Error terms, reporting

It is recommended that a minimum or three replicate measurements be made in order to compute a standard deviation, which is used as the error term associated with a mean of the replicate concentration results. If time and expense allow, measurement of additional replicates usually improves the accuracy of the mean value and lowers the magnitude of the standard deviation, which is the error term reported with the mean. Ten replicates are usually the practical upper limit on the number of repUcates that can be effectively used. Beyond 10 replicates, improvement in accuracy or precision of the reported concentration values is normally limited. 

Move 3 highlights the principal Endings of the work and is often the longest segment of the abstract. When practical, numerical values (with their error terms, e.g., standard errors or deviations) are reported otherwise, only the major trends suggested by the data are summarized. It is not appropriate to include a table in the abstract or to repeat all of the results presented in the paper. In many instances, the abstract ends with a concluding statement that draws attention to the major findings or impacts of the work. 

Move 3, the last and most important move of the abstract (and often the longest), highlights the principal Endings of the work. Three examples are considered (P12-P14). Only the most essential or representative data are reported, including numerical values, when appropriate. (Note that numerical data should include units and standard errors or deviations. Do not omit units or error terms to conserve space.) Move 3 may also inform readers about the contents of the full article. For example, P12 informs readers that acute toxicity information for three pesticides is presented in the text. Move 3 sometimes ends with a concluding remark. In P12 and P13, the data themselves end the abstract and no summative remarks are made in P14, the authors add a concluding remark. 

All models were fit using FOCE-I. Data are reported as estimate (standard error of the estimate).R denotes model minimized successfully but with R-matrix singularity. (A) denotes additive residual error term. (E) denotes exponential residual error term. 

Some recent NMR studies on the copolymerization of allyl acetate with methyl methacrylate, butyl acrylate, and styrene reported their reactivity ratios (cf Table IXb) [65]. The reported error terms, if we assume them to be standard deviations, are quite large with respect to the ri term. Therefore it is problematic whether these numbers are really meaningful. It would seem to us that the large f-2 terms imply that substantially only homopolymers of these three vinyl monomers form. This situation is modified in the case of allyl methacrylate or allyl acrylate copolymers, as will be mentioned below. With these acrylic derivatives, copolymerization depends on the acrylic bonds primarily with modifications due to the allylic hydrogen. Subsequently, the allylic units in a copolymer of allyl methacrylate with butyl methacrylate, for example, will be the sites for crosslinking. 

The copolymerization of vinyl fluoride has been studied systematically only with a few co-monomers. Table I [19, 20, 22, 23] lists some of the reactivity ratios which have been reported. The meaning of the error terms given in the table is, as is so often the case in the chemical literature, not at all clear. It is interesting to note that the same authors, in the same paper, using two different initiator systems now and again report two sets of reactivity ratios which do not always agree with each other even when the error term is added or subtracted. The Q-e values for vinyl fluoride copolymerizations have been reported as Q = 0.010 0.005 e = -0.8 0.2 [10] or g = 0.0084 e = 0.97 [22]. 

To achieve the best accuracy and precision for quantitative analysis, samples must be analyzed in—at least—triphcate.This accomplishes two objectives (1) The agreement between the three repUcates provides a basis for editing the data to reject outliers and (2) a measure of the determination of variance can be calculated from the three repHcates. Generally, by making a minimum of three replicate determinations, reruns, dictated by quality assurance protocols (see Chapter 10) will not be required or will be necessary only in unusual situations. Reporting results as a mean and standard deviation ( error term) provides data that have more interpretation value. 

When reporting the results of quantitative determinations, an error term assists the end user in interpreting the data. An example of the way the data should be reported is shown as follows ... 

Because the PARAFAC model makes no assumptions about spectral shapes nor the structure of parameters and error terms, if two completely independent models derived from different sets of samples arrive on similar spectral shapes, it provides strong evidence that the spectra represent underlying chemical phenomena. In split-half validation, independent halves of a data set are modeled separately. The model is validated when the same components are found in each half-data set, as this result could not reasonably arise from chance alone (Harshman and Lundy, 1994). When spectrally identical components are uncovered in completely unrelated data sets, as has been reported with increasing frequency (e.g., Stedmon et al., 2007 Murphy et al., 2011 this study), it can be taken as even stronger validation that such PARAFAC components are chemically meaningful. 

Note that the term e/D is the relative roughness from Figure 2-11. The solution of the above equation is trial and error. Colebrook [6] also proposed a direct solution equation that is reported [7] to have... 

Perhaps the most consistent effect of cannabis is consolidation of information from short-term memory (Dornbush et al 1971 Murray 1986). In contrast, cannabis does not appear to impair access to information already in long-term memory (Parley et al. 1977 Parker et al. 1980). While cannabis and placebo groups performed equally well on a word list recognition task, the cannabis group made more false positive errors (Abel 1970, 1971). Another effect on memory reported in severeal studies is increased intrusion of irrelevant material (Abel 1970, 1971 Clark et al. 1970 Tinklenberg et al. 1970 Pfefferbaum et al. 1977). 

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