Scatter diagram

Scatter diagrams are used to test a relationship between two different variables. There are mai relationships that can exist between variables. Some of these include positive relationship, negative relationship, no relationship, weak positive relationship, and weak negative relationship. There can also be troughs and peak-type relationships between variables. 

By using scatter diagrams, problem relationships can become apparent. For example, when a specific percentage of boron is in a piece of steel, it will crack. A scatter diagram can help us determine what level of boron can be present and still have the material function successfully. Matty times the use of scatter diagrams helps better define customer requirements and specifications. 

Decide what parameters might be related to each other or that the customer wants to know about. 

Develop a data collection plan that will collect the required variables. 

Plot the data with each axis being one of the variables. 

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The first step is the collection of data showing corresponding values of the variables under consideration. From a scatter diagram, a plot of Y (ordinate) versus X (abscissa), it is often possible to visualize a smooth curve approximating the data. For purposes of reference, several types of approximating curves and their equations are listed. All letters other than X and Yrepresent constants. 

The seventh tool is the scatter or correlation diagram also known as an XY plot (50). This plot of one variable vs another is most useful in confirming interrelationships. Thus, scatter diagrams can verify the relationships shown in the cause and effect diagram. 

The example spreadsheet covers a three-day test. Tests over a period of days provide an opportunity to ensure that the tower operated at steady state for a period of time. Three sets of compositions were measured, recorded, normalized, and averaged. The daily compositions can be compared graphically to the averages to show drift. Scatter-diagram graphs, such as those in the reconciliation section, are developed for this analysis. If no drift is identified, the scatter in the measurements with time can give an estimate of the random error (measurement and fluc tuations) in the measurements. 

Single-Module Analysis Consider the single-module unit shown in Fig. 30-10. If the measurements were complete, they would consist of compositions, flows, temperatures, and pressures. These would contain significant random and systematic errors. Consequently, as collected, they do not close the constraints of the unit being studied. The measurements are only estimates of the actual plant operation. If the actual operation were known, the analyst could prepare a scatter diagram comparing the measurements to the actual values, which is a useful analysis tool Figure 30-19 is an example. 

If the measurements were completely accurate and precise (i.e., they contained neither random nor systematic error), all of the symbols representing the individual measurements woiild fall on the zero deviation line. Since the data do contain error, the measurements should fall within 2 on this type of diagram. This example scatter diagram shows that some of the measurements do not compare well to the ac tual values. 

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

Scatter diagram A graph in which values of one variable are plotted against the corresponding values of another property. 

Scatter diagrams - used to illustrate the association between two pieces of corresponding data... 

It will be obvious that the treatment thus far includes only substituents that are meta or para to the reaction site. When Hammett plots are made with data for ortho-substituted reactants, scatter diagrams usually result. This failure might be attributed to steric effects, but this is not very helpful, and many attempts have been made... 

These Br nsted-type plots often seem to be scatter diagrams until the points are collated into groups related by specific structural features. Thus, p-nitrophenyl acetate gives four separate, but parallel, lines for reactions with pyridines, anilines, imidazoles, and oxygen nucleophiles.Figure 7-4 shows such a plot for the reaction of trans-cmmm c anhydride with primary and secondary aliphatic amines to give substituted cinnamamides.All of the primary amines without substituents on the a carbon (R-CHi-NHi) fall on a line of slope 0.62 cyclopentylamine also lies on this line. If this line is characteristic of normal behavior, most of the deviations become qualitatively explicable. The line drawn through the secondary amines (slope 1.98) connects amines with the structure R-CHi-NH-CHi-R. The different steric requirements in the acylation reaction and in the model process... 

Figure 8.44. Effect of paracrystalline distortions on a series of reflections in a scattering diagram after compensation of the decay according to POROD s law (lattice factor (1 /N) Z 2). The quadratic increase of integral breadths of the reflections is indicated by boxes of equal area and increasing integral breadth. L is the average long period...

Fig. 1 Scatter diagram and regression line of supernatant BOD5 and odour offensiveness rating.

A number of authors measured the influence of ring substituents on the rate of catalytic reduction of aromatic nitro compounds by hydrogen (5-7,114,128). The series have been composed in such a way as to allow the Hammett correlations, but, with a single exception, scatter diagrams resulted. The successful case by Rflzicka and Santrochova 128) (series 102, 12 points, slopes for three different platinum catalysts 0.24, 0.34, and 0.92, respectively) differs from the others in the use of platinum catalysts, whereas the other authors worked with rhodium (4,5), palladium (5,114), ruthenium... 

FIGURE 3-27. Scatter diagram of the conversion ratio fs based on particles smaller than 0.5Mm vs. 2-h averaged ozone concentration. Data from Hidy. ... 

A scatter diagram shows how two variables are related and is thus used to test for cause and effect relationships. It cannot prove that one variable causes the change in the other, only that a relationship exists and how strong it is. In a scatter diagram, the horizontal (x) axis represents the measurement values of one variable, and the vertical (y) axis represents the measurements of the second variable. 

We previously voiced our objection to the term phase used to designate irradiances. A less commonly encountered, although perhaps better term for the phase function is the scattering diagram. 

Figure 4.8 Scattering diagram for diffraction by a circular disk.

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

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