Comparing Theory and Measurement

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Presentation transcript:

Comparing Theory and Measurement Agreement ?

Comparing Theory and Measurement Agreement between theory and experiment does NOT imply correctness. Counter-examples include: bad theory agreeing with bad data bad theory agreeing with good data by coincidence good theory agreeing with bad data because a variable was not considered or controlled in the experiment Scientific information can be misused selectively. Comparisons must be made within the context of uncertainty.

Proper Graphical Comparison with Uncertainty Figure 9.1

How Sure Are We ? When a physical process is quantified, uncertainties associated with describing the process occur. Uncertainties result from Experiments Modeling calibration and use of instruments analytical assumptions numerical approximations experimental process fitting and analysis of data

Systematic and Random Uncertainties An error is the difference between the measured and the true value. An uncertainty is an estimate of the error. Uncertainties are categorized as either systematic (bias) or random (precision). An uncertainty is assumed to be systematic if no statistical information is provided.

Systematic and Random Uncertainties Systematic, Bi: arises from comparisons with standards (calibration) involves no statistics; the number is given alone related to the accuracy Random, Pi: based upon repeated measurements involves statistics ( ) related to the precision (scatter) for one more measurement for multiple measurements subscript i refers usually to variable i but possibly also to situation i

Systematic and Random Uncertainties Pi: based upon N, Sx, and % P Bi: based upon comparison between sample and true (population) means Figure 9.2

Precision and Accuracy Precision Accuracy good poor good good poor poor poor good