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## Intermediate Lab PHYS 3870

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**Intermediate Lab PHYS 3870**Lecture 5 Comparing Data and Models—Quantitatively Linear Regression**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”**Intermediate Lab PHYS 3870**Errors in Measurements and Models A Review of What We Know**Comparison with Other Data**Percent Error = |X1 – X2| / ½(X1 + X2)**Direct Comparison with Standard**Percent Error = |XMeasured – XStandard| / XStandard**Intermediate Lab PHYS 3870**Rejecting Data Chauvenet’s Criterion**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%.**Intermediate Lab PHYS 3870**Combining Data Sets Weighted Averages**Intermediate Lab PHYS 3870**Comparing Measurements to Models Qualitatively**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**Scientific Method:**• Leads to new discoveries → how scientific progress is made! • Careful measurements, • Experiments • Models, Empirical • Laws,Generalization Hypothesis,Theory**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.**Intermediate Lab PHYS 3870**Dimensional Analysis**Intermediate Lab PHYS 3870**Graphical Analysis**Special Graph Paper**Linear Semilog Log-Log**Special Graph Paper**Polar Linear**Intermediate Lab PHYS 3870**Comparing Measurements to Models Linear Regression