By Allison S. K., Duane W.
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Extra resources for Absorption Measurements of Certain Changes in the Average Wave-Length of Tertiary X-Rays
There are areas of science and engineering where this assumption is not really reasonable and therefore the method of least squares must be modified to take error correlation into consideration [DA95]. Davidian and Giltinan discuss problem in the biostatistics field in which repeated data measurements are taken. For example, in clinical trials, data might be taken for many different patients over a fixed time period. For such problems we can use the term Yijj to represent the measurement at time ti for patient j.
Not errors) and are perhaps due to an unexpected phenomenon. 48. This can happen, for example, when data is being collected by hand and the person recording the data misplaces the decimal point. 3. 3 Data Weighting 43 Note the very large value of the relative error for point 5. 2), statistical tests are discussed that allow us to measure the goodness of the fit without the need to examine all the relative errors. 986 Data generated with Eq. 3 y = a1 + a2x+ a3x2. Rel_Errorr is (Y - y) / σy . 3 when the values of σy vary significantly from point to point.
33). This is a very large range of probable results. , wi=1//σy2), can we improve upon these results? 0664. These values are considerably less than the values obtained using unit weighting. The reduction in the value of σ a1 is more than a factor of 10 and the reduction in σ a2 is almost a factor of 4. , σy) was also taken into consideration. We should also question the independence of a1 and a2. If for example, we repeat the experiment many times and determine many pairs of values for a1 and a2, how should the points be distributed in the two-dimensional space defined by a1 and a2?