A Data Tables

On entering SigmaPlot (we use version 5.0), one is presented with a data table that is essentially a spreadsheet. Enter T as the independent or A -variable into the first eolumn of the SigmaPlot data table and Cp/T as the dependent or y-variable into the second column. The SigmaPlot data table should resemble columns 1 and 3 of Table 1-3. Rounding to three significant figures is permissible. 

Given a data table with evenly spaced values of x, and rescaling x so that h = one unit, forward differences are usually used to find f(x) at x near the top of the table and backward differences at x near the bottom. Interpolation near the center of the set is best accomplished with central differences. 

Purpose Find correlations in a data table the data table is organized into M columns, each of which corresponds to a dimension, e.g., concentrations of impurities, pH, absorbance at various wavelengths, etc. Each row corresponds to a sample, e.g., a batch of material analyzed according to M methods. 

Modify Table) Once a data table is established, it can be manipulated in various ways The option offers Add/Delete Row/Column, and Change Entry choose the option and click on the appropriate item. If many rows or columns need to be added or deleted, it is easier to read the data file into Excel, do the modifications there, and reimport it using the (Import from Excel) option. 

We are asked to calculate and compare the pressures of methane gas using the van der Waals equation (Equation ) and the ideal gas equation (F V = K F TJ. Van der Waals constants a and b must be looked up in a data table such as Table 11-1. To calculate pressures, we rearrange the van der Waals equation... 

Analytical results are often represented in a data table, e.g., a table of the fatty acid compositions of a set of olive oils. Such a table is called a two-way multivariate data table. Because some olive oils may originate from the same region and others from a different one, the complete table has to be studied as a whole instead as a collection of individual samples, i.e., the results of each sample are interpreted in the context of the results obtained for the other samples. For example, one may ask for natural groupings of the samples in clusters with a common property, namely a similar fatty acid composition. This is the objective of cluster analysis (Chapter 30), which is one of the techniques of unsupervised pattern recognition. The results of the clustering do not depend on the way the results have been arranged in the table, i.e., the order of the objects (rows) or the order of the fatty acids (columns). In fact, the order of the variables or objects has no particular meaning. 

Clustering or cluster analysis is used to classify objects, characterized by the values of a set of variables, into groups. It is therefore an alternative to principal component analysis for describing the structure of a data table. Let us consider an example. 

In the previous subsection, we have described S and L as containing the coordinates of the rows and columns of a data table in factor-space. Below we show that, in some cases, it is possible to graphically reconstruct the data table and the two cross-product matrices derived from it. It is not possible, however, to reconstruct at the same time the data and all the cross-products, as will be seen. We distinguish between three types of reconstructions. 

Fig. 31.2. Geometrical example of the duality of data space and the concept of a common factor space, (a) Representation of n rows (circles) of a data table X in a space Sf spanned by p columns. The pattern P" is shown in the form of an equiprobabi lity ellipse. The latent vectors V define the orientations of the principal axes of inertia of the row-pattern, (b) Representation of p columns (squares) of a data table X in a space y spanned by n rows. The pattern / is shown in the form of an equiprobability ellipse. The latent vectors U define the orientations of the principal axes of inertia of the column-pattern, (c) Result of rotation of the original column-space S toward the factor-space S spanned by r latent vectors. The original data table X is transformed into the score matrix S and the geometric representation is called a score plot, (d) Result of rotation of the original row-space S toward the factor-space S spanned by r latent vectors. The original data table X is transformed into the loading table L and the geometric representation is referred to as a loading plot, (e) Superposition of the score and loading plot into a biplot.

Cluster analysis (which is covered extensively in Chapter 30) can be performed on the factor scores of a data table using a reduced number of factors (Section 31.1.4) rather than on the data table itself. This way, one can apply cluster analysis on the structural information only, while disregarding the noise or artefacts in the data. The number of structural factors may be determined by means of internal... 

The first step in analysing a data table is to determine how many pure factors have to be estimated. Basically, there are two approaches which we recommend. One starts with a PCA or else either with OPA or SIMPLISMA. PCA yields the number of factors and the significant principal components, which are abstract factors. OPA yields the number of factors and the purest rows (or columns) (factors) in the data table. If we suspect a certain order in the spectra, we preferentially apply evolutionary techniques such as FSWEFA or HELP to detect pure zones, or zones with two or more components. 

Although the decomposition of a data table yields the elution profiles of the individual compounds, a calibration step is still required to transform peak areas into concentrations. Essentially we can follow two approaches. The first one is to start with a decomposition of the peak cluster by one of the techniques described before, followed by the integration of the peak of the analyte. By comparing the peak area with those obtained for a number of standards we obtain the amount. One should realize that the decomposition step is necessary because the interfering compound is unknown. The second approach is to directly calibrate the method by RAFA, RBL or GRAFA or to decompose the three-way table by Parafac. A serious problem with these methods is that the data sets measured for the sample and for the standard solution should be perfectly synchronized. 

State the difference between a data table and a graph. 

Wait 3 min. Measure the temperature of the acid and record it in the Part A Data Table. 

Data obtained from environmental monitoring programs can be classified, according to their complexity, in data ordered in one direction (one-way data), two directions (two-way data), three directions (three-way data), and in multiple directions (multiway data) [9, 10]. Scalar numerical data (one variable measured in one sample) would correspond to data ordered in zero direction (zero-way), while vector data (for instance, different variables measured in one sample or one variable measured in different samples) are ordered in one direction. When different variables are measured in different samples, obtained data can be ordered in two directions, that is, in a data table or data matrix. Finally, the compilation of different... 

A data table of a case-base can be divided into input and output sections. Input parameters are retrieval parameters and output parameters are design specification parameters. The problem is characterized as input data to the system. In the retrieval phase a set of retrieval parameter values of all cases in the case-base are compared to the input data. The most similar cases are then selected and ranked based on the comparison. 

Scenario A student prepared a data table for the results that he got in doing this experiment ... 

Prepare a data table that will accommodate multiple titration trials. 

Data quality is a broad, often loosely defined term. There are many problem- and discipline-related definitions to be found in the literature. This section shall not try to define data quality in any comprehensive, far less complete sense - suffice to denounce any definition that does not include the specific aspect of sample representativity however. Data is often equated with information, but this can only be in a hidden, potential form. Only data analysis together with interpretation may reveal information - which will always be in a particular problem-specific context only. Such issues are not usually seen as problematic in chemometrics and in PAT, where the pre-history of a data table ( data ) in general receives but scant attention. One relevant, major exception is Martens and Martens (2001) [26] who focus comprehensively on Multivariate Analysis of Quality . But even here there is a narrow focus on quality of information only, defined as ... dependent on reliability and relevance , without further clarifying the definition of these open-ended adjectives. 

You should not be too surprised to discover an unusual emphasis on the collection of evidence and the expectation that there will be close ties between such evidence and your conclusions. Therefore, data collected in an experiment or investigation needs to be displayed in a way that is easy to understand, see connections and determine validity. This is most effectively done as a data table. From the data table below, it is easy to see that the temperature of the water is increasing as time is progressing. 

When displaying measurements in a data table follow these simple rules ... 

Report results in a Data Table with all the pertinent information and measurements. List reagents and their concentrations used for elution tests. 

Fig. 4.5 Water table transect (a) data table (b) well location (c) the transect, drawn through the numbered wells (x), having a NW-SE direction (o = other wells, not included in the transect).

Read through the steps in this Procedure. Prepare a data table to record the mass of the solute, the initial volume of water, the total volume of water after step 9, and the temperatures at which the solutions begin to crystallize. 

Write the steps that will allow you to measure the quantities you need. Design a data table for your results. Include a space for the name of the solute in your solution. 

Using pressure probes and a graphing calculator or computer interface, investigate the relationship between the pressure and the volume of a gas. Produce a data table and graphical interpretation of these results. 

Remember that a data table should be designed to present a set of data as clearly and concisely as possible. All columns and rows within the table should be clearly defined with respect to the identity and units associated with each value. In addition, the table should be titled to allow the reader to determine quickly what features of the table are relevant to the study or experiment. Table 1-2 presents examples of both a poorly designed and a properly designed data table. Note that the poorly designed table has no title, is very redundant, is cluttered, and is presented in a manner that does not allow the reader to easily see differences between (to compare) trials of the same experiment. The properly designed data table, in contrast, features the experimental values and quickly draws the reader s attention to differences between the values. 

This section adds a cooldown path to Fig. 13.2. It does so by preparing a data table which specifies that ... 

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