Estadistica

V. Uncertainty Analysis and Data Reporting
•  Most physical quantities require uncertainties
–  Observed or measured quantities –  Calculated quantities :
•  With measured input values •  Modeldependent e.g. Monte-Carlo simulations

•  Types of uncertainties
–  Systematic vs. statistical uncertainties –  Internal vs. external uncertainties

•  Objective of uncertainty analysis
–  Howaccurate is the measurement (ie the (deduced) observable)? –  Is the equipment working properly (according to expectation)? –  Is the underlying model correct?
Spring 2010 Radiation Detection &Measurements 1

Characterization of Data
•  Assume N independent measurements of the same physical quantity x1, x2, x3, …, xN: •  Experimental mean: •  Residual: •  Deviation from the (true) mean and itsvariance: •  Sample variance for finite number of measurements
(standard deviation σ is also referred to as external uncertainty in the mean):

Practical expression: Spring 2010 RadiationDetection & Measurements 2

Internal vs. External Uncertainties
•  Assume a-priori uncertainty σ (e.g. counting numbers) the uncertainty in the mean is •  Assume different uncertainties σi for xi:

– Weighted mean:

–  Error in weighted mean:

–  And:
Spring 2010 Radiation Detection & Measurements 3

Error-Propagation/ Uncertainty in a derived quantity
Assume N independent measurements ofthe same physical quantity x1, x2, x3, …, xN to which F is related by F=f(x1, x2,..): •  Uncertainty in F: •  Examples:
–  Sum and Differences (of counts) –  Multiplication or Division by a Constant–  Multiplication or Division (of counts)
Spring 2010 Radiation Detection & Measurements 4 Error Propagation Formula, assuming independent measurements

Examples, cont’d …
•  Counting rate R:R=n/T; n: number of counts; T: time;

•  Source counting rate corrected for background
RB: background rate; RS signal rate

Spring 2010

Radiation Detection & Measurements

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Correct...