Type A evaluation

Type A evaluation (of uncertainty) Method of evaluation of uncertainty by the statistical analysis of series of observations. 

Uncertainties from some sources may be quantified by doing experiments. From the results of repeated measurements we get a standard deviation which we can use directly as an estimate for the standard uncertainty. This is called type A evaluation of uncertainties. 

Each contribution is assessed as a standard uncertainty, either by statistical procedure on experimental data in the form of an a posteriori distribution, the so-called Type A evaluation, or by scientific judgement based on an a priori chosen distribution, Type B evaluation. The few standard uncertainties of important magnitude are combined quadraticahy, including any covariances, and the combined uncertainty, uc, is obtained as the positive square root. 

Some of these components can be estimated from a series of repeated observations, by calculating the familiar statistically estimated standard deviation, or by means of subsidiary experiments which are carried out to assess the size of the component. For example, the effect of temperature can be investigated by making measurements at different temperatures. This experimental determination is referred to in the ISO Guide as Type A evaluation . 

This type of uncertainty evaluation is an example of what the GUM calls a Type A evaluation of uncertainty, which is defined as an evaluation of uncertainty based on the statistical analysis of series of observations (ISO 1995). 

Sometimes a pair of input estimates x,- and Xj may be correlated, because they are not determined independently of each other or because there is some effect in the measurement process that influences the observed value of each. The estimated covariance of x, and Xj is denoted by u(Xi,Xj). A Type A evaluation of covariance may be performed in some cases by making a series of paired observations of the two input quantities, (Xij, X ,i), (x ,2, , (Xi, , Xy ), and performing the... 

One option for evaluating the uncertainty of the number of counts observed is to perform a Type A evaluation described in Section 10.3.1, where one repeats the measurement n times, obtaining the values Ci, C2,..., C , and calculates the arithmetic mean C, the experimental standard deviation of the values 5(C, ), and the experimental standard deviation of the mean s(C). The arithmetic mean C is then used as the measured value and the experimental standard deviation of the mean s(C) is used as its standard uncertainty. 

The uncertainty due to varying instrument background can be significant. If the background varies, the assumption of pure Poisson counting statistics to evaluate the uncertainty of the net count rate for a sample may seriously underestimate the uncertainty. Options include replicate background measurements to determine its uncertainty (Type A evaluation), or to evaluate an additional component of uncertainty to be added to the Poisson counting uncertainty. 

Kim KS, Byun YS, Kim YJ, Kim ST. Muscle weakness after repeated injection of botulinum toxin type A evaluated according to bite force measurement of human masseter muscle. Dermatol Surg 2009 35 (12) 1902-6. 

Depending on the method for deterrnining uncertainty components, the GUM distinguishes between type A and type B evaluations. Type A evaluations are based on a statistical analysis of a measurement series type B evaluations cover all other methods based on the available knowledge. Both components are combined and... 

Quantifying the main uncertainty contributions. Each of the input quantities receives a standard uncertainty m(x ) either in the form of a standard deviation of a measurement series (type A evaluation) or a standard deviation of a reasonable distribution of values (type B evaluation). In case of a normal... 

Gaussian) distribution of the measurement values in a type A evaluation, the experimental standard deviation s can be used as an estimate for the dispersion of the values and the arithmetic mean value as an estimate for the value of the input quantity ... 

For type A evaluations, the degrees of freedom shall be calculated. In the simple case of m independent observations, the degrees of freedom equal m — 1. However, when only a small number of observations have been made, the use of the Student s -distribution is more appropriate than a Gaussian distribution (see textbooks of statistics). 

Calibration measurements peak area Adb) The standard uncertainty u(Adt) is calculated by a type A evaluation from the standard deviation of the measurements (Eq. (6.13)) ... 

Note 3 Measurement uncertainty comprises, in general, many components. Some of these may be evaluated by Type A evaluation of measurement uncertainty from the statistical distribution of the quantity values from series of measurements and can be characterized by experimental standard deviations. The other components, which may be evaluated by Type B evaluation of measurement uncertainty, can also be characterized by standard deviations, evaluated from probability density functions based on experience or other information. The meaning of Type A and Type B will be clarified further in the text. 

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