  14. Central Probability of Gaussian Distribution

  15. Chauvenet’s Criterion

  16. Intermediate Lab PHYS 3870 Combining Data Sets Weighted Averages

  17. Weighted Averages

  18. Intermediate Lab PHYS 3870 Comparing Measurements to Models Qualitatively

  19. What is Science? • The scientific method goes further in: • Developing a description (model) of the system behavior based on observation • Generalizing this description (model) to other behavior and other systems • That is to say, the scientific method is experimentation and modeling intertwined • It is the scientific method that distinguishes science from other forms of endeavor

  20. Scientific Method: • Leads to new discoveries → how scientific progress is made! • Careful measurements, • Experiments • Models, Empirical • Laws,Generalization Hypothesis,Theory

  21. Uncertainties in Observations Input Output SYSTEM The Universe • Observations characterize the system to within the uncertainty of the measurements • Uncertainties can arise from: • Limitations of instrumentation or measurement methods • Statistical fluctuations of the system • Inherent uncertainties of the system • - Quantum fluctuations • - Non-deterministic processes (e.g., chaos): • - There are systems where uncertainties dominate and preclude models predicting the outcome • - We will not (intentionally) deal with this type of system.

  22. What is a Model?

  23. What is a Model?

  24. Intermediate Lab PHYS 3870 Dimensional Analysis

  25. Units and Dimensions

  26. Dimensional Analysis

  27. Intermediate Lab PHYS 3870 Graphical Analysis

  28. Graphical Analysis

  29. Is it Linear?

  30. Making It Linear

  31. Linearizing Equations (1)

  32. Linearizing Equations (2)

  33. Special Graph Paper Linear Semilog Log-Log

  34. Special Graph Paper Polar Linear

  35. Magic Graph Paper

  36. Intermediate Lab PHYS 3870 Comparing Measurements to Models Linear Regression