Two or more independent source data

The estimation of the systematic errors Sj (which, of course, have to relate to X and be expressed in the same units), can only be made by a person who is familiar with the experimental method. The uncertainty, c, has to correspond to the 95% confidence level preferred in this review. It should be noted that for all the corrections and recalculations made (e.g., temperature or ionic strength corrections) the rules of the propagation of errors have to be followed, as outlined in Section C.6.2. 

More often, the determination of sx is impossible because either only one or two data points are available, or the authors did not report the individual values. The uncertainty a in the resulting value can still be estimated using Eq. (C.5) assuming that 

6) and (C.7) may only be used if all the Xj belong to the same parent distribution. If there are serious discrepancies among the Xj, one proceeds as described below under Section C.4.1. It can be seen from Eq. (C.7) that Ojp is directly dependent on the absolute magnitude of the a, values, and not on the dispersion of the data points around the mean. This is reasonable because there are no discrepancies among the Xi, and because the a, values already represent the 95% confidence level. The selected uncertainty,, will therefore also represent the 95% confidence level. 

Five data sources report values for the thermodynamic quantity, X. The reviewer has assigned uncertainties that represent the 95% confidence level as described in Section 

The calculated uncertainty, = 0.2, appears relatively small, but is statistically correct, as the values are assumed to follow a Gaussian distribution. As a consequence of Eq. (C.7), will always come out smaller than the smallest a,. Assuming a4 = 0.10 instead of 0.25 would yield X = (25.0 + 0.1) and CT4 = 0.60 would result in X = (25.6 0.2). In fact, the values X-, a,) in this example are at the limit of consistency, i.e., the range (X4 + 04) does not overlap with the ranges X2 02) and (X3 03). There might be a better way to solve this problem. Three possible choices seem more reasonable  

Two data are called discrepant if they differ significantly, i.e., their uncertainty ranges do not overlap. In this context, two cases of discrepancies are considered. Case I Two significantly different source data are available. Case II Several, mostly consistent source data are available, one of them being significantly different, i.e., an outlier . 

The uncertainties have been assigned by the reviewer. Both experimental methods are satisfactory, and there is no justification to discard one of the data. The selected value is then  

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Data for the CFOl are compiled from various federal, state, and local administrative sources, including death certificates, workers compensation reports and claims, reports to various regulatory agencies, medical examiner reports, police reports, and news reports. Source documents are matched so that each fatality is counted only once. To ensure that a fatality occurred while at work, all information is verified from two or more independent source documents or from a source document and a follow-up questionnaire. Approximately 30 data elements are collected, coded, and tabulated, including information about the worker, the fatal incident, and the machinery or equipment involved. This database does not give any descriptions of the accidents (types or causes). 

When comparing means of two or more samples, analysis of variance (ANOVA) is a very useful technique. This method also assumes data are normally distributed and that the variances of the samples are homogeneous. The samples must also be independent (e.g. not sub-samples). The nested types of ANOVA are useful for letting you know the relative importance of different sources of variability in your data. Two-way and multi-way ANOVAs are useful for studying interactions between treatments. 

In the case of quartz (MINUSIL, Fig. 9), data from two different sources [42,43], which are not in agreement, can be made to coincide. The open symbols are the original data, which can be shifted by changing the zero level to yield the drawn lines and thus coincide more or less with the independently measured values. 

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