Inspection of the Data

One of the very first things that the analyst should do prior to attempting to fit a model to the data, is to inspect the data at hand. Visual inspection is a very powerful tool as the eye can often pick up an inconsistent behavior. The primary goal of this data-inspection is to spot potential outliers. 

Barnett et al. (1994) define outliers as the observations in a sample which appear to be inconsistent with the remainder of the sample. In engineering applications, an outlier is often the result of gross measurement error. This includes a mistake in the calculations or in data coding or even a copying error. An outlier could also be the result of inherent variability of the process although chances are it is not  

Besides visual inspection, there are several statistical procedures for detecting outliers (Barnett and Lewis, 1978). These tests are based on the examination of the residuals. Practically this means that if a residual is bigger than 3 or 4 standard 

A potential outlier should always be examined carefully. First we check if there was a simple mistake during the recording or the early manipulation of the data. If this is not the case, we proceed to a careful examination of the experimental circumstances during the particular experiment. We should be very careful not to discard ( reject ) an outlier unless we have strong non-statistical reasons for doing so. In the worst case, we should report both results, one with the outlier and the other without it. 

Instead of a detailed presentation of the effect of extreme values and outliers on least squares estimation, the following common sense approach is recommended in the analysis of engineering data  

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The particle sizes of fillers are usually collected and ordered to yield size distributions which are frequendy plotted as cumulative weight percent finer than vs diameter, often given as esd, on a log probabiUty graph. In this manner, most unmodified fillers yield a straight-line relationship or log normal distribution. Inspection of the data presented in this manner can yield valuable information about the filler. The coarseness of a filler is often quantified as the esd at the 99.9% finer-than value. Deviations from linearity at the high and low ends of the plot suggest that either fractionation has occurred to remove coarse or fine particles or the data are suspect in these ranges. 

Inspection of the data in Table 263 shows that the effects of substituents are larger in the less reactive system and this is consistent with the general effect noted in electrophilic aromatic substitution. 

The stereochemical predictions for the intramolecular cycloadditions described in Scheme 10 and Eq. (9) in terms of MMX calculations are compared to experimental results in Table 9. The most striking trend from inspection of the data is the predominance of trans cycloadduct. The computed energy difference between the transition states 88 and 89 (Fig. 1) when R = H corresponds to 1.42 kcal/mol. The experimental preference for the trans-cis isomers 72 a and 86 a is correctly predicted by the MMX calculations. It seems reasonable to invoke A strain which is present in the transition state 88 leading to the cis product 71 a to explain the trans over cis preference. Since the substituent R is... 

In principle, it is possible to fully automate the procedure (2) and software can be written to obtain the results to an operator spemFied precision, as the error equations are available. Unfortunately, this online procedure is sometimes difficult with catalysts because most supported metal catalysts contain only the order of one percent or less of metal, the peaks are broad due to the small size of the crystallites, and the large amount of support gives strong background scattering which has features of its own. Visual inspection of the data is often necessary prior to processing. 

Therefore, careful inspection of the data is highly advocated prior to using any parameter estimation software. 

Despite the differences between the estimated derivatives values, the computed profiles of the specific MAb production rate are quite similar. Upon inspection of the data, it is seen that during the batch period (up to t=2I2 h), qM is decreasing almost monotonically. It has a mean value of about 0.5 /ug/(l(f cells-h). Throughout the dialyzed continuous operation of the bioreactor, the average qM is about 0.6 fxg/(l(f cells-h) and it stays constant during the steady state around time... 

If an upper bound of 10-4 is adopted for maximum individual risk, from single events, then occupants of Building 2 are at, or slightly above, the upper-bound limit, while occupants of Building 3 appear to be in a region of tolerable risk. Also, from inspection of the data, it appears the individual risk to occupants of both buildings is almost 30 times greater from Process Unit 2 than from Process Unit 1. 

Despite the few discrepancies, inspection of the data reported in Table XIII indicates that a close correspondence exists between the 13C-n.m.r. chemical-shift data for compound 51 and those reported previously for compound 52. However, utilization of higher magnetic fields (100.61 MHz, instead of 50.3 MHz,for13C) allowed Pavia and Ferrari24 to assign all individual amino acid and carbohydrate resonances, and to correct some of the previous assignments. 

From the inspection of the data in Table 2.4, it is clear that NO changes its original molecular character after adsorption. In general, coordination of nitric oxide leads to a pronounced redistribution of the electron and spin densities, accompanied by modification of the N-0 bond order and its polarization. Thus, in the case of the (MNO 7 10 and ZnNO 11 species, slender shortening of the N-0 bond is observed, whereas for the MNO 6 and CuNO 11 complexes it is distinctly elongated. Interestingly, polarization of the bound nitric oxide assumes its extreme values in the complexes of the same formal electron count ( NiNO 10 and CuNO 10) exhibiting however different valence. 

In Figure 3, o/(X—X-z) is plotted against 1/X to obtain the constants 2Cj and 2C2 in the Mooney-Rivlin equation. The intercepts at 1/X = 0 and the slopes of the lines give the values of 2Cj and 2C2, respectively, listed in Table I. If these plots actually represent data accurately as X approaches unity, then 2(Cj + C2) would equal the shear modulus G which in turn equals E/3 where E is the Young s (tensile) modulus. An inspection of the data in Table I shows that 2(Cj + C2)/(E/3) is somewhat greater than one. This observation is in accord with the established fact that lines like those in Figure 3 overestimate the stress at small deformations, e.g., see ref. 15. 

Over time, statisticians have devised many tests for the distributions of data, including one that relies on visual inspection of a particular type of graph. Of course, this is no more than the direct visual inspection of the data or of the calibration residuals themselves. However, a statistical test is also available, this is the x2 test for distributions, which we have previously described. This test could be applied to the question, but shares many of the disadvantages of the F-test and other tests. The main difficulty is the practical one this test is very insensitive and therefore requires a large number of samples and a large departure from linearity in order for this test to be able to detect it. Also, like the F-test it is not specific for nonlinearity, false positive indication can also be triggered by other types of defects in the data. 

Following the same experimental protocol and analysis strategy, multiple sets of conductance values for 1,5-pentanedithiol (PDT), 1,6-hexanedithiol (HDT), 1,8-octanedithiol (ODT), and 1,10-decanedithiol (DDT) were measured. The results are summarized in Table 1. Inspection of the data reveals that the high-conductance values (H) are approximately five times larger than the medium-conductance values (M), while the low values (L) do not scale with a constant ratio with respect to the M or L data sets. 

Sampling of the dust concentration was made at the centerline and one point above and one point below the centerline. A close inspection of the data indicated that a higher dust concentration was observed at the bottom of the duct with essentially constant levels from the top of the duct to the centerline. 

By inspection of the data, A(< ) = 4, and the starting value is found from the boundary condition... 

When the yield coefficient yxs can be found by inspection of the data, the Monod equation can be put in the linearized form,... 

These four ingredients are utilized in a process falling into two broad phases an exploratory phase and a confirmatory phase. The exploratory phase isolates patterns in and features of, the data and reveals them, allowing an inspection of the data before any firm choice of actual hypothesis testing or modeling methods has been made. 

A solution-state and solid-state nuclear magnetic resonance study of the complex and its separate components in both their neutral and ionized (TMP hydrochloride and SMZ sodium salt) forms was undertaken in order to elucidate the TMP-SMZ interactions. Inspection of the data for the complex in the solid state shows that the 13C chemical shifts are consistent with the ionic structure proposed by Nakai and coworkers105 (14). Stabilization of the complex is achieved by the resulting ionic interaction and by the formation of two intermolecular hydrogen bonds. 

It was clear, from even a qualitative inspection of the data, that the presence of a methyl or fluoro group in the meta position had the effect of not only increasing activity versus the design insect, the southern armyworm, but also lead to dramatic increases in level of topical activity against other species. 

Data Followed by a Singular Verb That Agrees with a Different Noun Inspection of the data reveals... 

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