Sample Graphs

Common clinical trial graphics are the focus of this chapter. First, we discuss the types of graphs that are most often encountered in clinical trial analysis and reporting. Then we examine the various tools that SAS provides to help produce these graphs. Sample graph programs are provided to show how many of these graphs can be produced. 

Gn,u regroups all graphs with n vertices and m edges. To generate a graph sampled uniformly at random from the set one has to put m edges between vertex pairs chosen randomly from n initially unconnected vertices. 

The obtained graph is the basis for evaluating the stress while applying the probe to controlled elements made of the same material and subjected to identical thermal processing as the reference sample... 

The calibration graph for the probe using a strength machine, has been shown in Fig. 7 It can be observed that the dependence of indications of the device of Wirotest type on the loading is linear within the proportionality limit scope. After unloading the indications do not return to zero, but show own stress caused in effect of plastic deformation of the tested sample... 

Construct a graph of pH as a function of time, and suggest an appropriate sampling frequency for a long-term monitoring program. 

A graph of a sample s absorbance of electromagnetic radiation versus wavelength (or frequency or wavenumber). 

One method for measuring the temperature of the sea is to measure this ratio. Of course, if you were to do it now, you would take a thermometer and not a mass spectrometer. But how do you determine the temperature of the sea as it was 10,000 years ago The answer lies with tiny sea creatures called diatoms. These have shells made from calcium carbonate, itself derived from carbon dioxide in sea water. As the diatoms die, they fall to the sea floor and build a sediment of calcium carbonate. If a sample is taken from a layer of sediment 10,000 years old, the carbon dioxide can be released by addition of acid. If this carbon dioxide is put into a suitable mass spectrometer, the ratio of carbon isotopes can be measured accurately. From this value and the graph of solubilities of isotopic forms of carbon dioxide with temperature (Figure 46.5), a temperature can be extrapolated. This is the temperature of the sea during the time the diatoms were alive. To conduct such experiments in a significant manner, it is essential that the isotope abundance ratios be measured very accurately. 

As we did in the case of relaxation, we now compare the behavior predicted by the Voigt model—and, for that matter, the Maxwell model—with the behavior of actual polymer samples in a creep experiment. Figure 3.12 shows plots of such experiments for two polymers. The graph is on log-log coordinates and should therefore be compared with Fig. 3.11b. The polymers are polystyrene of molecular weight 6.0 X 10 at a reduced temperature of 100°C and cis-poly-isoprene of molecular weight 6.2 X 10 at a reduced temperature of -30°C. 

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

The suspended-solids concentration can be plotted on log-log paper as a function of the sampling (detention) time. A straight line usually wih resiilt, and the required static detention time t to achieve a certain suspended-sohds concentration C in the overflow of an ideal basin can be taken directly from the graph. If the plot is a straight hne, the data are described by the equation... 

As an example of a more speeifie applieation, Figure 2 illustrates a metallo-graph—a light microscope set up for the characterization of opaque samples. Figure 3 illustrates a research-grade microscope made specifically for materials science, i.e., for optically characterizing all transparent and translucent materials. 

With the same scanning capability, it is much faster and often more useful to simply scan one line on a sample. The data is again output to a color CRT, but it is presented as the modulation of the y-amplitude, which is determined by the intensity of the X-ray signal production ftom the ROI of the element of interest. As the probe scans along the line, the CRT plots a graph of the elemental counting rates versus distance. Here again, it is usually possible to plot the data from many ele-... 

Fig. 2. The master graph of reversible capacity for lithium plotted versus heat treatment temperature for a variety of carbon samples. The three regions of commereial relevance are marked. Solid symbols are data for soft carbons, open symbols are data for hard carbons.

F ig. 29. Schematic graph showing the definition of the parameter, R, used to empirically estimate the fraction of single graphene layers in hard carbon samples. 

Employing the data from Table 1 the values already calculated for (ropt) and (Lmin) the maximum sample volume was calculated for a range of values for (a) and the results are shown as a graph in Figure 10. 

Figure 10. Graph of Log of Maximum Sample Volume against the Separation Ratio of the Critical Pair...

Figure 4. Graphs of the Retention Distance of the Peaks of Benzene, Naphthalene and Anthracene against Sample Volume...

In tlie case of a random sample of observations on a continuous random variable assumed to have a so-called nonnal pdf, tlie graph of which is a bellshaped curve, tlie following statements give a more precise interpretation of the sample standard deviation S as a measure of spread or dispersion. 

To evaluate the fibrillation behavior of dispersed TLCP domains according to the - 5 relation discussed previously, different - 5 graphs were calculated by eliminating the thickness variable x. The result is reported in Fig. 18. It is obvious that all the points obtained are found to be relatively close to the critical curve by Taylor. The Taylor-limit is also shown in the figure with a solid curve. One finds that all the values calculated on sample 1 are completely above the limit, while all those determined on sample 4 are completely below the limit. The other two samples, 2 and 3, have the We - 5 relation just over the limit. 

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