Dealing with Uncertainties: A Guide to Error Analysis
Manfred Drosg
Language: English
Pages: 235
ISBN: 364201383X
Format: PDF / Kindle (mobi) / ePub
Dealing with Uncertainties is an innovative monograph that lays special emphasis on the deductive approach to uncertainties and on the shape of uncertainty distributions. This perspective has the potential for dealing with the uncertainty of a single data point and with sets of data that have different weights. It is shown that the inductive approach that is commonly used to estimate uncertainties is in fact not suitable for these two cases. The approach that is used to understand the nature of uncertainties is novel in that it is completely decoupled from measurements. Uncertainties which are the consequence of modern science provide a measure of confidence both in scientific data and in information in everyday life. Uncorrelated uncertainties and correlated uncertainties are fully covered and the weakness of using statistical weights in regression analysis is discussed. The text is abundantly illustrated with examples and includes more than 150 problems to help the reader master the subject.
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What is basically wrong with the uncertainty he gives? 6 Deductive Approach to Uncertainty 6.1 Theoretical Situation In Chap. 5 we found that in the case of random and identically distributed data values (like count rates of radioactive events) the probability of any data value xi to lie inside the interval m − σ and m + σ can be predicted if the true value m is known. In this special case for both the Poisson and √ Gaussian distributions (Sects. 5.2.2 and 5.2.3) the standard deviation √ is σ
with uncertainties of the same size. Consequently, applying it to data with internal uncertainties of the same size would easily be possible in a similar way by determining the mean value and its standard deviation. However, it cannot be applied to data with internal uncertainties of different sizes. In practice, though, such data are rather frequent. Thus it would be worthwhile to be able to determine whether an outlier (Sect. 3.2.4) may be discarded for statistical reasons in these cases, too.
Whether a best estimate is given by a single value or by just one parameter (like the mean value of a data set) it is always appropriate to add all uncertainties to yield the total uncertainty of this best estimate. Correlated uncertainty components of single data are combined linearly according to the general law of error propagation (see the beginning of this chapter). If done correctly, the combined correlated uncertainty components will not be correlated to other uncertainty contributions.
measurement setup, e.g., 3. By remeasuring a data point of a very well known value, a secondary “standard”, to calibrate the apparatus. 4. By “estimating the uncertainties”. If a known data value (naturally, of the same type as the unknown value we want to measure) is measured with the identical apparatus, we can derive the intrinsic accuracy of the measurement setup from the knowledge of the measured value and of the known (standard) value. Note: Interpreting the new measurement as a measurement
measurement value. Without actually recording the temperature she can determine the contribution of the temperature change to the uncertainty to be ± < 3θ%. If this contribution cannot be ignored, either the lab should be air-conditioned or the temperature during the measurement must be recorded as another measurement parameter. 2. Accuracy of the Measurement Time. In the example in Sect. 9.3. the uncertainty of the measurement time was estimated using the knowledge that the time base of the
