By Manfred Drosg
Dealing with Uncertainties proposes and explains a brand new process for the research of uncertainties. to start with, it truly is proven that uncertainties are the final result of contemporary technological know-how instead of of measurements. Secondly, it stresses the significance of the deductive method of uncertainties. this angle has the opportunity of facing the uncertainty of a unmarried info element and of information of a suite having differing weights. either instances can't be handled the inductive strategy, that's often taken. This leading edge monograph additionally totally covers either uncorrelated and correlated uncertainties. The weak point of utilizing statistical weights in regression research is mentioned. plentiful examples are given for correlation in and among info units and for the suggestions of uncertainties on scan design.
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Extra resources for Dealing with Uncertainties: A Guide to Error Analysis
These external uncertainties mirror the reproducibility (or repeatability) of the measurement result. The reproducibility is also called precision of the data and is given by the standard deviation σ of the mean. The term reproducibility can also be used in connection with other functional dependences between the data. First, one would put a linear dependence to the test using the linear regression (Sect. 3). In our example, where the measurement time is very short when compared to the half-life of the source, we can approximate the exponential decrease to a ﬁrst order by a linear dependence.
You may use Fig. 3 as a guide. 2 as gathered by repeating the same measurement? , their standard deviation Sm ) is dominated by the statistical nature of radioactive decay. Assuming that the radiation intensity has remained constant over the measuring time and that all data points are of the same precision, the external (uncorrelated) uncertainty of the data values equals the standard deviation Sm . These external uncertainties mirror the reproducibility (or repeatability) of the measurement result.
0 Fig. 1. 4 Multiple Uncertainty Components (Quadratic Sum) A velocity v is calculated using the measured values for the time t ± ∆t and the distance l ± ∆l. The uncertainty ∆v of the velocity can be expected to depend on the uncertainty ∆t of the time and on the uncertainty ∆l of the distance. , the correlation (Chap. 7) between the uncertainties of these quantities equals zero, which means that they are uncorrelated or totally independent of each other. A correlation between these quantities could exist, for instance, if the length measurement was done indirectly by measuring a time interval.
Dealing with Uncertainties: A Guide to Error Analysis by Manfred Drosg