Normalizing Data

When a data value is repeated multiple times in a column in a database, it is said to violate third normal form. For example, a table of values for logp might contain a column named ref having literature references. The value Hansch, et. al. (1995) might be repeated many times. It is easy to spot this, and easy to correct it as well. The following SQL can be used to help put a table of logp values and references into third normal form. 

This will create a table literature refs that will hold all the unique values of references that exist in the table logp. The comments in the above code should explain the steps in this process. Once the literature refs table is complete, a full reference can be obtained during a search of logp using SQL like this. 

Select cas, reference From logp Join literature refs Using (refid)  

A brief excerpt from a literature refs table is shown in Table A.l. It was constructed using this technique and nicely illustrates an advantage of normalizing a table in this way. 

Several SQL functions are discussed in the earlier chapters. This section shows the code needed to define these functions and make them available for use in a PostgreSQL database. 

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Sparse data on the pyrazole isomers, pyrazolenines and isopyrazoles, are presented in Table 12. Besides the obvious upheld effect on the chemical shift due to the suppression of the ring current, these compounds behave normally. Data on pyrazolidinones and their salts show the behaviour of cyclic hydrazides (66T2461,67BSF3502). 

Distributed Control System (DCS) A system that divides process control functions into specific areas interconnected by communications (normally data highways) to form a single entity. It is characterized by digital controllers, typically administered by central operation interfaces and intermittent scanning of the data highway. 

As a minimum, the program should be able to directly compare data from similar machines, normalize data into... 

The cause of the weaker G dependence must be ascribed to some particular feature of geometry, although exactly what it is has not been found. All of the three bundles involved had their rods supported and correctly positioned by wires wrapped helically around certain of the rods, and it is possible that the wires caused an unfavorable distribution of steam and water. However, it is doubtful that the wire wraps were themselves responsible, since several of the bundles conforming to Eq. (28) were also wire wrapped. (Other devices used for rod supports are suitably spaced grids and ferrules.) The explanation most probably lies in a combination of the effects of the wire wraps with the effects of given rod diameters and rod spacings. For ease of identification, the data that conform with Eq. (28) are hereafter called normal data. 

The analysis given in Macbeth (M4) continues by assuming that the term dh effectively represents the cross-sectional geometry of the normal rod-bundle data. If this assumption is correct, then the general correlation [Eq. (18)], may be applied by representing A and C as functions of G and dh for a given pressure. It was found that simple power functions were adequate, and a correlation was obtained by computer optimization which predicted 97% of the vertical-upflow normal data (Nos. 6-15 inclusive in Table V) to within 12%. 

The result of the computer optimization on the 1000 psia normal data with vertical-upflow is as follows ... 

All of the information obtained in this research area depends upon indirect evidence through the use of nonisotopic carriers or normalized data in the form of ratios. These are subject to error but the trends and insights that have been obtained are very useful to the description of the behavior of plutonium in the environment. Better thermodynamic data in the range of environmental concentrations would be helpful in further quantification of chemical species, as would phenomenalogical descriptions of the behavior of plutonium in reasonably good models of the environment. 

Figure 4.4. Optimization of parameters. The exponential equation (4.1) was fitted to the normalized data from Table 4.5.

Data in raw form is simply noise. The pyramid in Figure 7.1 has a hidden foundation—this is the data noise of an organization Normalized data is in... 

To reduce intensity effects, the data were normalized by reducing the area under each spectrum to a value of 1 [42]. Principal component analysis (PCA) was applied to the normalized data. This method is well suited to optimize the description of the fluorescence data sets by extracting the most useful data and rejecting the redundant ones [43]. From a data set, PCA assesses principal components and their corresponding spectral pattern. The principal components are used to draw maps that describe the physical and chemical variations observed between the samples. Software for PCA has been written by D. Bertrand (INRA Nantes) and is described elsewhere [44]. 

Program 3.5 Writing Custom SAS Code to Import Lab Normal Data... 

SAS provides several ways to read Microsoft Excel and Access files. We cover many of these import methods here using Microsoft formatted versions of the laboratory normal data used previously in this chapter. The examples here are based on the capabilities found in Base SAS and SAS/ACCESS for PC Files in SAS 9.1. In Microsoft Excel, the lab normal data file might look like the following ... 

In Microsoft Access the lab normal data might look like this ... 

There are two things that you may notice when looking at the lab normal data represented as XML. First, the file seems verbose. Whereas previously the lab normal file could be represented with three lines of pipe-delimited text, XML represents the same data with 30 lines of text. Second, you can read and somewhat understand the XML file just by looking at it if you know a markup language such as HTML or SGML. Let s look at how we can import these XML data into SAS. 

Because the XML map file is valid XML itself, you can read how the SAS variables are translated from the XML lab normals data file. Once the XML map file is defined, you just need the simple SAS program that follows to read the lab normals XML file into SAS. 

Data transposition is the process of changing the orientation of the data from a normalized structure to a non-normalized structure or vice versa. There are many definitions of normalization of data, and you should learn about normal forms and normalization. Here, in brief, normalization of data means the process of taking information out of the variable definitions and turning that information into row definitions/keys in order to reduce the overall number of variables. Normalized data may also be described as stacked, vertical, or tall and skinny, while non-normalized data are often called flat, wide, or short and fat. ... 

Typically, clinical data come to you in a shape that is dictated by the underlying CRF design and the clinical data management system. Most clinical data management systems use a relational data structure that is normalized and optimized for data management. Much of the time these normalized data are in a structure that is perfectly acceptable for analysis in SAS. However, sometimes the data need to be denormalized for proper analysis in SAS. 

A problem occurs when end users of the data cannot conceptualize how to handle normalized data. These users go out of their way to denormalize any normalized data that they see. I have seen entire databases denormalized so that a user could work with the data, and in some cases the user unknowingly renormalizes the data so that he or she can then analyze it properly. This type of user needs to be coached as to when denormalization is needed. 

Figure 5 gives the simulation results with the model given for the conditions used by Briggs et al. to obtain Fig. 3. Data points are shown in Fig. 5b, but not in 5a. Mass spectrometer readings were not calibrated, and only normalized data are shown in Fig. 3a. The simulation estimates the shape of the midbed temperature and the SO3 vol% variations successfully. It also reproduces the initial bed temperature lag for the first minute after introduction of the S03/S02 reactant mixture (Fig. 5b), as well as the absence of a lag when air is introduced to the catalyst bed displacing the reactant mixture (Fig. 5a). The model also gives the slow adjustment of the bed temperature after the maximum and minimum temperatures, although the rates of cooling and heating are not correct. The most serious deficiency of the model is that it overestimates the temperature rise and drop by 15 and 8°C, respectively.

However, although a characterization model is available for indoor emissions it is still difficult to take into account these indoor emissions because for the interpretation of the impact assessment also normalization data are desirable. For this a world covering estimate of the indoor emissions of toxic substances is necessary. 

As an example, we applied these concepts to the Anscombe data [7], Table 66-1 shows the results of applying this to both the normal data (Anscombe s XI, Y1 set) and the data showing nonlinearity. We also computed the nature of the fit using only a straight-line (linear) fit as was done originally by Anscombe and also fitted a polynomial using the quadratic term as well. It is interesting to compare results both ways. 

The improvement in the fit from the quadratic polynomial applied to the nonlinear data indicated that the square term was indeed an important factor in fitting that data. In fact, including the quadratic term gives well-nigh a perfect fit to that data set, limited only by the computer truncation precision. The coefficient obtained for the quadratic term is comparable in magnitude to the one for linear term, as we might expect from the amount of curvature of the line we see in Anscombe s plot [7], The coefficient of the quadratic term for the normal data, on the other hand, is much smaller than for the linear term. 

The ultrafast initial decay of the population of the diabatic S2 state is illustrated in Fig. 39 for the first 30 fs. Since the norm of the semiclassical wave function is only approximately conserved, the semiclassical results are displayed as rough data (dashed line) and normalized data (dotted line) [i.e., =... 

Shapiro Wilks W-test for normal data Shapiro Wilks W-test for exponential data Maximum studentlzed residual Median of deviations from sample median Andrew s rho for robust regression Classical methods of multiple comparisons Multivariate methods... 

Graph 8.4 Group data for the cholesterol microcrystal nucleation time (NT) measures in days. The value at 10 days represents the limit above which nucleation time is normal. Data taken from reference 18. 

Some data obtained from MCT, SFA, and TFB under similar conditions are compared in Fig. 2.20b. The SFA data were taken from reference [80]. They were obtained with hydrophobized mica surfaces, protein concentration of 0.1 wt%, and ionic strength of 10 mol/1. Data for TFB and MCT led to very similar results. However, comparison with the SFA data demonstrates that the force laws are only qualitatively similar the curves are parallel but the normalized data for liquid-liquid interfaces (TFB and MCT) lie about one decade below those obtained for solid-liquid interfaces (SFA). This result suggests that the proteins exhibit different adsorption abilities and or adopt different conformations at the two types of surfaces. 

Rgure 4.7. Evolution of the osmotic resistance H normalized by >w/ for PDMS-in-water emulsions. The dashed line is a visual guide. The solid line corresponds to the best fit of the normalized data obtained by Mason et al. [7]. (Adapted from [31].)... 

A set of experiments was performed at variable droplet sizes. The graph in Fig. 4.7 shows the dependence of the normalized (by Kint/a) osmotic resistance as a function of the oil volume fraction. The normalized values fall onto a single curve within reasonable experimental uncertainty. The results were compared to the normalized data obtained by Mason et al. [7] in the presence of surfactants. These latter are represented as a solid line that corresponds to the best fit to the experimental points (Eq. (4.18)). It is worth noting that the normalized pressures in solid-stabilized emulsions are much larger than the ones obtained in the presence of surfactants. 

Primitive mantle-normalized data show negative Eu and Sr in the feisic volcanic rocks. These negative anomalies are attributed to plagioclase fractionation and/or feldspar destructive hydrothermal alteration and removal of Eu during deposit formation. 

The concentration data obtained from each sample analysis were expressed as fractional parts and normalized to sum to 100. The normalized data were statistically analyzed, and three principal components (A=3, Equation [1]) were calculated. The PCB constituents (varlbles) are numbered sequentially and correspond to peak 1, peak 2,. .. to peak 105. The structure and retention index of each constituent in the mixture were reported by Schwartz et al. (9). The tabular listing of the data is availedile from the present authors. 

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